Chemical equilibrium
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2009) (Learn how and when to remove this template message)
In a chemical reaction, chemical equilibrium is the state in which both reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system.[1] Usually, this state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but equal. Thus, there are no net changes in the concentrations of the reactant(s) and product(s). Such a state is known as dynamic equilibrium.[2][3]
Contents
[hide]
1 Historical introduction
2 Thermodynamics
2.1 Addition of reactants or products
2.2 Treatment of activity
2.3 Concentration quotients
2.4 Metastable mixtures
3 Pure substances
4 Multiple equilibria
5 Effect of temperature
6 Effect of electric and magnetic fields
7 Types of equilibrium
8 Composition of a mixture
8.1 Mass-balance equations
8.1.1 Polybasic acids
8.1.2 Solution and precipitation
8.2 Minimization of Gibbs energy
9 See also
10 References
11 Further reading
Historical introduction[edit]
Burette, a common laboratory apparatus for carrying out titration, an important experimental technique in equilibrium and analytical chemistry.
The concept of chemical equilibrium was developed after Berthollet (1803) found that some chemical reactions are reversible.[4] For any reaction mixture to exist at equilibrium, the rates of the forward and backward (reverse) reactions are equal. In the following chemical equation with arrows pointing both ways to indicate equilibrium,[5] A and B are reactant chemical species, S and T are product species, and α, β, σ, and τ are the stoichiometric coefficients of the respective reactants and products:
α A + β B ⇌ σ S + τ T
The equilibrium concentration position of a reaction is said to lie "far to the right" if, at equilibrium, nearly all the reactants are consumed. Conversely the equilibrium position is said to be "far to the left" if hardly any product is formed from the reactants.
Guldberg and Waage (1865), building on Berthollet’s ideas, proposed the law of mass action:
forward reaction rate = k + A α B β backward reaction rate = k − S σ T τ {\displaystyle {\begin{aligned}{\ce {forward~reaction~rate}}&=k_{+}{\ce {A}}^{\alpha }{\ce {B}}^{\beta }\\{\ce {backward~reaction~rate}}&=k_{-}{\ce {S}}^{\sigma }{\ce {T}}^{\tau }\end{aligned}}}
where A, B, S and T are active masses and k+ and k− are rate constants. Since at equilibrium forward and backward rates are equal:
k + { A } α { B } β = k − { S } σ { T } τ {\displaystyle k_{+}\left\{{\ce {A}}\right\}^{\alpha }\left\{{\ce {B}}\right\}^{\beta }=k_{-}\left\{{\ce {S}}\right\}^{\sigma }\left\{{\ce {T}}\right\}^{\tau }\,}
and the ratio of the rate constants is also a constant, now known as an equilibrium constant.
K c = k + k − = { S } σ { T } τ { A } α { B } β {\displaystyle K_{c}={\frac {k_{+}}{k_{-}}}={\frac {\{{\ce {S}}\}^{\sigma }\{{\ce {T}}\}^{\tau }}{\{{\ce {A}}\}^{\alpha }\{{\ce {B}}\}^{\beta }}}}
By convention the products form the numerator. However, the law of mass action is valid only for concerted one-step reactions that proceed through a single transition state and is not valid in general because rate equations do not, in general, follow the stoichiometry of the reaction as Guldberg and Waage had proposed (see, for example, nucleophilic aliphatic substitution by SN1 or reaction of hydrogen and bromine to form hydrogen bromide). Equality of forward and backward reaction rates, however, is a necessary condition for chemical equilibrium, though it is not sufficient to explain why equilibrium occurs.
Despite the failure of this derivation, the equilibrium constant for a reaction is indeed a constant, independent of the activities of the various species involved, though it does depend on temperature as observed by the van 't Hoff equation. Adding a catalyst will affect both the forward reaction and the reverse reaction in the same way and will not have an effect on the equilibrium constant. The catalyst will speed up both reactions thereby increasing the speed at which equilibrium is reached.[2][6]
Although the macroscopic equilibrium concentrations are constant in time, reactions do occur at the molecular level. For example, in the case of acetic acid dissolved in water and forming acetate and hydronium ions,
CH3CO2H + H2O ⇌ CH
3CO−
2 + H3O+
a proton may hop from one molecule of acetic acid on to a water molecule and then on to an acetate anion to form another molecule of acetic acid and leaving the number of acetic acid molecules unchanged. This is an example of dynamic equilibrium. Equilibria, like the rest of thermodynamics, are statistical phenomena, averages of microscopic behavior.
Le Châtelier's principle (1884) gives an idea of the behavior of an equilibrium system when changes to its reaction conditions occur. If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to partially reverse the change. For example, adding more S from the outside will cause an excess of products, and the system will try to counteract this by increasing the reverse reaction and pushing the equilibrium point backward (though the equilibrium constant will stay the same).
If mineral acid is added to the acetic acid mixture, increasing the concentration of hydronium ion, the amount of dissociation must decrease as the reaction is driven to the left in accordance with this principle. This can also be deduced from the equilibrium constant expression for the reaction:
K = { CH 3 CO 2 − } { H 3 O + } { CH 3 CO 2 H } {\displaystyle K={\frac {\{{\ce {CH3CO2-}}\}\{{\ce {H3O+}}\}}{{\ce {\{CH3CO2H\}}}}}}
If {H3O+} increases {CH3CO2H} must increase and CH
3CO−
2 must decrease. The H2O is left out, as it is the solvent and its concentration remains high and nearly constant.
A quantitative version is given by the reaction quotient.
J. W. Gibbs suggested in 1873 that equilibrium is attained when the Gibbs free energy of the system is at its minimum value (assuming the reaction is carried out at constant temperature and pressure). What this means is that the derivative of the Gibbs energy with respect to reaction coordinate (a measure of the extent of reaction that has occurred, ranging from zero for all reactants to a maximum for all products) vanishes, signalling a stationary point. This derivative is called the reaction Gibbs energy (or energy change) and corresponds to the difference between the chemical potentials of reactants and products at the composition of the reaction mixture.[1] This criterion is both necessary and sufficient. If a mixture is not at equilibrium, the liberation of the excess Gibbs energy (or Helmholtz energy at constant volume reactions) is the "driving force" for the composition of the mixture to change until equilibrium is reached. The equilibrium constant can be related to the standard Gibbs free energy change for the reaction by the equation
Δ r G ⊖ = − R T ln ⁡ K eq {\displaystyle \Delta _{r}G^{\ominus }=-RT\ln K_{{\ce {eq}}}}
where R is the universal gas constant and T the temperature.
When the reactants are dissolved in a medium of high ionic strength the quotient of activity coefficients may be taken to be constant. In that case the concentration quotient, Kc,
K c = [ S ] σ [ T ] τ [ A ] α [ B ] β {\displaystyle K_{\ce {c}}={\frac {[{\ce {S}}]^{\sigma }[{\ce {T}}]^{\tau }}{[{\ce {A}}]^{\alpha }[{\ce {B}}]^{\beta }}}}
where [A] is the concentration of A, etc., is independent of the analytical concentration of the reactants. For this reason, equilibrium constants for solutions are usually determined in media of high ionic strength. Kc varies with ionic strength, temperature and pressure (or volume). Likewise Kp for gases depends on partial pressure. These constants are easier to measure and encountered in high-school chemistry courses.
Thermodynamics[edit]
At constant temperature and pressure, one must consider the Gibbs free energy, G, while at constant temperature and volume, one must consider the Helmholtz free energy: A, for the reaction; and at constant internal energy and volume, one must consider the entropy for the reaction: S.
The constant volume case is important in geochemistry and atmospheric chemistry where pressure variations are significant. Note that, if reactants and products were in standard state (completely pure), then there would be no reversibility and no equilibrium. Indeed, they would necessarily occupy disjoint volumes of space. The mixing of the products and reactants contributes a large entropy (known as entropy of mixing) to states containing equal mixture of products and reactants. The standard Gibbs energy change, together with the Gibbs energy of mixing, determine the equilibrium state.[7][8]
In this article only the constant pressure case is considered. The relation between the Gibbs free energy and the equilibrium constant can be found by considering chemical potentials.[1]
At constant temperature and pressure, the Gibbs free energy, G, for the reaction depends only on the extent of reaction: ξ (Greek letter xi), and can only decrease according to the second law of thermodynamics. It means that the derivative of G with ξ must be negative if the reaction happens; at the equilibrium the derivative being equal to zero.
( d G d ξ ) T , p = 0 {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=0~} : equilibrium
In order to meet the thermodynamic condition for equilibrium, the Gibbs energy must be stationary, meaning that the derivative of G with respect to the extent of reaction: ξ, must be zero. It can be shown that in this case, the sum of chemical potentials of the products is equal to the sum of those corresponding to the reactants. Therefore, the sum of the Gibbs energies of the reactants must be the equal to the sum of the Gibbs energies of the products.
α μ A + β μ B = σ μ S + τ μ T {\displaystyle \alpha \mu _{\mathrm {A} }+\beta \mu _{\mathrm {B} }=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }\,}
where μ is in this case a partial molar Gibbs energy, a chemical potential. The chemical potential of a reagent A is a function of the activity, {A} of that reagent.
μ A = μ A ⊖ + R T ln ⁡ { A } {\displaystyle \mu _{\mathrm {A} }=\mu _{A}^{\ominus }+RT\ln\{\mathrm {A} \}\,}
(where μo
A is the standard chemical potential).
The definition of the Gibbs energy equation interacts with the fundamental thermodynamic relation to produce
d G = V d p − S d T + ∑ i = 1 k μ i d N i {\displaystyle dG=Vdp-SdT+\sum _{i=1}^{k}\mu _{i}dN_{i}} .
Inserting dNi = νi dξ into the above equation gives a Stoichiometric coefficient ( ν i {\displaystyle \nu _{i}~} ) and a differential that denotes the reaction occurring once (dξ). At constant pressure and temperature the above equations can be written as
( d G d ξ ) T , p = ∑ i = 1 k μ i ν i = Δ r G T , p {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\sum _{i=1}^{k}\mu _{i}\nu _{i}=\Delta _{\mathrm {r} }G_{T,p}} which is the "Gibbs free energy change for the reaction .
This results in:
Δ r G T , p = σ μ S + τ μ T − α μ A − β μ B {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }-\alpha \mu _{\mathrm {A} }-\beta \mu _{\mathrm {B} }\,} .
By substituting the chemical potentials:
Δ r G T , p = ( σ μ S ⊖ + τ μ T ⊖ ) − ( α μ A ⊖ + β μ B ⊖ ) + ( σ R T ln ⁡ { S } + τ R T ln ⁡ { T } ) − ( α R T ln ⁡ { A } + β R T ln ⁡ { B } ) {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=(\sigma \mu _{\mathrm {S} }^{\ominus }+\tau \mu _{\mathrm {T} }^{\ominus })-(\alpha \mu _{\mathrm {A} }^{\ominus }+\beta \mu _{\mathrm {B} }^{\ominus })+(\sigma RT\ln\{\mathrm {S} \}+\tau RT\ln\{\mathrm {T} \})-(\alpha RT\ln\{\mathrm {A} \}+\beta RT\ln\{\mathrm {B} \})} ,
the relationship becomes:
Δ r G T , p = ∑ i = 1 k μ i ⊖ ν i + R T ln ⁡ { S } σ { T } τ { A } α { B } β {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}+RT\ln {\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}
∑ i = 1 k μ i ⊖ ν i = Δ r G ⊖ {\displaystyle \sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}=\Delta _{\mathrm {r} }G^{\ominus }} :
which is the standard Gibbs energy change for the reaction that can be calculated using thermodynamical tables. The reaction quotient is defined as:
Q r = { S } σ { T } τ { A } α { B } β {\displaystyle Q_{\mathrm {r} }={\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}
Therefore,
( d G d ξ ) T , p = Δ r G T , p = Δ r G ⊖ + R T ln ⁡ Q r {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln Q_{\mathrm {r} }}
At equilibrium:
( d G d ξ ) T , p = Δ r G T , p = 0 {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=0}
leading to:
0 = Δ r G ⊖ + R T ln ⁡ K e q {\displaystyle 0=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln K_{\mathrm {eq} }}
and
Δ r G ⊖ = − R T ln ⁡ K e q {\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\ln K_{\mathrm {eq} }}
Obtaining the value of the standard Gibbs energy change, allows the calculation of the equilibrium constant.
Addition of reactants or products[edit]
For a reactional system at equilibrium: Qr = Keq; ξ = ξeq.
If are modified activities of constituents, the value of the reaction quotient changes and becomes different from the equilibrium constant: Qr ≠ Keq
( d G d ξ ) T , p = Δ r G ⊖ + R T ln ⁡ Q r {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln Q_{\mathrm {r} }~}
and
Δ r G ⊖ = − R T ln ⁡ K e q {\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\ln K_{eq}~}
then
( d G d ξ ) T , p = R T ln ⁡ ( Q r K e q ) {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=RT\ln \left({\frac {Q_{\mathrm {r} }}{K_{\mathrm {eq} }}}\right)~}
If activity of a reagent i increases
Q r = ∏ ( a j ) ν j ∏ ( a i ) ν i {\displaystyle Q_{\mathrm {r} }={\frac {\prod (a_{j})^{\nu _{j}}}{\prod (a_{i})^{\nu _{i}}}}~} , the reaction quotient decreases.
then
Q r < K e q {\displaystyle Q_{\mathrm {r} }<K_{\mathrm {eq} }~} and ( d G d ξ ) T , p < 0 {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}<0~}
The reaction will shift to the right (i.e. in the forward direction, and thus more products will form).
If activity of a product j increases
then
Q r > K e q {\displaystyle Q_{\mathrm {r} }>K_{\mathrm {eq} }~} and ( d G d ξ ) T , p > 0 {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}>0~}
The reaction will shift to the left (i.e. in the reverse direction, and thus less products will form).
Note that activities and equilibrium constants are dimensionless numbers.
Treatment of activity[edit]
The expression for the equilibrium constant can be rewritten as the product of a concentration quotient, Kc and an activity coefficient quotient, Γ.
K = [ S ] σ [ T ] τ . . . [ A ] α [ B ] β . . . × γ S σ γ T τ . . . γ A α γ B β . . . = K c Γ {\displaystyle K={\frac {[\mathrm {S} ]^{\sigma }[\mathrm {T} ]^{\tau }...}{[\mathrm {A} ]^{\alpha }[\mathrm {B} ]^{\beta }...}}\times {\frac {{\gamma _{\mathrm {S} }}^{\sigma }{\gamma _{\mathrm {T} }}^{\tau }...}{{\gamma _{\mathrm {A} }}^{\alpha }{\gamma _{\mathrm {B} }}^{\beta }...}}=K_{\mathrm {c} }\Gamma }
[A] is the concentration of reagent A, etc. It is possible in principle to obtain values of the activity coefficients, γ. For solutions, equations such as the Debye–Hückel equation or extensions such as Davies equation[9] Specific ion interaction theory or Pitzer equations[10] may be used.Software (below). However this is not always possible. It is common practice to assume that Γ is a constant, and to use the concentration quotient in place of the thermodynamic equilibrium constant. It is also general practice to use the term equilibrium constant instead of the more accurate concentration quotient. This practice will be followed here.
For reactions in the gas phase partial pressure is used in place of concentration and fugacity coefficient in place of activity coefficient. In the real world, for example, when making ammonia in industry, fugacity coefficients must be taken into account. Fugacity, f, is the product of partial pressure and fugacity coefficient. The chemical potential of a species in the gas phase is given by
μ = μ ⊖ + R T ln ⁡ ( f b a r ) = μ ⊖ + R T ln ⁡ ( p b a r ) + R T ln ⁡ γ {\displaystyle \mu =\mu ^{\ominus }+RT\ln \left({\frac {f}{\mathrm {bar} }}\right)=\mu ^{\ominus }+RT\ln \left({\frac {p}{\mathrm {bar} }}\right)+RT\ln \gamma }
so the general expression defining an equilibrium constant is valid for both solution and gas phases.
Concentration quotients[edit]
In aqueous solution, equilibrium constants are usually determined in the presence of an "inert" electrolyte such as sodium nitrate NaNO3 or potassium perchlorate KClO4. The ionic strength of a solution is given by
I = 1 2 ∑ i = 1 N c i z i 2 {\displaystyle I={\frac {1}{2}}\sum _{i=1}^{N}c_{i}z_{i}^{2}}
where ci and zi stand for the concentration and ionic charge of ion type i, and the sum is taken over all the N types of charged species in solution. When the concentration of dissolved salt is much higher than the analytical concentrations of the reagents, the ions originating from the dissolved salt determine the ionic strength, and the ionic strength is effectively constant. Since activity coefficients depend on ionic strength the activity coefficients of the species are effectively independent of concentration. Thus, the assumption that Γ is constant is justified. The concentration quotient is a simple multiple of the equilibrium constant.[11]
K c = K Γ {\displaystyle K_{\mathrm {c} }={\frac {K}{\Gamma }}}
However, Kc will vary with ionic strength. If it is measured at a series of different ionic strengths the value can be extrapolated to zero ionic strength.[10] The concentration quotient obtained in this manner is known, paradoxically, as a thermodynamic equilibrium constant.
To use a published value of an equilibrium constant in conditions of ionic strength different from the conditions used in its determination, the value should be adjustedSoftware (below).
Metastable mixtures[edit]
A mixture may appear to have no tendency to change, though it is not at equilibrium. For example, a mixture of SO2 and O2 is metastable as there is a kinetic barrier to formation of the product, SO3.
2 SO2 + O2 ⇌ 2 SO3
The barrier can be overcome when a catalyst is also present in the mixture as in the contact process, but the catalyst does not affect the equilibrium concentrations.
Likewise, the formation of bicarbonate from carbon dioxide and water is very slow under normal conditions
CO2 + 2 H2O ⇌ HCO−
3 + H3O+
but almost instantaneous in the presence of the catalytic enzyme carbonic anhydrase.
Pure substances[edit]
When pure substances (liquids or solids) are involved in equilibria their activities do not appear in the equilibrium constant[12] because their numerical values are considered one.
Applying the general formula for an equilibrium constant to the specific case of a dilute solution of acetic acid in water one obtains
CH3CO2H + H2O ⇌ CH3CO2− + H3O+
K c = [ C H 3 C O 2 − ] [ H 3 O + ] [ C H 3 C O 2 H ] [ H 2 O ] {\displaystyle K_{\mathrm {c} }={\frac {\mathrm {[{CH_{3}CO_{2}}^{-}][{H_{3}O}^{+}]} }{\mathrm {[{CH_{3}CO_{2}H}][{H_{2}O}]} }}}
For all but very concentrated solutions, the water can be considered a "pure" liquid, and therefore it has an activity of one. The equilibrium constant expression is therefore usually written as
K = [ C H 3 C O 2 − ] [ H 3 O + ] [ C H 3 C O 2 H ] = K c {\displaystyle K={\frac {\mathrm {[{CH_{3}CO_{2}}^{-}][{H_{3}O}^{+}]} }{\mathrm {[{CH_{3}CO_{2}H}]} }}=K_{\mathrm {c} }} .
A particular case is the self-ionization of water itself
2 H2O ⇌ H3O+ + OH−
Because water is the solvent, and has an activity of one, the self-ionization constant of water is defined as
K w = [ H + ] [ O H − ] {\displaystyle K_{\mathrm {w} }=\mathrm {[H^{+}][OH^{-}]} }
It is perfectly legitimate to write [H+] for the hydronium ion concentration, since the state of solvation of the proton is constant (in dilute solutions) and so does not affect the equilibrium concentrations. Kw varies with variation in ionic strength and/or temperature.
The concentrations of H+ and OH− are not independent quantities. Most commonly [OH−] is replaced by Kw[H+]−1 in equilibrium constant expressions which would otherwise include hydroxide ion.
Solids also do not appear in the equilibrium constant expression, if they are considered to be pure and thus their activities taken to be one. An example is the Boudouard reaction:[12]
2 CO ⇌ CO2 + C
for which the equation (without solid carbon) is written as:
K c = [ C O 2 ] [ C O ] 2 {\displaystyle K_{\mathrm {c} }={\frac {\mathrm {[CO_{2}]} }{\mathrm {[CO]^{2}} }}}
Multiple equilibria[edit]
Consider the case of a dibasic acid H2A. When dissolved in water, the mixture will contain H2A, HA− and A2−. This equilibrium can be split into two steps in each of which one proton is liberated.
H 2 A ↽ − − ⇀ HA − + H + : K 1 = [ HA − ] [ H + ] [ H 2 A ] HA − ↽ − − ⇀ A 2 − + H + : K 2 = [ A 2 − ] [ H + ] [ HA − ] {\displaystyle {\begin{array}{rl}{\ce {H2A<=>{HA^{-}}+{H+}}}:&K_{1}={\frac {\ce {[HA-][H+]}}{\ce {[H2A]}}}\\{\ce {HA-<=>{A^{2-}}+{H+}}}:&K_{2}={\frac {\ce {[A^{2-}][H+]}}{\ce {[HA-]}}}\end{array}}}
K1 and K2 are examples of stepwise equilibrium constants. The overall equilibrium constant, βD, is product of the stepwise constants.
H 2 A ↽ − − ⇀ A 2 − + 2 H + {\displaystyle {\ce {{H2A}<=>{A^{2-}}+{2H+}}}} : β D = [ A 2 − ] [ H + ] 2 [ H 2 A ] = K 1 K 2 {\displaystyle \beta _{{\ce {D}}}={\frac {{\ce {[A^{2-}][H^+]^2}}}{{\ce {[H_2A]}}}}=K_{1}K_{2}}
Note that these constants are dissociation constants because the products on the right hand side of the equilibrium expression are dissociation products. In many systems, it is preferable to use association constants.
A 2 − + H + ↽ − − ⇀ HA − : β 1 = [ HA − ] [ A 2 − ] [ H + ] A 2 − + 2 H + ↽ − − ⇀ H 2 A : β 2 = [ H 2 A ] [ A 2 − ] [ H + ] 2 {\displaystyle {\begin{array}{ll}{\ce {{A^{2-}}+{H+}<=>HA-}}:&\beta _{1}={\frac {\ce {[HA^{-}]}}{\ce {[A^{2-}][H+]}}}\\{\ce {{A^{2-}}+{2H+}<=>H2A}}:&\beta _{2}={\frac {\ce {[H2A]}}{\ce {[A^{2-}][H+]^{2}}}}\end{array}}}
β1 and β2 are examples of association constants. Clearly β1 = 1/K2 and β2 = 1/βD; log β1 = pK2 and log β2 = pK2 + pK1[13] For multiple equilibrium systems, also see: theory of Response reactions.
Effect of temperature[edit]
The effect of changing temperature on an equilibrium constant is given by the van 't Hoff equation
d ln ⁡ K d T = Δ H m ⊖ R T 2 {\displaystyle {\frac {d\ln K}{dT}}={\frac {\Delta H_{\mathrm {m} }^{\ominus }}{RT^{2}}}}
Thus, for exothermic reactions (ΔH is negative), K decreases with an increase in temperature, but, for endothermic reactions, (ΔH is positive) K increases with an increase temperature. An alternative formulation is
d ln ⁡ K d ( T − 1 ) = − Δ H m ⊖ R {\displaystyle {\frac {d\ln K}{d(T^{-1})}}=-{\frac {\Delta H_{\mathrm {m} }^{\ominus }}{R}}}
At first sight this appears to offer a means of obtaining the standard molar enthalpy of the reaction by studying the variation of K with temperature. In practice, however, the method is unreliable because error propagation almost always gives very large errors on the values calculated in this way.
Effect of electric and magnetic fields[edit]
The effect of electric field on equilibrium has been studied by Manfred Eigen[citation needed] among others.
Types of equilibrium[edit]
Haber–Bosch process
# N2 (g) ⇌ N2 (adsorbed)
N2 (adsorbed) ⇌ 2 N (adsorbed)
H2 (g) ⇌ H2 (adsorbed)
H2 (adsorbed) ⇌ 2 H (adsorbed)
N (adsorbed) + 3 H(adsorbed) ⇌ NH3 (adsorbed)
NH3 (adsorbed) ⇌ NH3 (g)
In the gas phase: rocket engines[14]
The industrial synthesis such as ammonia in the Haber–Bosch process (depicted right) takes place through a succession of equilibrium steps including adsorption processes
Atmospheric chemistry
Seawater and other natural waters: chemical oceanography
Distribution between two phases
log D distribution coefficient: important for pharmaceuticals where lipophilicity is a significant property of a drug
Liquid–liquid extraction, Ion exchange, Chromatography
Solubility product
Uptake and release of oxygen by hemoglobin in blood
Acid–base equilibria: acid dissociation constant, hydrolysis, buffer solutions, indicators, acid–base homeostasis
Metal–ligand complexation: sequestering agents, chelation therapy, MRI contrast reagents, Schlenk equilibrium
Adduct formation: host–guest chemistry, supramolecular chemistry, molecular recognition, dinitrogen tetroxide
In certain oscillating reactions, the approach to equilibrium is not asymptotically but in the form of a damped oscillation .[12]
The related Nernst equation in electrochemistry gives the difference in electrode potential as a function of redox concentrations.
When molecules on each side of the equilibrium are able to further react irreversibly in secondary reactions, the final product ratio is determined according to the Curtin–Hammett principle.
In these applications, terms such as stability constant, formation constant, binding constant, affinity constant, association/dissociation constant are used. In biochemistry, it is common to give units for binding constants, which serve to define the concentration units used when the constant’s value was determined.
Composition of a mixture[edit]
When the only equilibrium is that of the formation of a 1:1 adduct as the composition of a mixture, there are many ways that the composition of a mixture can be calculated. For example, see ICE table for a traditional method of calculating the pH of a solution of a weak acid.
There are three approaches to the general calculation of the composition of a mixture at equilibrium.
The most basic approach is to manipulate the various equilibrium constants until the desired concentrations are expressed in terms of measured equilibrium constants (equivalent to measuring chemical potentials) and initial conditions.
Minimize the Gibbs energy of the system.[15][16]
Satisfy the equation of mass balance. The equations of mass balance are simply statements that demonstrate that the total concentration of each reactant must be constant by the law of conservation of mass.
Mass-balance equations[edit]
In general, the calculations are rather complicated or complex. For instance, in the case of a dibasic acid, H2A dissolved in water the two reactants can be specified as the conjugate base, A2−, and the proton, H+. The following equations of mass-balance could apply equally well to a base such as 1,2-diaminoethane, in which case the base itself is designated as the reactant A:
T A = [ A ] + [ H A ] + [ H 2 A ] {\displaystyle T_{\mathrm {A} }=\mathrm {[A]+[HA]+[H_{2}A]} \,}
T H = [ H ] + [ H A ] + 2 [ H 2 A ] − [ O H ] {\displaystyle T_{\mathrm {H} }=\mathrm {[H]+[HA]+2[H_{2}A]-[OH]} \,}
With TA the total concentration of species A. Note that it is customary to omit the ionic charges when writing and using these equations.
When the equilibrium constants are known and the total concentrations are specified there are two equations in two unknown "free concentrations" [A] and [H]. This follows from the fact that [HA] = β1[A][H], [H2A] = β2[A][H]2 and [OH] = Kw[H]−1
T A = [ A ] + β 1 [ A ] [ H ] + β 2 [ A ] [ H ] 2 {\displaystyle T_{\mathrm {A} }=\mathrm {[A]} +\beta _{1}\mathrm {[A][H]} +\beta _{2}\mathrm {[A][H]} ^{2}\,}
T H = [ H ] + β 1 [ A ] [ H ] + 2 β 2 [ A ] [ H ] 2 − K w [ H ] − 1 {\displaystyle T_{\mathrm {H} }=\mathrm {[H]} +\beta _{1}\mathrm {[A][H]} +2\beta _{2}\mathrm {[A][H]} ^{2}-K_{w}[\mathrm {H} ]^{-1}\,}
so the concentrations of the "complexes" are calculated from the free concentrations and the equilibrium constants. General expressions applicable to all systems with two reagents, A and B would be
T A = [ A ] + ∑ i p i β i [ A ] p i [ B ] q i {\displaystyle T_{\mathrm {A} }=[\mathrm {A} ]+\sum _{i}p_{i}\beta _{i}[\mathrm {A} ]^{p_{i}}[\mathrm {B} ]^{q_{i}}}
T B = [ B ] + ∑ i q i β i [ A ] p i [ B ] q i {\displaystyle T_{\mathrm {B} }=[\mathrm {B} ]+\sum _{i}q_{i}\beta _{i}[\mathrm {A} ]^{p_{i}}[\mathrm {B} ]^{q_{i}}}
It is easy to see how this can be extended to three or more reagents.
Polybasic acids[edit]
Species concentrations during hydrolysis of the aluminium.
The composition of solutions containing reactants A and H is easy to calculate as a function of p[H]. When [H] is known, the free concentration [A] is calculated from the mass-balance equation in A.
The diagram alongside, shows an example of the hydrolysis of the aluminium Lewis acid Al3+(aq)[17] shows the species concentrations for a 5 × 10−6 M solution of an aluminium salt as a function of pH. Each concentration is shown as a percentage of the total aluminium.
Solution and precipitation[edit]
The diagram above illustrates the point that a precipitate that is not one of the main species in the solution equilibrium may be formed. At pH just below 5.5 the main species present in a 5 μM solution of Al3+ are aluminium hydroxides Al(OH)2+, AlOH+
2 and Al
13(OH)7+
32, but on raising the pH Al(OH)3 precipitates from the solution. This occurs because Al(OH)3 has a very large lattice energy. As the pH rises more and more Al(OH)3 comes out of solution. This is an example of Le Châtelier's principle in action: Increasing the concentration of the hydroxide ion causes more aluminium hydroxide to precipitate, which removes hydroxide from the solution. When the hydroxide concentration becomes sufficiently high the soluble aluminate, Al(OH)−
4, is formed.
Another common instance where precipitation occurs is when a metal cation interacts with an anionic ligand to form an electrically neutral complex. If the complex is hydrophobic, it will precipitate out of water. This occurs with the nickel ion Ni2+ and dimethylglyoxime, (dmgH2): in this case the lattice energy of the solid is not particularly large, but it greatly exceeds the energy of solvation of the molecule Ni(dmgH)2.
Minimization of Gibbs energy[edit]
At equilibrium, at a specified temperature and pressure, the Gibbs energy G is at a minimum:
d G = ∑ j = 1 m μ j d N j = 0 {\displaystyle dG=\sum _{j=1}^{m}\mu _{j}\,dN_{j}=0}
For a closed system, no particles may enter or leave, although they may combine in various ways. The total number of atoms of each element will remain constant. This means that the minimization above must be subjected to the constraints:
∑ j = 1 m a i j N j = b i 0 {\displaystyle \sum _{j=1}^{m}a_{ij}N_{j}=b_{i}^{0}}
where aij is the number of atoms of element i in molecule j and b0
i is the total number of atoms of element i, which is a constant, since the system is closed. If there are a total of k types of atoms in the system, then there will be k such equations. If ions are involved, an additional row is added to the aij matrix specifying the respective charge on each molecule which will sum to zero.
This is a standard problem in optimisation, known as constrained minimisation. The most common method of solving it is using the method of Lagrange multipliers, also known as undetermined multipliers (though other methods may be used).
Define:
G = G + ∑ i = 1 k λ i ( ∑ j = 1 m a i j N j − b i 0 ) = 0 {\displaystyle {\mathcal {G}}=G+\sum _{i=1}^{k}\lambda _{i}\left(\sum _{j=1}^{m}a_{ij}N_{j}-b_{i}^{0}\right)=0}
where the λi are the Lagrange multipliers, one for each element. This allows each of the Nj and λj to be treated independently, and it can be shown using the tools of multivariate calculus that the equilibrium condition is given by
0 = ∂ G ∂ N j = μ j + ∑ i = 1 k λ i a i j {\displaystyle 0={\frac {\partial {\mathcal {G}}}{\partial N_{j}}}=\mu _{j}+\sum _{i=1}^{k}\lambda _{i}a_{ij}}
0 = ∂ G ∂ λ i = ∑ j = 1 m a i j N j − b i 0 {\displaystyle 0={\frac {\partial {\mathcal {G}}}{\partial \lambda _{i}}}=\sum _{j=1}^{m}a_{ij}N_{j}-b_{i}^{0}}
(For proof see Lagrange multipliers.) This is a set of (m + k) equations in (m + k) unknowns (the Nj and the λi) and may, therefore, be solved for the equilibrium concentrations Nj as long as the chemical potentials are known as functions of the concentrations at the given temperature and pressure. (See Thermodynamic databases for pure substances.) Note that the second equation is just the initial constraints for minimization.
This method of calculating equilibrium chemical concentrations is useful for systems with a large number of different molecules. The use of k atomic element conservation equations for the mass constraint is straightforward, and replaces the use of the stoichiometric coefficient equations.[14]. The results are consistent with those specified by chemical equations. For example, if equilibrium is specified by a single chemical equation: [18],
∑ j = 0 m ν j R j = 0 {\displaystyle \sum _{j=0}^{m}\nu _{j}R_{j}=0}
where νj is the stochiometric coefficient for the j th molecule (negative for reactants, positive for products) and Rj is the symbol for the j th molecule, a properly balanced equation will obey:
∑ j = 1 m a i j ν j = 0 {\displaystyle \sum _{j=1}^{m}a_{ij}\nu _{j}=0}
Multiplying the first equilibrium condition by νj yields
0 = ∑ j = 1 m ν j μ j + ∑ j = 1 m ∑ i = 1 k ν j λ i a i j = ∑ j = 1 m ν j μ j {\displaystyle 0=\sum _{j=1}^{m}\nu _{j}\mu _{j}+\sum _{j=1}^{m}\sum _{i=1}^{k}\nu _{j}\lambda _{i}a_{ij}=\sum _{j=1}^{m}\nu _{j}\mu _{j}}
As above, defining ΔG
Δ G = ∑ j = 1 m ν j μ j = ∑ j = 1 m ν j ( μ j ⊖ + R T ln ⁡ ( { R j } ) ) = Δ G ⊖ + R T ln ⁡ ( ∏ j = 1 m { R j } ν j ) = Δ G ⊖ + R T ln ⁡ ( Q r ) {\displaystyle \Delta G=\sum _{j=1}^{m}\nu _{j}\mu _{j}=\sum _{j=1}^{m}\nu _{j}(\mu _{j}^{\ominus }+RT\ln(\{R_{j}\}))=\Delta G^{\ominus }+RT\ln \left(\prod _{j=1}^{m}\{R_{j}\}^{\nu _{j}}\right)=\Delta G^{\ominus }+RT\ln(Q_{r})}
which will be zero at equilibrium.
See also[edit]
Acidosis
Alkalosis
Arterial blood gas
Benesi–Hildebrand method
Determination of equilibrium constants
Equilibrium constant
Henderson–Hasselbalch equation
Michaelis–Menten kinetics
pCO2
pH
pKa
Redox equilibria
Steady state (chemistry)
Thermodynamic databases for pure substances
Non-random two-liquid model (NRTL model) - Phase equilibrium calculations
UNIQUAC model - Phase equilibrium calculations
References[edit]
^ Jump up to: a b c Atkins, Peter; De Paula, Julio (2006). Atkins' Physical Chemistry (8th ed.). W. H. Freeman. pp. 200–202. ISBN 0-7167-8759-8.
^ Jump up to: a b Atkins, Peter W.; Jones, Loretta. Chemical Principles: The Quest for Insight (2nd ed.). ISBN 0-7167-9903-0.
Jump up ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "chemical equilibrium".
Jump up ^ Berthollet, C.L. (1803). Essai de statique chimique [Essay on chemical statics] (in French). Paris, France: Firmin Didot. On pp. 404–407, Berthellot mentions that when he accompanied Napoleon on his expedition to Egypt, he (Berthellot) visited Lake Natron and found sodium carbonate along its shores. He realized that this was a product of the reverse of the usual reaction Na2CO3 + CaCl2 → 2NaCl + CaCO3↓ and therefore that the final state of a reaction was a state of equilibrium between two opposing processes. From p. 405: " … la décomposition du muriate de soude continue donc jusqu'à ce qu'il se soit formé assez de muriate de chaux, parce que l'acide muriatique devant se partager entre les deux bases en raison de leur action, il arrive un terme où leurs forces se balancent." ( … the decomposition of the sodium chloride thus continues until enough calcium chloride is formed, because the hydrochloric acid must be shared between the two bases in the ratio of their action [i.e., capacity to react]; it reaches an end [point] at which their forces are balanced.)
Jump up ^ The notation ⇌ was proposed in 1884 by the Dutch chemist Jacobus Henricus van 't Hoff. See: van 't Hoff, J.H. (1884). Études de Dynamique Chemique [Studies of chemical dynamics] (in French). Amsterdam, Netherlands: Frederik Muller & Co. pp. 4–5. Van 't Hoff called reactions that didn't proceed to completion "limited reactions". From pp. 4–5: "Or M. Pfaundler a relié ces deux phénomênes … s'accomplit en même temps dans deux sens opposés." (Now Mr. Pfaundler has joined these two phenomena in a single concept by considering the observed limit as the result of two opposing reactions, driving the one in the example cited to the formation of sea salt [i.e., NaCl] and nitric acid, [and] the other to hydrochloric acid and sodium nitrate. This consideration, which experiment validates, justifies the expression "chemical equilibrium", which is used to characterize the final state of limited reactions. I would propose to translate this expression by the following symbol:
HCl + NO3 Na ⇌ NO3 H + Cl Na .
I thus replace, in this case, the = sign in the chemical equation by the sign ⇌, which in reality doesn't express just equality but shows also the direction of the reaction. This clearly expresses that a chemical action occurs simultaneously in two opposing directions.)
Jump up ^ Brady, James E. Chemistry: Matter and Its Changes (4th ed.). Fred Senese. ISBN 0-471-21517-1.
Jump up ^ Schultz, Mary Jane (1999). "Why Equilibrium? Understanding Entropy of Mixing". Journal of Chemical Education. 76 (10): 1391. Bibcode:1999JChEd..76.1391S. doi:10.1021/ed076p1391.
Jump up ^ Clugston, Michael J. (1990). "A mathematical verification of the second law of thermodynamics from the entropy of mixing". Journal of Chemical Education. 67 (3): 203. Bibcode:1990JChEd..67Q.203C. doi:10.1021/ed067p203.
Jump up ^ Davies, C. W. (1962). Ion Association. Butterworths.
^ Jump up to: a b Grenthe, I.; Wanner, H. "Guidelines for the extrapolation to zero ionic strength" (PDF).
Jump up ^ Rossotti, F. J. C.; Rossotti, H. (1961). The Determination of Stability Constants. McGraw-Hill.
^ Jump up to: a b c Concise Encyclopedia Chemistry. 1994. ISBN 0-89925-457-8.
Jump up ^ Beck, M. T.; Nagypál, I. (1990). Chemistry of Complex Equilibria (2nd ed.). Budapest: Akadémiai Kaidó.
^ Jump up to: a b "Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications" (PDF). NASA Reference publication 1311. NASA. 1994.
Jump up ^ Smith, W. R.; Missen, R. W. (1991). Chemical Reaction Equilibrium Analysis: Theory and Algorithms (Reprinted ed.). Malabar, FL: Krieger Publishing.
Jump up ^ "Mathtrek Systems".
Jump up ^ The diagram was created with the program HySS
Jump up ^ C. Kittel, H. Kroemer (1980). "9". Thermal Physics (2 ed.). W. H. Freeman Company. ISBN 0-7167-1088-9.
Further reading[edit]
Library resources about
Chemical equilibrium
Resources in your library
Van Zeggeren, F.; Storey, S. H. (1970). The Computation of Chemical Equilibria. Cambridge University Press. Mainly concerned with gas-phase equilibria.
Leggett, D. J., ed. (1985). Computational Methods for the Determination of Formation Constants. Plenum Press.
Martell, A. E.; Motekaitis, R. J. (1992). The Determination and Use of Stability Constants. Wiley-VCH.
Gans, P. (2004). Stability Constants: Determination and Uses (CD-ROM)|format= requires |url= (help). Leeds: Protonic Software.
[hide]
v
t
e
Chemical equilibria
Concepts
Acid dissociation constant
Binding constant
Binding selectivity
Buffer solution
Chemical equilibrium
Chemical stability
Chelation
Determination of equilibrium constants
Dissociation constant
Distribution coefficient
Dynamic equilibrium
Equilibrium chemistry
Equilibrium constant
Equilibrium unfolding
Equilibrium stage
Hammett acidity function
Henry's law
Liquid–liquid extraction
Macrocycle effect
Phase diagram
Predominance diagram
Phase rule
Reaction quotient
Self-ionization of water
Solubility equilibrium
Stability constants of complexes
Thermodynamic equilibrium
Thermodynamic activity
Vapor–liquid equilibrium
Retrieved from "https://en.wikipedia.org/w/index.php?title=Chemical_equilibrium&oldid=837361611"
Categories:
Equilibrium chemistry
Analytical chemistry
Physical chemistry
Hidden categories:
CS1 French-language sources (fr)
Articles needing additional references from March 2009
All articles needing additional references
All articles with unsourced statements
Articles with unsourced statements from July 2013
Pages using citations with format and no URL
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Wikibooks
Languages
Afrikaans
العربية
Asturianu
বাংলা
Bân-lâm-gú
Беларуская
Български
Bosanski
Català
Čeština
Dansk
Deutsch
Eesti
Español
Esperanto
Euskara
فارسی
Français
Galego
한국어
Հայերեն
हिन्दी
Hrvatski
Ido
Bahasa Indonesia
Italiano
עברית
ქართული
Kreyòl ayisyen
Magyar
Македонски
മലയാളം
Nederlands
日本語
Norsk
Polski
Português
Română
Runa Simi
Русский
Slovenčina
کوردی
Српски / srpski
Srpskohrvatski / српскохрватски
Suomi
Svenska
Tagalog
தமிழ்
ไทย
Türkçe
Українська
中文
43 more
Edit links
This page was last edited on 20 April 2018, at 10:32.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

div
id class
mw-page-base noprint
html
local
div
id class
mw-head-base noprint
html
local
a
id
top
html
local
div
id class
siteNotice centralNotice mw-body-content
html
local
div
class
mw-indicators mw-body-content
html
local
h1
id class lang
firstHeading firstHeading en
html
local
div
id class
siteSub noprint
html
local
div
id
contentSub
html
local
a
href
#mw-head
html
local
a
href
#p-search
html
local
div
id class
jump-to-nav mw-jump
html
local
img
alt src width height srcset data-file-width data-file-height
//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png 50 39 //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x 512 399
html
local
a
href class
/wiki/File:Question_book-new.svg image
html
local
div
style
width:52px
html
local
td
class
mbox-image
html
local
a
href title
/wiki/Wikipedia:Verifiability Wikipedia:Verifiability
html
local
b
html
local
a
class href
external text //en.wikipedia.org/w/index.php?title=Chemical_equilibrium&action=edit
html
local
a
href title
/wiki/Help:Introduction_to_referencing_with_Wiki_Markup/1 Help:Introduction to referencing with Wiki Markup/1
html
local
span
class
hide-when-compact
html
local
i
html
local
small
html
local
a
href title
/wiki/Help:Maintenance_template_removal Help:Maintenance template removal
html
local
i
html
local
small
class
hide-when-compact
html
local
div
class
mbox-text-span
html
local
td
class
mbox-text
html
local
tr
html
local
tbody
html
local
table
class role
plainlinks metadata ambox ambox-content ambox-Refimprove presentation
html
local
a
href title
/wiki/Chemical_reaction Chemical reaction
html
local
b
html
local
a
href title
/wiki/Concentration Concentration
html
local
a
href
#cite_note-Atkins-1
html
local
sup
id class
cite_ref-Atkins_1-0 reference
html
local
a
href title
/wiki/Reversible_reaction Reversible reaction
html
local
a
href title
/wiki/Reaction_rate Reaction rate
html
local
a
href title
/wiki/Dynamic_equilibrium Dynamic equilibrium
html
local
a
href
#cite_note-aj-2
html
local
sup
id class
cite_ref-aj_2-0 reference
html
local
a
href
#cite_note-3
html
local
sup
id class
cite_ref-3 reference
html
local
p
html
local
p
html
local
h2
html
local
a
role tabindex class
button 0 togglelink
html
local
span
class
toctoggle
html
local
div
class dir xml:lang
toctitle ltr en
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Historical_introduction
html
local
li
class
toclevel-1 tocsection-1
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Thermodynamics
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Addition_of_reactants_or_products
html
local
li
class
toclevel-2 tocsection-3
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Treatment_of_activity
html
local
li
class
toclevel-2 tocsection-4
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Concentration_quotients
html
local
li
class
toclevel-2 tocsection-5
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Metastable_mixtures
html
local
li
class
toclevel-2 tocsection-6
html
local
ul
html
local
li
class
toclevel-1 tocsection-2
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Pure_substances
html
local
li
class
toclevel-1 tocsection-7
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Multiple_equilibria
html
local
li
class
toclevel-1 tocsection-8
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Effect_of_temperature
html
local
li
class
toclevel-1 tocsection-9
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Effect_of_electric_and_magnetic_fields
html
local
li
class
toclevel-1 tocsection-10
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Types_of_equilibrium
html
local
li
class
toclevel-1 tocsection-11
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Composition_of_a_mixture
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Mass-balance_equations
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Polybasic_acids
html
local
li
class
toclevel-3 tocsection-14
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Solution_and_precipitation
html
local
li
class
toclevel-3 tocsection-15
html
local
ul
html
local
li
class
toclevel-2 tocsection-13
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Minimization_of_Gibbs_energy
html
local
li
class
toclevel-2 tocsection-16
html
local
ul
html
local
li
class
toclevel-1 tocsection-12
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#See_also
html
local
li
class
toclevel-1 tocsection-17
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#References
html
local
li
class
toclevel-1 tocsection-18
html
local
span
class
tocnumber
html
local
span
class
toctext
html
local
a
href
#Further_reading
html
local
li
class
toclevel-1 tocsection-19
html
local
ul
html
local
div
id class
toc toc
html
local
p
html
local
span
class id
mw-headline Historical_introduction
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=1 Edit section: Historical introduction
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
img
alt src width height class srcset data-file-width data-file-height
//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Burette.svg/100px-Burette.svg.png 100 680 thumbimage //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Burette.svg/150px-Burette.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Burette.svg/200px-Burette.svg.png 2x 100 680
html
local
a
href class
/wiki/File:Burette.svg image
html
local
a
href class title
/wiki/File:Burette.svg internal Enlarge
html
local
div
class
magnify
html
local
a
href title
/wiki/Burette Burette
html
local
a
href title
/wiki/Titration Titration
html
local
a
href title
/wiki/Analytical_chemistry Analytical chemistry
html
local
div
class
thumbcaption
html
local
div
class style
thumb tright thumbinner width:102px;
html
local
a
href title
/wiki/Claude_Louis_Berthollet Claude Louis Berthollet
html
local
a
href title
/wiki/Chemical_reaction Chemical reaction
html
local
a
href title
/wiki/Reversible_reaction Reversible reaction
html
local
a
href
#cite_note-4
html
local
sup
id class
cite_ref-4 reference
html
local
a
href title
/wiki/Reaction_rate Reaction rate
html
local
a
href title
/wiki/Chemical_equation Chemical equation
html
local
a
href
#cite_note-5
html
local
sup
id class
cite_ref-5 reference
html
local
a
href class title
/wiki/Reactant mw-redirect Reactant
html
local
i
html
local
a
href class title
/wiki/Alpha_(letter) mw-redirect Alpha (letter)
html
local
i
html
local
a
href class title
/wiki/Beta_(letter) mw-redirect Beta (letter)
html
local
i
html
local
a
href title
/wiki/Sigma Sigma
html
local
i
html
local
a
href title
/wiki/Tau Tau
html
local
a
href class title
/wiki/Stoichiometric_coefficient mw-redirect Stoichiometric coefficient
html
local
p
html
local
i
html
local
i
html
local
i
html
local
i
html
local
dd
html
local
dl
html
local
p
html
local
a
href title
/wiki/Cato_Maximilian_Guldberg Cato Maximilian Guldberg
html
local
a
href title
/wiki/Peter_Waage Peter Waage
html
local
a
href title
/wiki/Law_of_mass_action Law of mass action
html
local
p
html
local
mtext
html
local
mtext
html
local
mtext
html
local
mtext
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mtd
html
local
mi
html
local
mo
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mtd
html
local
mtr
html
local
mtext
html
local
mtext
html
local
mtext
html
local
mtext
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mtd
html
local
mi
html
local
mo
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mtd
html
local
mtr
html
local
mtable
columnalign rowspacing columnspacing displaystyle
right left right left right left right left right left right left 3pt 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em true
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle {\begin{aligned}{\ce {forward~reaction~rate}}&=k_{+}{\ce {A}}^{\alpha }{\ce {B}}^{\beta }\\{\ce {backward~reaction~rate}}&=k_{-}{\ce {S}}^{\sigma }{\ce {T}}^{\tau }\end{aligned}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/1907a547b230273a81ce1a0d44f97b2bce214b99 mwe-math-fallback-image-inline true vertical-align: -2.241ex; margin-bottom: -0.264ex; width:35.496ex; height:6.176ex; {\displaystyle {\begin{aligned}{\ce {forward~reaction~rate}}&=k_{+}{\ce {A}}^{\alpha }{\ce {B}}^{\beta }\\{\ce {backward~reaction~rate}}&=k_{-}{\ce {S}}^{\sigma }{\ce {T}}^{\tau }\end{aligned}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
a
href class title
/wiki/Activity_(chemistry) mw-redirect Activity (chemistry)
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
a
href class title
/wiki/Rate_constant mw-redirect Rate constant
html
local
p
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mspace
width
thinmathspace
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle k_{+}\left\{{\ce {A}}\right\}^{\alpha }\left\{{\ce {B}}\right\}^{\beta }=k_{-}\left\{{\ce {S}}\right\}^{\sigma }\left\{{\ce {T}}\right\}^{\tau }\,}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/8b6933778c88f49ff52b6aecbd4fc6c36d91f984 mwe-math-fallback-image-inline true vertical-align: -0.838ex; width:29.301ex; height:3.343ex; {\displaystyle k_{+}\left\{{\ce {A}}\right\}^{\alpha }\left\{{\ce {B}}\right\}^{\beta }=k_{-}\left\{{\ce {S}}\right\}^{\sigma }\left\{{\ce {T}}\right\}^{\tau }\,}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
a
href title
/wiki/Equilibrium_constant Equilibrium constant
html
local
p
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mo
fence stretchy
false false
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
fence stretchy
false false
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mo
fence stretchy
false false
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
fence stretchy
false false
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle K_{c}={\frac {k_{+}}{k_{-}}}={\frac {\{{\ce {S}}\}^{\sigma }\{{\ce {T}}\}^{\tau }}{\{{\ce {A}}\}^{\alpha }\{{\ce {B}}\}^{\beta }}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/89e6da4abda58f6f54ca008ba9303b41fda46d0c mwe-math-fallback-image-inline true vertical-align: -2.671ex; width:24.005ex; height:6.509ex; {\displaystyle K_{c}={\frac {k_{+}}{k_{-}}}={\frac {\{{\ce {S}}\}^{\sigma }\{{\ce {T}}\}^{\tau }}{\{{\ce {A}}\}^{\alpha }\{{\ce {B}}\}^{\beta }}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
a
href class title
/wiki/Numerator mw-redirect Numerator
html
local
a
href title
/wiki/Law_of_mass_action Law of mass action
html
local
a
href title
/wiki/Transition_state Transition state
html
local
b
html
local
a
href title
/wiki/Reaction_rate#Rate_equation Reaction rate
html
local
a
href title
/wiki/Stoichiometry Stoichiometry
html
local
a
href class title
/wiki/Nucleophilic_aliphatic_substitution mw-redirect Nucleophilic aliphatic substitution
html
local
sub
html
local
a
href title
/wiki/Hydrogen Hydrogen
html
local
a
href title
/wiki/Bromine Bromine
html
local
a
href title
/wiki/Hydrogen_bromide Hydrogen bromide
html
local
a
href class title
/wiki/Necessary_and_sufficient_conditions mw-redirect Necessary and sufficient conditions
html
local
a
href class title
/wiki/Necessary_and_sufficient_conditions mw-redirect Necessary and sufficient conditions
html
local
p
html
local
a
href title
/wiki/Van_%27t_Hoff_equation Van 't Hoff equation
html
local
a
href class title
/wiki/Catalyst mw-redirect Catalyst
html
local
a
href
#cite_note-aj-2
html
local
sup
id class
cite_ref-aj_2-1 reference
html
local
a
href
#cite_note-6
html
local
sup
id class
cite_ref-6 reference
html
local
p
html
local
a
href class title
/wiki/Macroscopic mw-redirect Macroscopic
html
local
a
href title
/wiki/Acetic_acid Acetic acid
html
local
a
href title
/wiki/Acetate Acetate
html
local
a
href title
/wiki/Hydronium Hydronium
html
local
p
html
local
sub
html
local
sub
html
local
sub
html
local
br
html
local
sub
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
span
style
display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left
html
local
sup
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
br
html
local
sub
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
span
style
display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left
html
local
span
class
chemf nowrap
html
local
sub
html
local
sup
html
local
dd
html
local
dl
html
local
a
href title
/wiki/Dynamic_equilibrium Dynamic equilibrium
html
local
p
html
local
a
href class title
/wiki/Le_Ch%C3%A2telier%27s_principle mw-redirect Le Châtelier's principle
html
local
b
html
local
i
html
local
p
html
local
a
href title
/wiki/Mineral_acid Mineral acid
html
local
p
html
local
mi
html
local
mo
html
local
mo
fence stretchy
false false
html
local
mtext
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width height depth
0pt 0pt .2em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mtext
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mo
fence stretchy
false false
html
local
mtext
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width height depth
0pt 0pt .2em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mrow
html
local
mo
fence stretchy
false false
html
local
mtext
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width height depth
0pt 0pt .2em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mtext
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width height depth
0pt 0pt .2em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mtext
html
local
mo
fence stretchy
false false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle K={\frac {\{{\ce {CH3CO2-}}\}\{{\ce {H3O+}}\}}{{\ce {\{CH3CO2H\}}}}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/fa570c835789ef3e11986bfd83e66252edb6ff19 mwe-math-fallback-image-inline true vertical-align: -2.838ex; width:26.239ex; height:7.009ex; {\displaystyle K={\frac {\{{\ce {CH3CO2-}}\}\{{\ce {H3O+}}\}}{{\ce {\{CH3CO2H\}}}}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
sub
html
local
sup
html
local
sub
html
local
sub
html
local
br
html
local
sub
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
span
style
display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left
html
local
sup
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
br
html
local
sub
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
span
style
display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left
html
local
span
class
chemf nowrap
html
local
sub
html
local
p
html
local
a
href title
/wiki/Reaction_quotient Reaction quotient
html
local
p
html
local
a
href title
/wiki/Josiah_Willard_Gibbs Josiah Willard Gibbs
html
local
a
href title
/wiki/Chemical_potential Chemical potential
html
local
a
href title
/wiki/Reaction_coordinate Reaction coordinate
html
local
a
href title
/wiki/Extent_of_reaction Extent of reaction
html
local
a
href title
/wiki/Stationary_point Stationary point
html
local
a
href title
/wiki/Chemical_potential Chemical potential
html
local
a
href
#cite_note-Atkins-1
html
local
sup
id class
cite_ref-Atkins_1-1 reference
html
local
a
href class title
/wiki/Helmholtz_energy mw-redirect Helmholtz energy
html
local
a
href class title
/wiki/Gibbs_energy mw-redirect Gibbs energy
html
local
p
html
local
mi
mathvariant
normal
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \Delta _{r}G^{\ominus }=-RT\ln K_{{\ce {eq}}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/0732d8eab406e9febbc7db71ac5e9f7cce955f23 mwe-math-fallback-image-inline true vertical-align: -1.005ex; width:21.071ex; height:3.176ex; {\displaystyle \Delta _{r}G^{\ominus }=-RT\ln K_{{\ce {eq}}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
a
href class title
/wiki/Universal_gas_constant mw-redirect Universal gas constant
html
local
a
href title
/wiki/Temperature Temperature
html
local
p
html
local
a
href title
/wiki/Solution Solution
html
local
a
href title
/wiki/Ionic_strength Ionic strength
html
local
a
href title
/wiki/Activity_coefficient Activity coefficient
html
local
b
html
local
i
html
local
sub
html
local
p
html
local
mi
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mo
stretchy
false
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle K_{\ce {c}}={\frac {[{\ce {S}}]^{\sigma }[{\ce {T}}]^{\tau }}{[{\ce {A}}]^{\alpha }[{\ce {B}}]^{\beta }}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/c2ac61ea07e9614e7c3e261d737d856396c1b178 mwe-math-fallback-image-inline true vertical-align: -2.671ex; width:15.304ex; height:6.509ex; {\displaystyle K_{\ce {c}}={\frac {[{\ce {S}}]^{\sigma }[{\ce {T}}]^{\tau }}{[{\ce {A}}]^{\alpha }[{\ce {B}}]^{\beta }}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
a
href title
/wiki/Concentration Concentration
html
local
a
href class title
/wiki/Analytical_concentration mw-redirect Analytical concentration
html
local
a
href title
/wiki/Solution Solution
html
local
a
href title
/wiki/Determination_of_equilibrium_constants Determination of equilibrium constants
html
local
sub
html
local
i
html
local
a
href title
/wiki/Ionic_strength Ionic strength
html
local
sub
html
local
i
html
local
a
href title
/wiki/Partial_pressure Partial pressure
html
local
p
html
local
span
class id
mw-headline Thermodynamics
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=2 Edit section: Thermodynamics
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
a
href title
/wiki/Gibbs_free_energy Gibbs free energy
html
local
i
html
local
a
href title
/wiki/Helmholtz_free_energy Helmholtz free energy
html
local
i
html
local
i
html
local
p
html
local
a
href title
/wiki/Geochemistry Geochemistry
html
local
a
href title
/wiki/Atmospheric_chemistry Atmospheric chemistry
html
local
a
href title
/wiki/Standard_state Standard state
html
local
a
href title
/wiki/Entropy_of_mixing Entropy of mixing
html
local
a
href
#cite_note-7
html
local
sup
id class
cite_ref-7 reference
html
local
a
href
#cite_note-8
html
local
sup
id class
cite_ref-8 reference
html
local
p
html
local
b
html
local
a
href title
/wiki/Chemical_potential Chemical potential
html
local
a
href
#cite_note-Atkins-1
html
local
sup
id class
cite_ref-Atkins_1-2 reference
html
local
p
html
local
a
href title
/wiki/Gibbs_free_energy Gibbs free energy
html
local
i
html
local
a
href title
/wiki/Extent_of_reaction Extent of reaction
html
local
i
html
local
a
href title
/wiki/Xi_(letter) Xi (letter)
html
local
a
href title
/wiki/Second_law_of_thermodynamics Second law of thermodynamics
html
local
i
html
local
i
html
local
p
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
html
local
mi
html
local
mi
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mn
html
local
mtext
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=0~}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/5babfc9bf7581b626ed039500568ae6b15638b4e mwe-math-fallback-image-inline true vertical-align: -2.838ex; width:14.815ex; height:6.509ex; \left({\frac {dG}{d\xi }}\right)_{T,p}=0~
html
local
span
class
mwe-math-element
html
local
span
class
nowrap
html
local
dd
html
local
dl
html
local
i
html
local
a
href title
/wiki/Extent_of_reaction Extent of reaction
html
local
i
html
local
a
href title
/wiki/Chemical_potential Chemical potential
html
local
p
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mspace
width
thinmathspace
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \alpha \mu _{\mathrm {A} }+\beta \mu _{\mathrm {B} }=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }\,}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/e673c9a9320a593edd85dfb251dfce8e9580db02 mwe-math-fallback-image-inline true vertical-align: -0.838ex; width:25.55ex; height:2.676ex; {\displaystyle \alpha \mu _{\mathrm {A} }+\beta \mu _{\mathrm {B} }=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }\,}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
i
html
local
a
href title
/wiki/Mu_(letter) Mu (letter)
html
local
a
href title
/wiki/Chemical_potential Chemical potential
html
local
a
href class title
/wiki/Activity_(chemistry) mw-redirect Activity (chemistry)
html
local
p
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mspace
width
thinmathspace
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \mu _{\mathrm {A} }=\mu _{A}^{\ominus }+RT\ln\{\mathrm {A} \}\,}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/c1609d5df45d0f2c914ac2d44dbea82c284a0483 mwe-math-fallback-image-inline true vertical-align: -1.005ex; width:21.9ex; height:3.176ex; {\displaystyle \mu _{\mathrm {A} }=\mu _{A}^{\ominus }+RT\ln\{\mathrm {A} \}\,}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
i
html
local
s
html
local
sup
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
br
html
local
sub
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
span
style
display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left
html
local
b
html
local
p
html
local
a
href class title
/wiki/Gibbs_energy mw-redirect Gibbs energy
html
local
a
href title
/wiki/Fundamental_thermodynamic_relation Fundamental thermodynamic relation
html
local
p
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle dG=Vdp-SdT+\sum _{i=1}^{k}\mu _{i}dN_{i}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/17f993d14dc653081e044da42ec50e2f8a19bcf3 mwe-math-fallback-image-inline true vertical-align: -3.005ex; width:30.171ex; height:7.343ex; dG=Vdp-SdT+\sum _{i=1}^{k}\mu _{i}dN_{i}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
sub
html
local
i
html
local
sub
html
local
i
html
local
a
href class title
/wiki/Stoichiometric_coefficient mw-redirect Stoichiometric coefficient
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mtext
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \nu _{i}~}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/dfb56c1abefd260da0785b2a43fb0b2f2d35030c mwe-math-fallback-image-inline true vertical-align: -0.671ex; width:2.529ex; height:2.009ex; \nu _{i}~
html
local
span
class
mwe-math-element
html
local
i
html
local
p
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
html
local
mi
html
local
mi
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\sum _{i=1}^{k}\mu _{i}\nu _{i}=\Delta _{\mathrm {r} }G_{T,p}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/e310488e7eb878b5da2279bf27ccb507badb3b3b mwe-math-fallback-image-inline true vertical-align: -3.005ex; width:31.375ex; height:7.343ex; {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\sum _{i=1}^{k}\mu _{i}\nu _{i}=\Delta _{\mathrm {r} }G_{T,p}}
html
local
span
class
mwe-math-element
html
local
b
html
local
dd
html
local
dl
html
local
p
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mspace
width
thinmathspace
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }-\alpha \mu _{\mathrm {A} }-\beta \mu _{\mathrm {B} }\,}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/5d0a006e3eb1249c479bcd032798a00dff080296 mwe-math-fallback-image-inline true vertical-align: -1.005ex; width:35.703ex; height:2.843ex; {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }-\alpha \mu _{\mathrm {A} }-\beta \mu _{\mathrm {B} }\,}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mo
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mo
stretchy
false
html
local
mo
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mo
html
local
mi
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mo
stretchy
false
html
local
mo
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mo
stretchy
false
html
local
mo
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mo
stretchy
false
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=(\sigma \mu _{\mathrm {S} }^{\ominus }+\tau \mu _{\mathrm {T} }^{\ominus })-(\alpha \mu _{\mathrm {A} }^{\ominus }+\beta \mu _{\mathrm {B} }^{\ominus })+(\sigma RT\ln\{\mathrm {S} \}+\tau RT\ln\{\mathrm {T} \})-(\alpha RT\ln\{\mathrm {A} \}+\beta RT\ln\{\mathrm {B} \})}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/04b31e3abb53748c8d89f5c101f4f1b85571d5e6 mwe-math-fallback-image-inline true vertical-align: -1.005ex; width:98.45ex; height:3.176ex; {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=(\sigma \mu _{\mathrm {S} }^{\ominus }+\tau \mu _{\mathrm {T} }^{\ominus })-(\alpha \mu _{\mathrm {A} }^{\ominus }+\beta \mu _{\mathrm {B} }^{\ominus })+(\sigma RT\ln\{\mathrm {S} \}+\tau RT\ln\{\mathrm {T} \})-(\alpha RT\ln\{\mathrm {A} \}+\beta RT\ln\{\mathrm {B} \})}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}+RT\ln {\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/63e6e34d974dfa8662d2cb8c97553ceec7078143 mwe-math-fallback-image-inline true vertical-align: -3.005ex; width:39.301ex; height:7.343ex; {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}+RT\ln {\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}=\Delta _{\mathrm {r} }G^{\ominus }}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/ef9f37fc80b36755d22536457d39df78403cf0fe mwe-math-fallback-image-inline true vertical-align: -3.005ex; width:17.851ex; height:7.343ex; {\displaystyle \sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}=\Delta _{\mathrm {r} }G^{\ominus }}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
b
html
local
a
href title
/wiki/Reaction_quotient Reaction quotient
html
local
p
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
fence stretchy
false false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle Q_{\mathrm {r} }={\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/058366834e379a53b6ab637429ad66a13e6bea42 mwe-math-fallback-image-inline true vertical-align: -2.671ex; width:17.147ex; height:6.509ex; {\displaystyle Q_{\mathrm {r} }={\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
html
local
mi
html
local
mi
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln Q_{\mathrm {r} }}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/d937ec08f9592f6dd0c45ea9053db51d41825712 mwe-math-fallback-image-inline true vertical-align: -2.838ex; width:41.303ex; height:6.509ex; {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln Q_{\mathrm {r} }}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
html
local
mi
html
local
mi
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mn
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=0}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/5242c9ed73cf9a746b019b269fbbb74725b971b7 mwe-math-fallback-image-inline true vertical-align: -2.838ex; width:24.646ex; height:6.509ex; {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=0}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
mn
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle 0=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln K_{\mathrm {eq} }}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/4a59263b2243498ea38734b7244e37fa1d553343 mwe-math-fallback-image-inline true vertical-align: -1.005ex; width:23.18ex; height:3.176ex; {\displaystyle 0=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln K_{\mathrm {eq} }}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\ln K_{\mathrm {eq} }}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/d11d70ecf3178d504f6f5a9e5286fa2f59a386cf mwe-math-fallback-image-inline true vertical-align: -1.005ex; width:20.985ex; height:3.176ex; {\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\ln K_{\mathrm {eq} }}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
img
alt src width height class srcset data-file-width data-file-height
Diag eq.svg //upload.wikimedia.org/wikipedia/commons/thumb/b/be/Diag_eq.svg/350px-Diag_eq.svg.png 350 396 thumbimage //upload.wikimedia.org/wikipedia/commons/thumb/b/be/Diag_eq.svg/525px-Diag_eq.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/be/Diag_eq.svg/700px-Diag_eq.svg.png 2x 168 190
html
local
a
href class
/wiki/File:Diag_eq.svg image
html
local
a
href class title
/wiki/File:Diag_eq.svg internal Enlarge
html
local
div
class
thumbcaption magnify
html
local
div
class style
thumb tright thumbinner width:352px;
html
local
span
class id
mw-headline Addition_of_reactants_or_products
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=3 Edit section: Addition of reactants or products
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h3
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
i
html
local
i
html
local
sub
html
local
p
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
li
html
local
ul
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
html
local
mi
html
local
mi
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mtext
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln Q_{\mathrm {r} }~}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/68d3521885d339e28d7ea069a99c3256ee89d204 mwe-math-fallback-image-inline true vertical-align: -2.838ex; width:31.472ex; height:6.509ex; {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln Q_{\mathrm {r} }~}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
dd
html
local
dl
html
local
dd
html
local
dl
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mtext
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\ln K_{eq}~}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/7d53bf7e850b78d105a00e0239ca1df5bb650d59 mwe-math-fallback-image-inline true vertical-align: -1.005ex; width:21.479ex; height:3.176ex; {\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\ln K_{eq}~}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
dd
html
local
dl
html
local
dd
html
local
dl
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
html
local
mi
html
local
mi
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mtext
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=RT\ln \left({\frac {Q_{\mathrm {r} }}{K_{\mathrm {eq} }}}\right)~}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/f84df236bbe91b1362990b0d6964966a3c285f66 mwe-math-fallback-image-inline true vertical-align: -2.838ex; width:27.451ex; height:6.509ex; {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=RT\ln \left({\frac {Q_{\mathrm {r} }}{K_{\mathrm {eq} }}}\right)~}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
dd
html
local
dl
html
local
i
html
local
li
html
local
ul
html
local
br
html
local
p
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mo
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mtext
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle Q_{\mathrm {r} }={\frac {\prod (a_{j})^{\nu _{j}}}{\prod (a_{i})^{\nu _{i}}}}~}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/301e9a893d4dc9553eb89a098208091acc69fffa mwe-math-fallback-image-inline true vertical-align: -2.671ex; width:15.132ex; height:6.509ex; {\displaystyle Q_{\mathrm {r} }={\frac {\prod (a_{j})^{\nu _{j}}}{\prod (a_{i})^{\nu _{i}}}}~}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
dd
html
local
dd
html
local
dl
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mtext
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle Q_{\mathrm {r} }<K_{\mathrm {eq} }~}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/e9e9dc4b6f1756eb62b666984bb7225d745a8f6e mwe-math-fallback-image-inline true vertical-align: -1.005ex; width:10.209ex; height:2.843ex; {\displaystyle Q_{\mathrm {r} }<K_{\mathrm {eq} }~}
html
local
span
class
mwe-math-element
html
local
span
class
nowrap
html
local
span
class
nowrap
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
html
local
mi
html
local
mi
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mn
html
local
mtext
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}<0~}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/05ebd028652e757ea67e82262b5d9a8043b6a6cc mwe-math-fallback-image-inline true vertical-align: -2.838ex; width:14.815ex; height:6.509ex; \left({\frac {dG}{d\xi }}\right)_{T,p}<0~
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
dd
html
local
dd
html
local
dl
html
local
i
html
local
li
html
local
ul
html
local
dd
html
local
dl
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mtext
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle Q_{\mathrm {r} }>K_{\mathrm {eq} }~}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/1c712cabbcd8232733ceef132c807675cd9c637e mwe-math-fallback-image-inline true vertical-align: -1.005ex; width:10.209ex; height:2.843ex; {\displaystyle Q_{\mathrm {r} }>K_{\mathrm {eq} }~}
html
local
span
class
mwe-math-element
html
local
span
class
nowrap
html
local
span
class
nowrap
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
html
local
mi
html
local
mi
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mn
html
local
mtext
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}>0~}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/b31683ea47379fb55171d7a91a5962b9b1a41228 mwe-math-fallback-image-inline true vertical-align: -2.838ex; width:14.815ex; height:6.509ex; \left({\frac {dG}{d\xi }}\right)_{T,p}>0~
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
dd
html
local
dd
html
local
dl
html
local
p
html
local
span
class id
mw-headline Treatment_of_activity
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=4 Edit section: Treatment of activity
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h3
html
local
i
html
local
sub
html
local
a
href title
/wiki/Activity_coefficient Activity coefficient
html
local
i
html
local
p
html
local
mi
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mo
html
local
mo
html
local
mrow
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mo
html
local
mo
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mo
html
local
mo
html
local
mrow
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mo
html
local
mo
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle K={\frac {[\mathrm {S} ]^{\sigma }[\mathrm {T} ]^{\tau }...}{[\mathrm {A} ]^{\alpha }[\mathrm {B} ]^{\beta }...}}\times {\frac {{\gamma _{\mathrm {S} }}^{\sigma }{\gamma _{\mathrm {T} }}^{\tau }...}{{\gamma _{\mathrm {A} }}^{\alpha }{\gamma _{\mathrm {B} }}^{\beta }...}}=K_{\mathrm {c} }\Gamma }
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/160fbc88403a037161d2c9a44d10cd44746215e8 mwe-math-fallback-image-inline true vertical-align: -2.671ex; width:38.755ex; height:6.509ex; {\displaystyle K={\frac {[\mathrm {S} ]^{\sigma }[\mathrm {T} ]^{\tau }...}{[\mathrm {A} ]^{\alpha }[\mathrm {B} ]^{\beta }...}}\times {\frac {{\gamma _{\mathrm {S} }}^{\sigma }{\gamma _{\mathrm {T} }}^{\tau }...}{{\gamma _{\mathrm {A} }}^{\alpha }{\gamma _{\mathrm {B} }}^{\beta }...}}=K_{\mathrm {c} }\Gamma }
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
a
href title
/wiki/Debye%E2%80%93H%C3%BCckel_equation Debye–Hückel equation
html
local
a
href title
/wiki/Davies_equation Davies equation
html
local
a
href
#cite_note-9
html
local
sup
id class
cite_ref-9 reference
html
local
a
href title
/wiki/Specific_ion_interaction_theory Specific ion interaction theory
html
local
a
href title
/wiki/Pitzer_equations Pitzer equations
html
local
a
href
#cite_note-davies-10
html
local
sup
id class
cite_ref-davies_10-0 reference
html
local
a
href
#Software_for_chemical_equilibria
html
local
sup
html
local
i
html
local
i
html
local
i
html
local
p
html
local
a
href title
/wiki/Partial_pressure Partial pressure
html
local
a
href class title
/wiki/Fugacity_coefficient mw-redirect Fugacity coefficient
html
local
a
href title
/wiki/Haber_process Haber process
html
local
i
html
local
p
html
local
mi
html
local
mo
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mo
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \mu =\mu ^{\ominus }+RT\ln \left({\frac {f}{\mathrm {bar} }}\right)=\mu ^{\ominus }+RT\ln \left({\frac {p}{\mathrm {bar} }}\right)+RT\ln \gamma }
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/d03b3affef391d49f01ba91ff665f771ccd6e5bf mwe-math-fallback-image-inline true vertical-align: -2.505ex; width:55.377ex; height:6.176ex; {\displaystyle \mu =\mu ^{\ominus }+RT\ln \left({\frac {f}{\mathrm {bar} }}\right)=\mu ^{\ominus }+RT\ln \left({\frac {p}{\mathrm {bar} }}\right)+RT\ln \gamma }
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
span
class id
mw-headline Concentration_quotients
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=5 Edit section: Concentration quotients
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h3
html
local
a
href title
/wiki/Sodium_nitrate Sodium nitrate
html
local
sub
html
local
a
href title
/wiki/Potassium_perchlorate Potassium perchlorate
html
local
sub
html
local
a
href title
/wiki/Ionic_strength Ionic strength
html
local
p
html
local
mi
html
local
mo
html
local
mn
html
local
mn
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle I={\frac {1}{2}}\sum _{i=1}^{N}c_{i}z_{i}^{2}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/88e01c8f87d4fb3dea0e90e8807179de2dbb1b1a mwe-math-fallback-image-inline true vertical-align: -3.005ex; width:14.349ex; height:7.343ex; {\displaystyle I={\frac {1}{2}}\sum _{i=1}^{N}c_{i}z_{i}^{2}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
sub
html
local
i
html
local
sub
html
local
i
html
local
i
html
local
i
html
local
i
html
local
a
href title
/wiki/Gamma Gamma
html
local
a
href
#cite_note-11
html
local
sup
id class
cite_ref-11 reference
html
local
p
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle K_{\mathrm {c} }={\frac {K}{\Gamma }}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/3afe716ce40e5e475d1a67426f7b5b79801cd160 mwe-math-fallback-image-inline true vertical-align: -1.838ex; width:8.936ex; height:5.176ex; {\displaystyle K_{\mathrm {c} }={\frac {K}{\Gamma }}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
i
html
local
sub
html
local
a
href
#cite_note-davies-10
html
local
sup
id class
cite_ref-davies_10-1 reference
html
local
p
html
local
a
href
#Software_for_chemical_equilibria
html
local
sup
html
local
p
html
local
span
class id
mw-headline Metastable_mixtures
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=6 Edit section: Metastable mixtures
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h3
html
local
sub
html
local
a
href title
/wiki/Sulfur_dioxide Sulfur dioxide
html
local
sub
html
local
a
href title
/wiki/Oxygen Oxygen
html
local
a
href title
/wiki/Metastability Metastability
html
local
a
href title
/wiki/Activation_energy Activation energy
html
local
sub
html
local
a
href title
/wiki/Sulfur_trioxide Sulfur trioxide
html
local
p
html
local
sub
html
local
sub
html
local
sub
html
local
dd
html
local
dl
html
local
a
href title
/wiki/Catalysis Catalysis
html
local
a
href title
/wiki/Contact_process Contact process
html
local
p
html
local
a
href title
/wiki/Bicarbonate Bicarbonate
html
local
a
href title
/wiki/Carbon_dioxide Carbon dioxide
html
local
a
href title
/wiki/Water Water
html
local
p
html
local
sub
html
local
sub
html
local
sup
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
br
html
local
sub
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
span
style
display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left
html
local
span
class
chemf nowrap
html
local
sub
html
local
sup
html
local
dd
html
local
dl
html
local
a
href title
/wiki/Enzyme Enzyme
html
local
a
href title
/wiki/Carbonic_anhydrase Carbonic anhydrase
html
local
p
html
local
span
class id
mw-headline Pure_substances
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=7 Edit section: Pure substances
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
a
href
#cite_note-CEM-12
html
local
sup
id class
cite_ref-CEM_12-0 reference
html
local
p
html
local
p
html
local
sub
html
local
sub
html
local
sub
html
local
sub
html
local
sub
html
local
sup
html
local
sub
html
local
sup
html
local
dd
html
local
dl
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle K_{\mathrm {c} }={\frac {\mathrm {[{CH_{3}CO_{2}}^{-}][{H_{3}O}^{+}]} }{\mathrm {[{CH_{3}CO_{2}H}][{H_{2}O}]} }}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/53b93bf6dae8354f02ab3e935fca63b9bd4a16c4 mwe-math-fallback-image-inline true vertical-align: -2.671ex; width:26.1ex; height:6.676ex; {\displaystyle K_{\mathrm {c} }={\frac {\mathrm {[{CH_{3}CO_{2}}^{-}][{H_{3}O}^{+}]} }{\mathrm {[{CH_{3}CO_{2}H}][{H_{2}O}]} }}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
mi
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle K={\frac {\mathrm {[{CH_{3}CO_{2}}^{-}][{H_{3}O}^{+}]} }{\mathrm {[{CH_{3}CO_{2}H}]} }}=K_{\mathrm {c} }}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/472d349477dcf83e95cb3c3423e8ba247ff1d23a mwe-math-fallback-image-inline true vertical-align: -2.671ex; width:31.265ex; height:6.676ex; {\displaystyle K={\frac {\mathrm {[{CH_{3}CO_{2}}^{-}][{H_{3}O}^{+}]} }{\mathrm {[{CH_{3}CO_{2}H}]} }}=K_{\mathrm {c} }}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
a
href title
/wiki/Self-ionization_of_water Self-ionization of water
html
local
p
html
local
sub
html
local
sub
html
local
sup
html
local
sup
html
local
dd
html
local
dl
html
local
p
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle K_{\mathrm {w} }=\mathrm {[H^{+}][OH^{-}]} }
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/02e72380cadad70b38e1a6f42ce8b217618bc11f mwe-math-fallback-image-inline true vertical-align: -0.838ex; width:17.394ex; height:3.009ex; {\displaystyle K_{\mathrm {w} }=\mathrm {[H^{+}][OH^{-}]} }
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
sup
html
local
a
href class title
/wiki/Hydronium_ion mw-redirect Hydronium ion
html
local
a
href title
/wiki/Solvation Solvation
html
local
i
html
local
sub
html
local
p
html
local
sup
html
local
sup
html
local
sup
html
local
i
html
local
sub
html
local
sup
html
local
sup
html
local
a
href class title
/wiki/Hydroxide_ion mw-redirect Hydroxide ion
html
local
p
html
local
a
href title
/wiki/Boudouard_reaction Boudouard reaction
html
local
a
href
#cite_note-CEM-12
html
local
sup
id class
cite_ref-CEM_12-1 reference
html
local
p
html
local
sub
html
local
dd
html
local
dl
html
local
p
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle K_{\mathrm {c} }={\frac {\mathrm {[CO_{2}]} }{\mathrm {[CO]^{2}} }}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/df7ff1e7f45707791cfd9dd8e697fe5695e94f60 mwe-math-fallback-image-inline true vertical-align: -2.671ex; width:12.704ex; height:6.509ex; {\displaystyle K_{\mathrm {c} }={\frac {\mathrm {[CO_{2}]} }{\mathrm {[CO]^{2}} }}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
span
class id
mw-headline Multiple_equilibria
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=8 Edit section: Multiple equilibria
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
sub
html
local
sub
html
local
sup
html
local
sup
html
local
p
html
local
mtext
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width height depth
0pt 0pt .2em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mtext
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
negativethinmathspace
html
local
mspace
width
negativethinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mpadded
height depth
0 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-OP MJX-fixedlimits
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
negativethinmathspace
html
local
mspace
width
negativethinmathspace
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
false 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mover
html
local
mrow
class
MJX-TeXAtom-REL
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mtd
html
local
mi
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
html
local
mo
stretchy
false
html
local
mtext
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width height depth
0pt 0pt .2em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mtext
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mtd
html
local
mtr
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
negativethinmathspace
html
local
mspace
width
negativethinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mpadded
height depth
0 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-OP MJX-fixedlimits
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
negativethinmathspace
html
local
mspace
width
negativethinmathspace
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
false 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mover
html
local
mrow
class
MJX-TeXAtom-REL
html
local
mtext
html
local
mn
html
local
mspace
width
thinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mtd
html
local
mi
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mtext
html
local
mn
html
local
mspace
width
thinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
html
local
mo
stretchy
false
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mtd
html
local
mtr
html
local
mtable
columnalign rowspacing columnspacing
right left 4pt 1em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle {\begin{array}{rl}{\ce {H2A<=>{HA^{-}}+{H+}}}:&K_{1}={\frac {\ce {[HA-][H+]}}{\ce {[H2A]}}}\\{\ce {HA-<=>{A^{2-}}+{H+}}}:&K_{2}={\frac {\ce {[A^{2-}][H+]}}{\ce {[HA-]}}}\end{array}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/02fc199cec1e474859edf9723bf1aa772591e5a7 mwe-math-fallback-image-inline true vertical-align: -4.419ex; margin-bottom: -0.252ex; width:39.836ex; height:10.509ex; {\displaystyle {\begin{array}{rl}{\ce {H2A<=>{HA^{-}}+{H+}}}:&K_{1}={\frac {\ce {[HA-][H+]}}{\ce {[H2A]}}}\\{\ce {HA-<=>{A^{2-}}+{H+}}}:&K_{2}={\frac {\ce {[A^{2-}][H+]}}{\ce {[HA-]}}}\end{array}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
i
html
local
i
html
local
i
html
local
sub
html
local
p
html
local
mtext
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width height depth
0pt 0pt .2em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
negativethinmathspace
html
local
mspace
width
negativethinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mpadded
height depth
0 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-OP MJX-fixedlimits
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
negativethinmathspace
html
local
mspace
width
negativethinmathspace
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
false 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mover
html
local
mrow
class
MJX-TeXAtom-REL
html
local
mtext
html
local
mn
html
local
mspace
width
thinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mn
html
local
mspace
width
thinmathspace
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle {\ce {{H2A}<=>{A^{2-}}+{2H+}}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/a482f908f1eb2a0713600eb64da4a43ec0d0ead8 mwe-math-fallback-image-inline true vertical-align: -1.005ex; width:21.295ex; height:3.343ex; {\displaystyle {\ce {{H2A}<=>{A^{2-}}+{2H+}}}}
html
local
span
class
mwe-math-element
html
local
span
class
nowrap
html
local
mi
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mtext
html
local
mn
html
local
mspace
width
thinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mtext
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width height depth
0pt 0pt .2em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mtext
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mi
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \beta _{{\ce {D}}}={\frac {{\ce {[A^{2-}][H^+]^2}}}{{\ce {[H_2A]}}}}=K_{1}K_{2}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/c204101410770f2cc038f6d29c1a7a0da1d363a1 mwe-math-fallback-image-inline true vertical-align: -2.838ex; width:27.25ex; height:7.176ex; {\displaystyle \beta _{{\ce {D}}}={\frac {{\ce {[A^{2-}][H^+]^2}}}{{\ce {[H_2A]}}}}=K_{1}K_{2}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
a
href title
/wiki/Acid_dissociation_constant Acid dissociation constant
html
local
p
html
local
mtext
html
local
mn
html
local
mspace
width
thinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
negativethinmathspace
html
local
mspace
width
negativethinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mpadded
height depth
0 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-OP MJX-fixedlimits
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
negativethinmathspace
html
local
mspace
width
negativethinmathspace
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
false 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mover
html
local
mrow
class
MJX-TeXAtom-REL
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mtd
html
local
mi
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mtext
html
local
mn
html
local
mspace
width
thinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mtd
html
local
mtr
html
local
mtext
html
local
mn
html
local
mspace
width
thinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mn
html
local
mspace
width
thinmathspace
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
negativethinmathspace
html
local
mspace
width
negativethinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mpadded
height depth
0 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-OP MJX-fixedlimits
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
negativethinmathspace
html
local
mspace
width
negativethinmathspace
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
false 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mover
html
local
mrow
class
MJX-TeXAtom-REL
html
local
mtext
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width height depth
0pt 0pt .2em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mtext
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mtd
html
local
mi
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mtext
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width height depth
0pt 0pt .2em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mtext
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mtext
html
local
mn
html
local
mspace
width
thinmathspace
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mtext
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mtd
html
local
mtr
html
local
mtable
columnalign rowspacing columnspacing
left left 4pt 1em
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle {\begin{array}{ll}{\ce {{A^{2-}}+{H+}<=>HA-}}:&\beta _{1}={\frac {\ce {[HA^{-}]}}{\ce {[A^{2-}][H+]}}}\\{\ce {{A^{2-}}+{2H+}<=>H2A}}:&\beta _{2}={\frac {\ce {[H2A]}}{\ce {[A^{2-}][H+]^{2}}}}\end{array}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/3bd8050bd8872f9cbd63bffcc07ebc25c6875c3a mwe-math-fallback-image-inline true vertical-align: -4.71ex; margin-bottom: -0.294ex; width:40.551ex; height:11.176ex; {\displaystyle {\begin{array}{ll}{\ce {{A^{2-}}+{H+}<=>HA-}}:&\beta _{1}={\frac {\ce {[HA^{-}]}}{\ce {[A^{2-}][H+]}}}\\{\ce {{A^{2-}}+{2H+}<=>H2A}}:&\beta _{2}={\frac {\ce {[H2A]}}{\ce {[A^{2-}][H+]^{2}}}}\end{array}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
span
style
display:block; line-height:1em; margin:0 0.1em;
html
local
span
class
visualhide
html
local
i
html
local
sub
html
local
span
style
display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;
html
local
span
class style
sfrac nowrap display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;
html
local
span
class
texhtml
html
local
i
html
local
sub
html
local
span
style
display:block; line-height:1em; margin:0 0.1em;
html
local
span
class
visualhide
html
local
i
html
local
sub
html
local
span
style
display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;
html
local
span
class style
sfrac nowrap display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;
html
local
span
class
texhtml
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
span
class
texhtml
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
span
class
texhtml
html
local
a
href
#cite_note-13
html
local
sup
id class
cite_ref-13 reference
html
local
a
href title
/wiki/Response_reactions Response reactions
html
local
p
html
local
span
class id
mw-headline Effect_of_temperature
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=9 Edit section: Effect of temperature
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
a
href title
/wiki/Van_%27t_Hoff_equation Van 't Hoff equation
html
local
p
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
html
local
mi
html
local
mi
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mrow
html
local
mi
html
local
mi
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle {\frac {d\ln K}{dT}}={\frac {\Delta H_{\mathrm {m} }^{\ominus }}{RT^{2}}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/8392cb1f47c3596a51623e15d5bf76644b08de1d mwe-math-fallback-image-inline true vertical-align: -2.171ex; width:16.316ex; height:5.843ex; {\displaystyle {\frac {d\ln K}{dT}}={\frac {\Delta H_{\mathrm {m} }^{\ominus }}{RT^{2}}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
a
href class title
/wiki/Exothermic mw-redirect Exothermic
html
local
i
html
local
i
html
local
a
href class title
/wiki/Endothermic mw-redirect Endothermic
html
local
i
html
local
p
html
local
mi
html
local
mi
html
local
mo
html
local
mi
html
local
mrow
html
local
mi
html
local
mo
stretchy
false
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mrow
html
local
mi
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle {\frac {d\ln K}{d(T^{-1})}}=-{\frac {\Delta H_{\mathrm {m} }^{\ominus }}{R}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/4699785667c5faa06434bdb1a1f7d124331309f7 mwe-math-fallback-image-inline true vertical-align: -2.671ex; width:19.207ex; height:6.343ex; {\displaystyle {\frac {d\ln K}{d(T^{-1})}}=-{\frac {\Delta H_{\mathrm {m} }^{\ominus }}{R}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
i
html
local
p
html
local
span
class id
mw-headline Effect_of_electric_and_magnetic_fields
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=10 Edit section: Effect of electric and magnetic fields
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
a
href title
/wiki/Manfred_Eigen Manfred Eigen
html
local
span
title
Eigen measured reaction *rates* near equilibrium by the electric-field jump method, not the effect on the '''position''' of equilibrium (July 2013)
html
local
a
href title
/wiki/Wikipedia:Citation_needed Wikipedia:Citation needed
html
local
i
html
local
sup
class style
noprint Inline-Template Template-Fact white-space:nowrap;
html
local
p
html
local
span
class id
mw-headline Types_of_equilibrium
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=11 Edit section: Types of equilibrium
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
a
href class title
/wiki/Haber%E2%80%93Bosch_process mw-redirect Haber–Bosch process
html
local
div
class style
background-color: #F9F9F9; color: black; text-align: center; font-size: larger; font-weight: bold;
html
local
sub
html
local
sub
html
local
sub
html
local
li
html
local
sub
html
local
sub
html
local
li
html
local
sub
html
local
li
html
local
sub
html
local
li
html
local
sub
html
local
sub
html
local
li
html
local
ol
html
local
div
class style
position: relative; text-align: left;
html
local
div
class style
quotebox pullquote float: right; clear: right; margin: 0.5em 0 0.8em 1.4em; padding: 10px; border: 1px solid #aaa; font-size: 88%; background-color: #F9F9F9;
html
local
a
href title
/wiki/Rocket_engine Rocket engine
html
local
a
href
#cite_note-nasa-14
html
local
sup
id class
cite_ref-nasa_14-0 reference
html
local
li
html
local
a
href title
/wiki/Ammonia Ammonia
html
local
a
href class title
/wiki/Haber%E2%80%93Bosch_process mw-redirect Haber–Bosch process
html
local
a
href title
/wiki/Adsorption Adsorption
html
local
li
html
local
a
href title
/wiki/Atmospheric_chemistry Atmospheric chemistry
html
local
li
html
local
a
href title
/wiki/Chemical_oceanography Chemical oceanography
html
local
li
html
local
i
html
local
a
href title
/wiki/Partition_coefficient Partition coefficient
html
local
li
html
local
a
href title
/wiki/Liquid%E2%80%93liquid_extraction Liquid–liquid extraction
html
local
a
href title
/wiki/Ion_exchange Ion exchange
html
local
a
href title
/wiki/Chromatography Chromatography
html
local
li
html
local
a
href title
/wiki/Solubility_equilibrium Solubility equilibrium
html
local
li
html
local
a
href title
/wiki/Hemoglobin Hemoglobin
html
local
li
html
local
ul
html
local
li
html
local
a
href title
/wiki/Acid_dissociation_constant Acid dissociation constant
html
local
a
href title
/wiki/Hydrolysis Hydrolysis
html
local
a
href title
/wiki/Buffer_solution Buffer solution
html
local
a
href title
/wiki/PH_indicator PH indicator
html
local
a
href title
/wiki/Acid%E2%80%93base_homeostasis Acid–base homeostasis
html
local
li
html
local
a
href title
/wiki/Chelation Chelation
html
local
a
href title
/wiki/Chelation_therapy Chelation therapy
html
local
a
href title
/wiki/Magnetic_resonance_imaging Magnetic resonance imaging
html
local
a
href title
/wiki/Schlenk_equilibrium Schlenk equilibrium
html
local
li
html
local
a
href title
/wiki/Host%E2%80%93guest_chemistry Host–guest chemistry
html
local
a
href title
/wiki/Supramolecular_chemistry Supramolecular chemistry
html
local
a
href title
/wiki/Molecular_recognition Molecular recognition
html
local
a
href title
/wiki/Dinitrogen_tetroxide Dinitrogen tetroxide
html
local
li
html
local
a
href class title
/wiki/Oscillating_reaction mw-redirect Oscillating reaction
html
local
a
href
#cite_note-CEM-12
html
local
sup
id class
cite_ref-CEM_12-2 reference
html
local
li
html
local
a
href title
/wiki/Nernst_equation Nernst equation
html
local
li
html
local
a
href title
/wiki/Curtin%E2%80%93Hammett_principle Curtin–Hammett principle
html
local
li
html
local
ul
html
local
p
html
local
span
class id
mw-headline Composition_of_a_mixture
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=12 Edit section: Composition of a mixture
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
a
href class title
/wiki/ICE_table mw-redirect ICE table
html
local
p
html
local
p
html
local
li
html
local
a
href
#cite_note-15
html
local
sup
id class
cite_ref-15 reference
html
local
a
href
#cite_note-16
html
local
sup
id class
cite_ref-16 reference
html
local
li
html
local
a
href title
/wiki/Mass_balance Mass balance
html
local
a
href title
/wiki/Conservation_of_mass Conservation of mass
html
local
li
html
local
ol
html
local
span
class id
mw-headline Mass-balance_equations
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=13 Edit section: Mass-balance equations
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h3
html
local
sub
html
local
a
href class title
/wiki/Conjugate_base mw-redirect Conjugate base
html
local
sup
html
local
a
href title
/wiki/Hydronium Hydronium
html
local
sup
html
local
a
href title
/wiki/Ethylenediamine Ethylenediamine
html
local
p
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
thinmathspace
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle T_{\mathrm {A} }=\mathrm {[A]+[HA]+[H_{2}A]} \,}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/b4caf4ff0552bd0430f4b305b3b92c05aef15aa2 mwe-math-fallback-image-inline true vertical-align: -0.838ex; width:25.64ex; height:2.843ex; {\displaystyle T_{\mathrm {A} }=\mathrm {[A]+[HA]+[H_{2}A]} \,}
html
local
span
class
mwe-math-element
html
local
dd
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mo
html
local
mn
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mspace
width
thinmathspace
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle T_{\mathrm {H} }=\mathrm {[H]+[HA]+2[H_{2}A]-[OH]} \,}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/094ecf5d3e87ba5a02d744835486f24086804cfc mwe-math-fallback-image-inline true vertical-align: -0.838ex; width:34.487ex; height:2.843ex; {\displaystyle T_{\mathrm {H} }=\mathrm {[H]+[HA]+2[H_{2}A]-[OH]} \,}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
sub
html
local
p
html
local
i
html
local
sub
html
local
sub
html
local
i
html
local
sub
html
local
sup
html
local
i
html
local
sub
html
local
sup
html
local
p
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mi
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mi
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mspace
width
thinmathspace
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle T_{\mathrm {A} }=\mathrm {[A]} +\beta _{1}\mathrm {[A][H]} +\beta _{2}\mathrm {[A][H]} ^{2}\,}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/f6ae376d767bfb698f8d771a8aa374366c647255 mwe-math-fallback-image-inline true vertical-align: -0.838ex; width:32.967ex; height:3.343ex; {\displaystyle T_{\mathrm {A} }=\mathrm {[A]} +\beta _{1}\mathrm {[A][H]} +\beta _{2}\mathrm {[A][H]} ^{2}\,}
html
local
span
class
mwe-math-element
html
local
dd
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mi
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mn
html
local
mi
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mo
stretchy
false
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mspace
width
thinmathspace
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle T_{\mathrm {H} }=\mathrm {[H]} +\beta _{1}\mathrm {[A][H]} +2\beta _{2}\mathrm {[A][H]} ^{2}-K_{w}[\mathrm {H} ]^{-1}\,}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/25502da2d24e51d7cb6c53782a5392673c4b0819 mwe-math-fallback-image-inline true vertical-align: -0.838ex; width:45.721ex; height:3.343ex; {\displaystyle T_{\mathrm {H} }=\mathrm {[H]} +\beta _{1}\mathrm {[A][H]} +2\beta _{2}\mathrm {[A][H]} ^{2}-K_{w}[\mathrm {H} ]^{-1}\,}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mo
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munder
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle T_{\mathrm {A} }=[\mathrm {A} ]+\sum _{i}p_{i}\beta _{i}[\mathrm {A} ]^{p_{i}}[\mathrm {B} ]^{q_{i}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/de4c20306740d1b3f30387f17ac264b500d313b8 mwe-math-fallback-image-inline true vertical-align: -3.005ex; width:28.875ex; height:5.509ex; {\displaystyle T_{\mathrm {A} }=[\mathrm {A} ]+\sum _{i}p_{i}\beta _{i}[\mathrm {A} ]^{p_{i}}[\mathrm {B} ]^{q_{i}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
mi
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mo
html
local
mo
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munder
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
stretchy
false
html
local
mi
mathvariant
normal
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle T_{\mathrm {B} }=[\mathrm {B} ]+\sum _{i}q_{i}\beta _{i}[\mathrm {A} ]^{p_{i}}[\mathrm {B} ]^{q_{i}}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/4c9dea321370bf3d5b01364cfed9dbe3c941ce31 mwe-math-fallback-image-inline true vertical-align: -3.005ex; width:28.576ex; height:5.509ex; {\displaystyle T_{\mathrm {B} }=[\mathrm {B} ]+\sum _{i}q_{i}\beta _{i}[\mathrm {A} ]^{p_{i}}[\mathrm {B} ]^{q_{i}}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
span
class id
mw-headline Polybasic_acids
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=14 Edit section: Polybasic acids
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h4
html
local
img
alt src width height class srcset data-file-width data-file-height
//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Al_hydrolysis.svg/220px-Al_hydrolysis.svg.png 220 145 thumbimage //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Al_hydrolysis.svg/330px-Al_hydrolysis.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Al_hydrolysis.svg/440px-Al_hydrolysis.svg.png 2x 1133 749
html
local
a
href class
/wiki/File:Al_hydrolysis.svg image
html
local
a
href class title
/wiki/File:Al_hydrolysis.svg internal Enlarge
html
local
div
class
magnify
html
local
a
href title
/wiki/Hydrolysis Hydrolysis
html
local
a
href title
/wiki/Aluminium Aluminium
html
local
div
class
thumbcaption
html
local
div
class style
thumb tright thumbinner width:222px;
html
local
a
href title
/wiki/PH PH
html
local
p
html
local
a
href title
/wiki/Aluminium Aluminium
html
local
a
href class title
/wiki/Lewis_acid mw-redirect Lewis acid
html
local
sup
html
local
sub
html
local
a
href
#cite_note-17
html
local
sup
id class
cite_ref-17 reference
html
local
sup
html
local
p
html
local
span
class id
mw-headline Solution_and_precipitation
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=15 Edit section: Solution and precipitation
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h4
html
local
a
href title
/wiki/Precipitation_(chemistry) Precipitation (chemistry)
html
local
sup
html
local
a
href title
/wiki/Aluminium_hydroxide Aluminium hydroxide
html
local
sup
html
local
sup
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
br
html
local
sub
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
span
style
display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left
html
local
span
class
chemf nowrap
html
local
br
html
local
sub
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
span
style
display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left
html
local
sup
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
br
html
local
sub
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
span
style
display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left
html
local
span
class
chemf nowrap
html
local
sub
html
local
a
href title
/wiki/Aluminium_hydroxide Aluminium hydroxide
html
local
sub
html
local
a
href title
/wiki/Lattice_energy Lattice energy
html
local
sub
html
local
a
href class title
/wiki/Le_Ch%C3%A2telier%27s_principle mw-redirect Le Châtelier's principle
html
local
sup
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
br
html
local
sub
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
span
style
display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left
html
local
span
class
chemf nowrap
html
local
p
html
local
a
href class title
/wiki/Hydrophobic mw-redirect Hydrophobic
html
local
a
href title
/wiki/Nickel Nickel
html
local
sup
html
local
a
href title
/wiki/Dimethylglyoxime Dimethylglyoxime
html
local
sub
html
local
a
href title
/wiki/Solvation Solvation
html
local
sub
html
local
p
html
local
span
class id
mw-headline Minimization_of_Gibbs_energy
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=16 Edit section: Minimization of Gibbs energy
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h3
html
local
i
html
local
p
html
local
mi
html
local
mi
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mspace
width
thinmathspace
html
local
mi
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mn
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle dG=\sum _{j=1}^{m}\mu _{j}\,dN_{j}=0}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/97f9cd17aa556265ad968921ad9ad52632af0e44 mwe-math-fallback-image-inline true vertical-align: -3.338ex; width:20.834ex; height:7.176ex; dG=\sum _{j=1}^{m}\mu _{j}\,dN_{j}=0
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \sum _{j=1}^{m}a_{ij}N_{j}=b_{i}^{0}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/4ca1f6c276a7396c9f6ecb4d4f08cfdd17055a00 mwe-math-fallback-image-inline true vertical-align: -3.338ex; width:14.375ex; height:7.176ex; \sum _{j=1}^{m}a_{ij}N_{j}=b_{i}^{0}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
sub
html
local
i
html
local
i
html
local
i
html
local
i
html
local
sup
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
br
html
local
i
html
local
sub
style
font-size:inherit;line-height:inherit;vertical-align:baseline
html
local
span
style
display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left
html
local
i
html
local
i
html
local
i
html
local
sub
html
local
p
html
local
a
href class title
/wiki/Optimization_(mathematics) mw-redirect Optimization (mathematics)
html
local
a
href class title
/w/index.php?title=Constrained_minimisation&action=edit&redlink=1 new Constrained minimisation (page does not exist)
html
local
a
href class title
/wiki/Lagrange_multipliers mw-redirect Lagrange multipliers
html
local
a
href class title
/w/index.php?title=Undetermined_multipliers&action=edit&redlink=1 new Undetermined multipliers (page does not exist)
html
local
p
html
local
p
html
local
mi
class mathvariant
MJX-tex-caligraphic script
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mi
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mrow
html
local
mo
html
local
mrow
html
local
mo
html
local
mn
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle {\mathcal {G}}=G+\sum _{i=1}^{k}\lambda _{i}\left(\sum _{j=1}^{m}a_{ij}N_{j}-b_{i}^{0}\right)=0}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/271296211e841a65d4ae2de76aea7ecfa58892a7 mwe-math-fallback-image-inline true vertical-align: -3.338ex; width:37.501ex; height:7.676ex; {\mathcal {G}}=G+\sum _{i=1}^{k}\lambda _{i}\left(\sum _{j=1}^{m}a_{ij}N_{j}-b_{i}^{0}\right)=0
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
sub
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
i
html
local
a
href class title
/wiki/Multivariate_calculus mw-redirect Multivariate calculus
html
local
p
html
local
mn
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
class mathvariant
MJX-tex-caligraphic script
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
html
local
mi
mathvariant
normal
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle 0={\frac {\partial {\mathcal {G}}}{\partial N_{j}}}=\mu _{j}+\sum _{i=1}^{k}\lambda _{i}a_{ij}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/a9cb0e5646a70132b2bf8230a9bacc2f2f68c501 mwe-math-fallback-image-inline true vertical-align: -3.005ex; width:26.045ex; height:7.343ex; {\displaystyle 0={\frac {\partial {\mathcal {G}}}{\partial N_{j}}}=\mu _{j}+\sum _{i=1}^{k}\lambda _{i}a_{ij}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
mn
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
class mathvariant
MJX-tex-caligraphic script
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mrow
html
local
mi
mathvariant
normal
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
html
local
mfrac
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle 0={\frac {\partial {\mathcal {G}}}{\partial \lambda _{i}}}=\sum _{j=1}^{m}a_{ij}N_{j}-b_{i}^{0}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/a72c85da6db39dacc6ced766eb60977fe3b9fa89 mwe-math-fallback-image-inline true vertical-align: -3.338ex; width:25.786ex; height:7.176ex; {\displaystyle 0={\frac {\partial {\mathcal {G}}}{\partial \lambda _{i}}}=\sum _{j=1}^{m}a_{ij}N_{j}-b_{i}^{0}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
a
href class title
/wiki/Lagrange_multipliers mw-redirect Lagrange multipliers
html
local
i
html
local
i
html
local
i
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
i
html
local
sub
html
local
i
html
local
a
href title
/wiki/Thermodynamic_databases_for_pure_substances Thermodynamic databases for pure substances
html
local
p
html
local
i
html
local
a
href
#cite_note-nasa-14
html
local
sup
id class
cite_ref-nasa_14-1 reference
html
local
a
href
#cite_note-K&K-18
html
local
sup
id class
cite_ref-K&K_18-0 reference
html
local
p
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mn
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \sum _{j=0}^{m}\nu _{j}R_{j}=0}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/ba3811d74344d946f77509d10b54228fde7aadb5 mwe-math-fallback-image-inline true vertical-align: -3.338ex; width:12.735ex; height:7.176ex; {\displaystyle \sum _{j=0}^{m}\nu _{j}R_{j}=0}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
sub
html
local
i
html
local
sub
html
local
i
html
local
i
html
local
p
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mn
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \sum _{j=1}^{m}a_{ij}\nu _{j}=0}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/e81e0c7b05933b577951c9f21a93976c0cd6507c mwe-math-fallback-image-inline true vertical-align: -3.338ex; width:12.768ex; height:7.176ex; {\displaystyle \sum _{j=1}^{m}a_{ij}\nu _{j}=0}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
sub
html
local
p
html
local
mn
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle 0=\sum _{j=1}^{m}\nu _{j}\mu _{j}+\sum _{j=1}^{m}\sum _{i=1}^{k}\nu _{j}\lambda _{i}a_{ij}=\sum _{j=1}^{m}\nu _{j}\mu _{j}}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/3350eae241164b8517a096e19d0827637404a6e9 mwe-math-fallback-image-inline true vertical-align: -3.338ex; width:40.827ex; height:7.676ex; {\displaystyle 0=\sum _{j=1}^{m}\nu _{j}\mu _{j}+\sum _{j=1}^{m}\sum _{i=1}^{k}\nu _{j}\lambda _{i}a_{ij}=\sum _{j=1}^{m}\nu _{j}\mu _{j}}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
mi
mathvariant
normal
html
local
mi
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msubsup
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
stretchy
false
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
fence stretchy
false false
html
local
mo
stretchy
false
html
local
mo
stretchy
false
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
html
local
mo
html
local
mi
html
local
mo
html
local
mn
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
munderover
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
fence stretchy
false false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mrow
html
local
mo
html
local
mrow
html
local
mo
html
local
mi
mathvariant
normal
html
local
mi
html
local
mo
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msup
html
local
mo
html
local
mi
html
local
mi
html
local
mi
html
local
mo
html
local
mo
stretchy
false
html
local
mi
html
local
mi
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
msub
html
local
mo
stretchy
false
html
local
mstyle
displaystyle scriptlevel
true 0
html
local
mrow
class
MJX-TeXAtom-ORD
html
local
annotation
encoding
application/x-tex
html
local
semantics
html
local
math
xmlns alttext
http://www.w3.org/1998/Math/MathML {\displaystyle \Delta G=\sum _{j=1}^{m}\nu _{j}\mu _{j}=\sum _{j=1}^{m}\nu _{j}(\mu _{j}^{\ominus }+RT\ln(\{R_{j}\}))=\Delta G^{\ominus }+RT\ln \left(\prod _{j=1}^{m}\{R_{j}\}^{\nu _{j}}\right)=\Delta G^{\ominus }+RT\ln(Q_{r})}
html
local
span
class style
mwe-math-mathml-inline mwe-math-mathml-a11y display: none;
html
local
img
src class aria-hidden style alt
https://wikimedia.org/api/rest_v1/media/math/render/svg/e19f7cce6f147ff460c7404f0889dabbd7f5208b mwe-math-fallback-image-inline true vertical-align: -3.338ex; width:95.876ex; height:7.676ex; {\displaystyle \Delta G=\sum _{j=1}^{m}\nu _{j}\mu _{j}=\sum _{j=1}^{m}\nu _{j}(\mu _{j}^{\ominus }+RT\ln(\{R_{j}\}))=\Delta G^{\ominus }+RT\ln \left(\prod _{j=1}^{m}\{R_{j}\}^{\nu _{j}}\right)=\Delta G^{\ominus }+RT\ln(Q_{r})}
html
local
span
class
mwe-math-element
html
local
dd
html
local
dl
html
local
p
html
local
span
class id
mw-headline See_also
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=17 Edit section: See also
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
a
href title
/wiki/Acidosis Acidosis
html
local
li
html
local
a
href title
/wiki/Alkalosis Alkalosis
html
local
li
html
local
a
href class title
/wiki/Arterial_blood_gas mw-redirect Arterial blood gas
html
local
li
html
local
a
href title
/wiki/Benesi%E2%80%93Hildebrand_method Benesi–Hildebrand method
html
local
li
html
local
a
href title
/wiki/Determination_of_equilibrium_constants Determination of equilibrium constants
html
local
li
html
local
a
href title
/wiki/Equilibrium_constant Equilibrium constant
html
local
li
html
local
a
href title
/wiki/Henderson%E2%80%93Hasselbalch_equation Henderson–Hasselbalch equation
html
local
li
html
local
a
href title
/wiki/Michaelis%E2%80%93Menten_kinetics Michaelis–Menten kinetics
html
local
li
html
local
sub
html
local
a
href title
/wiki/PCO2 PCO2
html
local
li
html
local
a
href title
/wiki/PH PH
html
local
li
html
local
i
html
local
sub
html
local
a
href class title
/wiki/PKa mw-redirect PKa
html
local
li
html
local
a
href title
/wiki/Standard_electrode_potential Standard electrode potential
html
local
li
html
local
a
href title
/wiki/Steady_state_(chemistry) Steady state (chemistry)
html
local
li
html
local
a
href title
/wiki/Thermodynamic_databases_for_pure_substances Thermodynamic databases for pure substances
html
local
li
html
local
a
href title
/wiki/Non-random_two-liquid_model Non-random two-liquid model
html
local
li
html
local
a
href title
/wiki/UNIQUAC UNIQUAC
html
local
li
html
local
ul
html
local
span
class id
mw-headline References
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=18 Edit section: References
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
span
class
cite-accessibility-label
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-Atkins_1-0
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-Atkins_1-1
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-Atkins_1-2
html
local
span
class
mw-cite-backlink
html
local
i
html
local
a
href title
/wiki/International_Standard_Book_Number International Standard Book Number
html
local
a
href title
/wiki/Special:BookSources/0-7167-8759-8 Special:BookSources/0-7167-8759-8
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Atkins%27+Physical+Chemistry&rft.pages=200-202&rft.edition=8th&rft.pub=W.+H.+Freeman&rft.date=2006&rft.isbn=0-7167-8759-8&rft.aulast=Atkins&rft.aufirst=Peter&rft.au=De+Paula%2C+Julio&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-Atkins-1
html
local
span
class
cite-accessibility-label
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-aj_2-0
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-aj_2-1
html
local
span
class
mw-cite-backlink
html
local
i
html
local
a
href title
/wiki/International_Standard_Book_Number International Standard Book Number
html
local
a
href title
/wiki/Special:BookSources/0-7167-9903-0 Special:BookSources/0-7167-9903-0
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemical+Principles%3A+The+Quest+for+Insight&rft.edition=2nd&rft.isbn=0-7167-9903-0&rft.aulast=Atkins&rft.aufirst=Peter+W.&rft.au=Jones%2C+Loretta&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-aj-2
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-3
html
local
b
html
local
span
class
mw-cite-backlink
html
local
a
href title
/wiki/International_Union_of_Pure_and_Applied_Chemistry International Union of Pure and Applied Chemistry
html
local
a
href class title
/wiki/Compendium_of_Chemical_Terminology mw-redirect Compendium of Chemical Terminology
html
local
i
html
local
a
rel class href
nofollow external text http://goldbook.iupac.org/C01023.html
html
local
span
class
reference-text
html
local
li
id
cite_note-3
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-4
html
local
b
html
local
span
class
mw-cite-backlink
html
local
i
html
local
a
rel class href
nofollow external text https://books.google.com/books?id=W-sTAAAAQAAJ&pg=PP7#v=onepage&q&f=false
html
local
i
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Essai+de+statique+chimique&rft.place=Paris%2C+France&rft.pub=Firmin+Didot&rft.date=1803&rft.aulast=Berthollet&rft.aufirst=C.L.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DW-sTAAAAQAAJ%26pg%3DPP7%23v%3Donepage%26q%26f%3Dfalse&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
sub
html
local
sub
html
local
sub
html
local
sub
html
local
i
html
local
span
class
reference-text
html
local
li
id
cite_note-4
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-5
html
local
b
html
local
span
class
mw-cite-backlink
html
local
a
href title
/wiki/Jacobus_Henricus_van_%27t_Hoff Jacobus Henricus van 't Hoff
html
local
i
html
local
a
rel class href
nofollow external text https://archive.org/stream/etudesdedynamiqu00hoff#page/4/mode/2up
html
local
i
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%C3%89tudes+de+Dynamique+Chemique&rft.place=Amsterdam%2C+Netherlands&rft.pages=4-5&rft.pub=Frederik+Muller+%26+Co.&rft.date=1884&rft.aulast=van+%27t+Hoff&rft.aufirst=J.H.&rft_id=https%3A%2F%2Farchive.org%2Fstream%2Fetudesdedynamiqu00hoff%23page%2F4%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
i
html
local
span
class
reference-text
html
local
sub
html
local
sub
html
local
dd
html
local
dl
html
local
li
id
cite_note-5
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-6
html
local
b
html
local
span
class
mw-cite-backlink
html
local
i
html
local
a
href title
/wiki/International_Standard_Book_Number International Standard Book Number
html
local
a
href title
/wiki/Special:BookSources/0-471-21517-1 Special:BookSources/0-471-21517-1
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemistry%3A+Matter+and+Its+Changes&rft.edition=4th&rft.pub=Fred+Senese&rft.isbn=0-471-21517-1&rft.aulast=Brady&rft.aufirst=James+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-6
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-7
html
local
b
html
local
span
class
mw-cite-backlink
html
local
i
html
local
b
html
local
a
href title
/wiki/Bibcode Bibcode
html
local
a
rel class href
nofollow external text http://adsabs.harvard.edu/abs/1999JChEd..76.1391S
html
local
a
href title
/wiki/Digital_object_identifier Digital object identifier
html
local
a
rel class href
nofollow external text //doi.org/10.1021%2Fed076p1391
html
local
cite
class
citation journal
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Chemical+Education&rft.atitle=Why+Equilibrium%3F+Understanding+Entropy+of+Mixing&rft.volume=76&rft.issue=10&rft.pages=1391&rft.date=1999&rft_id=info%3Adoi%2F10.1021%2Fed076p1391&rft_id=info%3Abibcode%2F1999JChEd..76.1391S&rft.aulast=Schultz&rft.aufirst=Mary+Jane&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-7
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-8
html
local
b
html
local
span
class
mw-cite-backlink
html
local
i
html
local
b
html
local
a
href title
/wiki/Bibcode Bibcode
html
local
a
rel class href
nofollow external text http://adsabs.harvard.edu/abs/1990JChEd..67Q.203C
html
local
a
href title
/wiki/Digital_object_identifier Digital object identifier
html
local
a
rel class href
nofollow external text //doi.org/10.1021%2Fed067p203
html
local
cite
class
citation journal
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Chemical+Education&rft.atitle=A+mathematical+verification+of+the+second+law+of+thermodynamics+from+the+entropy+of+mixing&rft.volume=67&rft.issue=3&rft.pages=203&rft.date=1990&rft_id=info%3Adoi%2F10.1021%2Fed067p203&rft_id=info%3Abibcode%2F1990JChEd..67Q.203C&rft.aulast=Clugston&rft.aufirst=Michael+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-8
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-9
html
local
b
html
local
span
class
mw-cite-backlink
html
local
i
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ion+Association&rft.pub=Butterworths&rft.date=1962&rft.aulast=Davies&rft.aufirst=C.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-9
html
local
span
class
cite-accessibility-label
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-davies_10-0
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-davies_10-1
html
local
span
class
mw-cite-backlink
html
local
a
rel class href
nofollow external text http://www.nea.fr/html/dbtdb/guidelines/tdb2.pdf
html
local
span
style
font-size:85%;
html
local
cite
class
citation web
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Guidelines+for+the+extrapolation+to+zero+ionic+strength&rft.aulast=Grenthe&rft.aufirst=I.&rft.au=Wanner%2C+H.&rft_id=http%3A%2F%2Fwww.nea.fr%2Fhtml%2Fdbtdb%2Fguidelines%2Ftdb2.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-davies-10
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-11
html
local
b
html
local
span
class
mw-cite-backlink
html
local
i
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Determination+of+Stability+Constants&rft.pub=McGraw-Hill&rft.date=1961&rft.aulast=Rossotti&rft.aufirst=F.+J.+C.&rft.au=Rossotti%2C+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-11
html
local
span
class
cite-accessibility-label
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-CEM_12-0
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-CEM_12-1
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-CEM_12-2
html
local
span
class
mw-cite-backlink
html
local
i
html
local
a
href title
/wiki/International_Standard_Book_Number International Standard Book Number
html
local
a
href title
/wiki/Special:BookSources/0-89925-457-8 Special:BookSources/0-89925-457-8
html
local
cite
class
citation encyclopaedia
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Concise+Encyclopedia+Chemistry&rft.date=1994&rft.isbn=0-89925-457-8&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-CEM-12
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-13
html
local
b
html
local
span
class
mw-cite-backlink
html
local
i
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemistry+of+Complex+Equilibria&rft.place=Budapest&rft.edition=2nd&rft.pub=Akad%C3%A9miai+Kaid%C3%B3&rft.date=1990&rft.aulast=Beck&rft.aufirst=M.+T.&rft.au=Nagyp%C3%A1l%2C+I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-13
html
local
span
class
cite-accessibility-label
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-nasa_14-0
html
local
b
html
local
i
html
local
sup
html
local
a
href
#cite_ref-nasa_14-1
html
local
span
class
mw-cite-backlink
html
local
a
rel class href
nofollow external text https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19950013764_1995113764.pdf
html
local
span
style
font-size:85%;
html
local
cite
class
citation web
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Computer+Program+for+Calculation+of+Complex+Chemical+Equilibrium+Compositions+and+Applications&rft.series=NASA+Reference+publication+1311&rft.pub=NASA&rft.date=1994&rft_id=https%3A%2F%2Fntrs.nasa.gov%2Farchive%2Fnasa%2Fcasi.ntrs.nasa.gov%2F19950013764_1995113764.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-nasa-14
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-15
html
local
b
html
local
span
class
mw-cite-backlink
html
local
i
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemical+Reaction+Equilibrium+Analysis%3A+Theory+and+Algorithms&rft.place=Malabar%2C+FL&rft.edition=Reprinted&rft.pub=Krieger+Publishing&rft.date=1991&rft.aulast=Smith&rft.aufirst=W.+R.&rft.au=Missen%2C+R.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-15
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-16
html
local
b
html
local
span
class
mw-cite-backlink
html
local
a
rel class href
nofollow external text http://www.mathtrek.com
html
local
cite
class
citation web
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Mathtrek+Systems&rft_id=http%3A%2F%2Fwww.mathtrek.com&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-16
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-17
html
local
b
html
local
span
class
mw-cite-backlink
html
local
a
rel class href
nofollow external text http://www.hyperquad.co.uk/hyss.htm
html
local
span
class
reference-text
html
local
li
id
cite_note-17
html
local
span
class
cite-accessibility-label
html
local
a
href
#cite_ref-K&K_18-0
html
local
b
html
local
span
class
mw-cite-backlink
html
local
i
html
local
a
href title
/wiki/International_Standard_Book_Number International Standard Book Number
html
local
a
href title
/wiki/Special:BookSources/0-7167-1088-9 Special:BookSources/0-7167-1088-9
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=9&rft.btitle=Thermal+Physics&rft.edition=2&rft.pub=W.+H.+Freeman+Company&rft.date=1980&rft.isbn=0-7167-1088-9&rft.au=C.+Kittel%2C+H.+Kroemer&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
span
class
reference-text
html
local
li
id
cite_note-K&K-18
html
local
ol
class
references
html
local
div
class style
reflist columns references-column-width -moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;
html
local
span
class id
mw-headline Further_reading
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=edit&section=19 Edit section: Further reading
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
a
href class title
/wiki/Wikipedia:LIBRARY mw-redirect Wikipedia:LIBRARY
html
local
br
html
local
b
html
local
hr
html
local
td
style
padding-top:0.4em;line-height:1.2em
html
local
tr
html
local
a
class href
external text //tools.wmflabs.org/ftl/cgi-bin/ftl?st=wp&su=Chemical+equilibrium
html
local
li
html
local
ul
html
local
td
class style
plainlist padding:0 0.1em 0.4em;text-align:left;
html
local
tr
html
local
tbody
html
local
table
class style
vertical-navbox nowraplinks infobox float:right;clear:right;width:auto;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%
html
local
i
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Computation+of+Chemical+Equilibria&rft.pub=Cambridge+University+Press&rft.date=1970&rft.aulast=Van+Zeggeren&rft.aufirst=F.&rft.au=Storey%2C+S.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
li
html
local
i
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+Methods+for+the+Determination+of+Formation+Constants&rft.pub=Plenum+Press&rft.date=1985&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
li
html
local
i
html
local
cite
class
citation book
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Determination+and+Use+of+Stability+Constants&rft.pub=Wiley-VCH&rft.date=1992&rft.aulast=Martell&rft.aufirst=A.+E.&rft.au=Motekaitis%2C+R.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
li
html
local
i
html
local
span
style
font-size:85%;
html
local
code
style
color:inherit; border:inherit; padding:inherit;
html
local
code
style
color:inherit; border:inherit; padding:inherit;
html
local
a
href title
/wiki/Help:CS1_errors#format_missing_url Help:CS1 errors
html
local
span
style class
display:none;font-size:100% error citation-comment
html
local
cite
class
citation audio-visual
html
local
span
style
display:none;
html
local
span
title class
ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Stability+Constants%3A+Determination+and+Uses&rft.place=Leeds&rft.pub=Protonic+Software&rft.date=2004&rft.aulast=Gans&rft.aufirst=P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+equilibrium Z3988
html
local
li
html
local
ul
html
local
a
id href
collapseButton0 #
html
local
span
class
collapseButton
html
local
abbr
title style
View this template ;;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none;
html
local
a
href title
/wiki/Template:Chemical_equilibria Template:Chemical equilibria
html
local
li
class
nv-view
html
local
abbr
title style
Discuss this template ;;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none;
html
local
a
href title
/wiki/Template_talk:Chemical_equilibria Template talk:Chemical equilibria
html
local
li
class
nv-talk
html
local
abbr
title style
Edit this template ;;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none;
html
local
a
class href
external text //en.wikipedia.org/w/index.php?title=Template:Chemical_equilibria&action=edit
html
local
li
class
nv-edit
html
local
ul
html
local
div
class
plainlinks hlist navbar mini
html
local
a
class
mw-selflink selflink
html
local
div
id style
Chemical_equilibria font-size:114%;margin:0 4em
html
local
th
scope class colspan
col navbox-title 2
html
local
tr
html
local
th
scope class style
row navbox-group width:1%
html
local
a
href title
/wiki/Acid_dissociation_constant Acid dissociation constant
html
local
li
html
local
a
href title
/wiki/Binding_constant Binding constant
html
local
li
html
local
a
href title
/wiki/Binding_selectivity Binding selectivity
html
local
li
html
local
a
href title
/wiki/Buffer_solution Buffer solution
html
local
li
html
local
a
class
mw-selflink selflink
html
local
li
html
local
a
href title
/wiki/Chemical_stability Chemical stability
html
local
li
html
local
a
href title
/wiki/Chelation Chelation
html
local
li
html
local
a
href title
/wiki/Determination_of_equilibrium_constants Determination of equilibrium constants
html
local
li
html
local
a
href title
/wiki/Dissociation_constant Dissociation constant
html
local
li
html
local
a
href title
/wiki/Partition_coefficient Partition coefficient
html
local
li
html
local
a
href title
/wiki/Dynamic_equilibrium Dynamic equilibrium
html
local
li
html
local
a
href title
/wiki/Equilibrium_chemistry Equilibrium chemistry
html
local
li
html
local
a
href title
/wiki/Equilibrium_constant Equilibrium constant
html
local
li
html
local
a
href title
/wiki/Equilibrium_unfolding Equilibrium unfolding
html
local
li
html
local
a
href class title
/wiki/Equilibrium_stage mw-redirect Equilibrium stage
html
local
li
html
local
a
href title
/wiki/Hammett_acidity_function Hammett acidity function
html
local
li
html
local
a
href title
/wiki/Henry%27s_law Henry's law
html
local
li
html
local
a
href title
/wiki/Liquid%E2%80%93liquid_extraction Liquid–liquid extraction
html
local
li
html
local
a
href title
/wiki/Macrocycle Macrocycle
html
local
li
html
local
a
href title
/wiki/Phase_diagram Phase diagram
html
local
li
html
local
a
href title
/wiki/Predominance_diagram Predominance diagram
html
local
li
html
local
a
href title
/wiki/Phase_rule Phase rule
html
local
li
html
local
a
href title
/wiki/Reaction_quotient Reaction quotient
html
local
li
html
local
a
href title
/wiki/Self-ionization_of_water Self-ionization of water
html
local
li
html
local
a
href title
/wiki/Solubility_equilibrium Solubility equilibrium
html
local
li
html
local
a
href title
/wiki/Stability_constants_of_complexes Stability constants of complexes
html
local
li
html
local
a
href title
/wiki/Thermodynamic_equilibrium Thermodynamic equilibrium
html
local
li
html
local
a
href title
/wiki/Thermodynamic_activity Thermodynamic activity
html
local
li
html
local
a
href title
/wiki/Vapor%E2%80%93liquid_equilibrium Vapor–liquid equilibrium
html
local
li
html
local
ul
html
local
div
style
padding:0em 0.25em
html
local
td
class style
navbox-list navbox-odd hlist text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px
html
local
tr
html
local
tbody
html
local
table
class style id
nowraplinks collapsible autocollapse navbox-inner border-spacing:0;background:transparent;color:inherit collapsibleTable0
html
local
div
role class aria-labelledby style
navigation navbox Chemical_equilibria padding:3px
html
local
div
class
mw-parser-output
html
local
img
src alt title width height style
//en.wikipedia.org/wiki/Special:CentralAutoLogin/start?type=1x1 1 1 border: none; position: absolute;
html
local
noscript
html
local
div
id lang dir class
mw-content-text en ltr mw-content-ltr
html
local
a
dir href
ltr https://en.wikipedia.org/w/index.php?title=Chemical_equilibrium&oldid=837361611
html
local
div
class
printfooter
html
local
a
href title
/wiki/Help:Category Help:Category
html
local
a
href title
/wiki/Category:Equilibrium_chemistry Category:Equilibrium chemistry
html
local
li
html
local
a
href title
/wiki/Category:Analytical_chemistry Category:Analytical chemistry
html
local
li
html
local
a
href title
/wiki/Category:Physical_chemistry Category:Physical chemistry
html
local
li
html
local
ul
html
local
div
id class
mw-normal-catlinks mw-normal-catlinks
html
local
a
href title
/wiki/Category:CS1_French-language_sources_(fr) Category:CS1 French-language sources (fr)
html
local
li
html
local
a
href title
/wiki/Category:Articles_needing_additional_references_from_March_2009 Category:Articles needing additional references from March 2009
html
local
li
html
local
a
href title
/wiki/Category:All_articles_needing_additional_references Category:All articles needing additional references
html
local
li
html
local
a
href title
/wiki/Category:All_articles_with_unsourced_statements Category:All articles with unsourced statements
html
local
li
html
local
a
href title
/wiki/Category:Articles_with_unsourced_statements_from_July_2013 Category:Articles with unsourced statements from July 2013
html
local
li
html
local
a
href title
/wiki/Category:Pages_using_citations_with_format_and_no_URL Category:Pages using citations with format and no URL
html
local
li
html
local
ul
html
local
div
id class
mw-hidden-catlinks mw-hidden-catlinks mw-hidden-cats-hidden
html
local
div
id class data-mw
catlinks catlinks interface
html
local
div
class
visualClear
html
local
div
id class
bodyContent mw-body-content
html
local
div
id class role
content mw-body main
html
local
h2
html
local
h3
id
p-personal-label
html
local
li
id
pt-anonuserpage
html
local
a
href title accesskey
/wiki/Special:MyTalk Discussion about edits from this IP address [ctrl-alt-n] n
html
local
li
id
pt-anontalk
html
local
a
href title accesskey
/wiki/Special:MyContributions A list of edits made from this IP address [ctrl-alt-y] y
html
local
li
id
pt-anoncontribs
html
local
a
href title
/w/index.php?title=Special:CreateAccount&returnto=Chemical+equilibrium You are encouraged to create an account and log in; however, it is not mandatory
html
local
li
id
pt-createaccount
html
local
a
href title accesskey
/w/index.php?title=Special:UserLogin&returnto=Chemical+equilibrium You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o] o
html
local
li
id
pt-login
html
local
ul
html
local
div
id role class aria-labelledby
p-personal navigation p-personal-label
html
local
h3
id
p-namespaces-label
html
local
a
href title accesskey
/wiki/Chemical_equilibrium View the content page [ctrl-alt-c] c
html
local
span
html
local
li
id class
ca-nstab-main selected
html
local
a
href rel title accesskey
/wiki/Talk:Chemical_equilibrium discussion Discussion about the content page [ctrl-alt-t] t
html
local
span
html
local
li
id
ca-talk
html
local
ul
html
local
div
id role class aria-labelledby
p-namespaces navigation vectorTabs p-namespaces-label
html
local
input
type class aria-labelledby
checkbox vectorMenuCheckbox p-variants-label
html
local
span
html
local
h3
id
p-variants-label
html
local
ul
html
local
div
class
menu
html
local
div
id role class aria-labelledby
p-variants navigation vectorMenu emptyPortlet p-variants-label
html
local
div
id
left-navigation
html
local
h3
id
p-views-label
html
local
a
href
/wiki/Chemical_equilibrium
html
local
span
html
local
li
id class
ca-view collapsible selected
html
local
a
href title accesskey
/w/index.php?title=Chemical_equilibrium&action=edit Edit this page [ctrl-alt-e] e
html
local
span
html
local
li
id class
ca-edit collapsible
html
local
a
href title accesskey
/w/index.php?title=Chemical_equilibrium&action=history Past revisions of this page [ctrl-alt-h] h
html
local
span
html
local
li
id class
ca-history collapsible
html
local
ul
html
local
div
id role class aria-labelledby
p-views navigation vectorTabs p-views-label
html
local
input
type class aria-labelledby
checkbox vectorMenuCheckbox p-cactions-label
html
local
span
html
local
h3
id
p-cactions-label
html
local
ul
html
local
div
class
menu
html
local
div
id role class aria-labelledby
p-cactions navigation vectorMenu emptyPortlet p-cactions-label
html
local
label
for
searchInput
html
local
h3
html
local
div
id role
p-search search
html
local
div
id
right-navigation
html
local
div
id
mw-head
html
local
a
class href title
mw-wiki-logo /wiki/Main_Page Visit the main page
html
local
div
id role
p-logo banner
html
local
h3
id
p-navigation-label
html
local
a
href title accesskey
/wiki/Main_Page Visit the main page [ctrl-alt-z] z
html
local
li
id
n-mainpage-description
html
local
a
href title
/wiki/Portal:Contents Guides to browsing Wikipedia
html
local
li
id
n-contents
html
local
a
href title
/wiki/Portal:Featured_content Featured content – the best of Wikipedia
html
local
li
id
n-featuredcontent
html
local
a
href title
/wiki/Portal:Current_events Find background information on current events
html
local
li
id
n-currentevents
html
local
a
href title accesskey
/wiki/Special:Random Load a random article [ctrl-alt-x] x
html
local
li
id
n-randompage
html
local
a
href title
https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en Support us
html
local
li
id
n-sitesupport
html
local
a
href title
//shop.wikimedia.org Visit the Wikipedia store
html
local
li
id
n-shoplink
html
local
ul
html
local
div
class
body
html
local
div
class role id aria-labelledby
portal navigation p-navigation p-navigation-label
html
local
h3
id
p-interaction-label
html
local
a
href title
/wiki/Help:Contents Guidance on how to use and edit Wikipedia
html
local
li
id
n-help
html
local
a
href title
/wiki/Wikipedia:About Find out about Wikipedia
html
local
li
id
n-aboutsite
html
local
a
href title
/wiki/Wikipedia:Community_portal About the project, what you can do, where to find things
html
local
li
id
n-portal
html
local
a
href title accesskey
/wiki/Special:RecentChanges A list of recent changes in the wiki [ctrl-alt-r] r
html
local
li
id
n-recentchanges
html
local
a
href title
//en.wikipedia.org/wiki/Wikipedia:Contact_us How to contact Wikipedia
html
local
li
id
n-contactpage
html
local
ul
html
local
div
class
body
html
local
div
class role id aria-labelledby
portal navigation p-interaction p-interaction-label
html
local
h3
id
p-tb-label
html
local
a
href title accesskey
/wiki/Special:WhatLinksHere/Chemical_equilibrium List of all English Wikipedia pages containing links to this page [ctrl-alt-j] j
html
local
li
id
t-whatlinkshere
html
local
a
href rel title accesskey
/wiki/Special:RecentChangesLinked/Chemical_equilibrium nofollow Recent changes in pages linked from this page [ctrl-alt-k] k
html
local
li
id
t-recentchangeslinked
html
local
a
href title accesskey
/wiki/Wikipedia:File_Upload_Wizard Upload files [ctrl-alt-u] u
html
local
li
id
t-upload
html
local
a
href title accesskey
/wiki/Special:SpecialPages A list of all special pages [ctrl-alt-q] q
html
local
li
id
t-specialpages
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&oldid=837361611 Permanent link to this revision of the page
html
local
li
id
t-permalink
html
local
a
href title
/w/index.php?title=Chemical_equilibrium&action=info More information about this page
html
local
li
id
t-info
html
local
a
href title accesskey
https://www.wikidata.org/wiki/Special:EntityPage/Q189520 Link to connected data repository item [ctrl-alt-g] g
html
local
li
id
t-wikibase
html
local
a
href title
/w/index.php?title=Special:CiteThisPage&page=Chemical_equilibrium&id=837361611 Information on how to cite this page
html
local
li
id
t-cite
html
local
ul
html
local
div
class
body
html
local
div
class role id aria-labelledby
portal navigation p-tb p-tb-label
html
local
h3
id
p-coll-print_export-label
html
local
a
href
/w/index.php?title=Special:Book&bookcmd=book_creator&referer=Chemical+equilibrium
html
local
li
id
coll-create_a_book
html
local
a
href
/w/index.php?title=Special:ElectronPdf&page=Chemical+equilibrium&action=show-download-screen
html
local
li
id
coll-download-as-rdf2latex
html
local
a
href title accesskey
/w/index.php?title=Chemical_equilibrium&printable=yes Printable version of this page [ctrl-alt-p] p
html
local
li
id
t-print
html
local
ul
html
local
div
class
body
html
local
div
class role id aria-labelledby
portal navigation p-coll-print_export p-coll-print_export-label
html
local
h3
id
p-wikibase-otherprojects-label
html
local
a
href hreflang
https://commons.wikimedia.org/wiki/Category:Chemical_equilibria en
html
local
li
class
wb-otherproject-link wb-otherproject-commons
html
local
a
href hreflang
https://en.wikibooks.org/wiki/General_Chemistry/Chemical_Equilibria/Equilibrium en
html
local
li
class
wb-otherproject-link wb-otherproject-wikibooks
html
local
ul
html
local
div
class
body
html
local
div
class role id aria-labelledby
portal navigation p-wikibase-otherprojects p-wikibase-otherprojects-label
html
local
button
class title
uls-settings-trigger Language settings
html
local
h3
id
p-lang-label
html
local
a
href title lang hreflang class
https://af.wikipedia.org/wiki/Chemiese_ewewig Chemiese ewewig – Afrikaans af af interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-af display: none;
html
local
a
href title lang hreflang class
https://ar.wikipedia.org/wiki/%D8%AA%D9%88%D8%A7%D8%B2%D9%86_%D9%83%D9%8A%D9%85%D9%8A%D8%A7%D8%A6%D9%8A توازن كيميائي – Arabic ar ar interlanguage-link-target
html
local
li
class
interlanguage-link interwiki-ar
html
local
a
href title lang hreflang class
https://ast.wikipedia.org/wiki/Equilibriu_qu%C3%ADmicu Equilibriu químicu – Asturian ast ast interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-ast display: none;
html
local
a
href title lang hreflang class
https://bn.wikipedia.org/wiki/%E0%A6%B0%E0%A6%BE%E0%A6%B8%E0%A6%BE%E0%A6%AF%E0%A6%BC%E0%A6%A8%E0%A6%BF%E0%A6%95_%E0%A6%B8%E0%A6%BE%E0%A6%AE%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AC%E0%A6%B8%E0%A7%8D%E0%A6%A5%E0%A6%BE রাসায়নিক সাম্যাবস্থা – Bangla bn bn interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-bn display: none;
html
local
a
href title lang hreflang class
https://zh-min-nan.wikipedia.org/wiki/H%C3%B2a-ha%CC%8Dk_p%C3%AAng-h%C3%AAng Hòa-ha̍k pêng-hêng – Chinese (Min Nan) zh-min-nan zh-min-nan interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-zh-min-nan display: none;
html
local
a
href title lang hreflang class
https://be.wikipedia.org/wiki/%D0%A5%D1%96%D0%BC%D1%96%D1%87%D0%BD%D0%B0%D1%8F_%D1%80%D0%B0%D1%9E%D0%BD%D0%B0%D0%B2%D0%B0%D0%B3%D0%B0 Хімічная раўнавага – Belarusian be be interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-be display: none;
html
local
a
href title lang hreflang class
https://bg.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BC%D0%B8%D1%87%D0%BD%D0%BE_%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%D0%B2%D0%B5%D1%81%D0%B8%D0%B5 Химично равновесие – Bulgarian bg bg interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-bg display: none;
html
local
a
href title lang hreflang class
https://bs.wikipedia.org/wiki/Hemijska_ravnote%C5%BEa Hemijska ravnoteža – Bosnian bs bs interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-bs display: none;
html
local
a
href title lang hreflang class
https://ca.wikipedia.org/wiki/Equilibri_qu%C3%ADmic Equilibri químic – Catalan ca ca interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-ca display: none;
html
local
a
href title lang hreflang class
https://cs.wikipedia.org/wiki/Chemick%C3%A1_rovnov%C3%A1ha Chemická rovnováha – Czech cs cs interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-cs display: none;
html
local
a
href title lang hreflang class
https://da.wikipedia.org/wiki/Kemisk_ligev%C3%A6gt Kemisk ligevægt – Danish da da interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-da display: none;
html
local
a
href title lang hreflang class
https://de.wikipedia.org/wiki/Chemisches_Gleichgewicht Chemisches Gleichgewicht – German de de interlanguage-link-target
html
local
li
class
interlanguage-link interwiki-de
html
local
a
href title lang hreflang class
https://et.wikipedia.org/wiki/Keemiline_tasakaal Keemiline tasakaal – Estonian et et interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-et display: none;
html
local
a
href title lang hreflang class
https://es.wikipedia.org/wiki/Equilibrio_qu%C3%ADmico Equilibrio químico – Spanish es es interlanguage-link-target
html
local
li
class
interlanguage-link interwiki-es
html
local
a
href title lang hreflang class
https://eo.wikipedia.org/wiki/Kemia_ekvilibro Kemia ekvilibro – Esperanto eo eo interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-eo display: none;
html
local
a
href title lang hreflang class
https://eu.wikipedia.org/wiki/Oreka_kimiko Oreka kimiko – Basque eu eu interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-eu display: none;
html
local
a
href title lang hreflang class
https://fa.wikipedia.org/wiki/%D8%AA%D8%B9%D8%A7%D8%AF%D9%84_%D8%B4%DB%8C%D9%85%DB%8C%D8%A7%DB%8C%DB%8C تعادل شیمیایی – Persian fa fa interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-fa display: none;
html
local
a
href title lang hreflang class
https://fr.wikipedia.org/wiki/%C3%89quilibre_chimique Équilibre chimique – French fr fr interlanguage-link-target
html
local
li
class
interlanguage-link interwiki-fr
html
local
a
href title lang hreflang class
https://gl.wikipedia.org/wiki/Equilibrio_qu%C3%ADmico Equilibrio químico – Galician gl gl interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-gl display: none;
html
local
a
href title lang hreflang class
https://ko.wikipedia.org/wiki/%ED%99%94%ED%95%99_%ED%8F%89%ED%98%95 화학 평형 – Korean ko ko interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-ko display: none;
html
local
a
href title lang hreflang class
https://hy.wikipedia.org/wiki/%D5%94%D5%AB%D5%B4%D5%AB%D5%A1%D5%AF%D5%A1%D5%B6_%D5%B0%D5%A1%D5%BE%D5%A1%D5%BD%D5%A1%D6%80%D5%A1%D5%AF%D5%B7%D5%BC%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6 Քիմիական հավասարակշռություն – Armenian hy hy interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-hy display: none;
html
local
a
href title lang hreflang class
https://hi.wikipedia.org/wiki/%E0%A4%B0%E0%A4%BE%E0%A4%B8%E0%A4%BE%E0%A4%AF%E0%A4%A8%E0%A4%BF%E0%A4%95_%E0%A4%B8%E0%A4%BE%E0%A4%AE%E0%A5%8D%E0%A4%AF रासायनिक साम्य – Hindi hi hi interlanguage-link-target
html
local
li
class
interlanguage-link interwiki-hi
html
local
a
href title lang hreflang class
https://hr.wikipedia.org/wiki/Kemijska_ravnote%C5%BEa Kemijska ravnoteža – Croatian hr hr interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-hr display: none;
html
local
a
href title lang hreflang class
https://io.wikipedia.org/wiki/Kemiala_equilibro Kemiala equilibro – Ido io io interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-io display: none;
html
local
a
href title lang hreflang class
https://id.wikipedia.org/wiki/Kesetimbangan_kimia Kesetimbangan kimia – Indonesian id id interlanguage-link-target
html
local
li
class
interlanguage-link interwiki-id
html
local
a
href title lang hreflang class
https://it.wikipedia.org/wiki/Equilibrio_chimico Equilibrio chimico – Italian it it interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-it display: none;
html
local
a
href title lang hreflang class
https://he.wikipedia.org/wiki/%D7%A9%D7%99%D7%95%D7%95%D7%99_%D7%9E%D7%A9%D7%A7%D7%9C_%D7%9B%D7%99%D7%9E%D7%99 שיווי משקל כימי – Hebrew he he interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-he display: none;
html
local
a
href title lang hreflang class
https://ka.wikipedia.org/wiki/%E1%83%A5%E1%83%98%E1%83%9B%E1%83%98%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%AC%E1%83%9D%E1%83%9C%E1%83%90%E1%83%A1%E1%83%AC%E1%83%9D%E1%83%A0%E1%83%9D%E1%83%91%E1%83%90 ქიმიური წონასწორობა – Georgian ka ka interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-ka display: none;
html
local
a
href title lang hreflang class
https://ht.wikipedia.org/wiki/Ekilib_chimik Ekilib chimik – Haitian Creole ht ht interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-ht display: none;
html
local
a
href title lang hreflang class
https://hu.wikipedia.org/wiki/Dinamikus_egyens%C3%BAly Dinamikus egyensúly – Hungarian hu hu interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-hu display: none;
html
local
a
href title lang hreflang class
https://mk.wikipedia.org/wiki/%D0%A5%D0%B5%D0%BC%D0%B8%D1%81%D0%BA%D0%B0_%D1%80%D0%B0%D0%BC%D0%BD%D0%BE%D1%82%D0%B5%D0%B6%D0%B0 Хемиска рамнотежа – Macedonian mk mk interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-mk display: none;
html
local
a
href title lang hreflang class
https://ml.wikipedia.org/wiki/%E0%B4%B0%E0%B4%BE%E0%B4%B8%E0%B4%B8%E0%B4%82%E0%B4%A4%E0%B5%81%E0%B4%B2%E0%B4%A8%E0%B4%82 രാസസംതുലനം – Malayalam ml ml interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-ml display: none;
html
local
a
href title lang hreflang class
https://nl.wikipedia.org/wiki/Chemisch_evenwicht Chemisch evenwicht – Dutch nl nl interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-nl display: none;
html
local
a
href title lang hreflang class
https://ja.wikipedia.org/wiki/%E5%8C%96%E5%AD%A6%E5%B9%B3%E8%A1%A1 化学平衡 – Japanese ja ja interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-ja display: none;
html
local
a
href title lang hreflang class
https://no.wikipedia.org/wiki/Kjemisk_likevekt Kjemisk likevekt – Norwegian no no interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-no display: none;
html
local
a
href title lang hreflang class
https://pl.wikipedia.org/wiki/R%C3%B3wnowaga_reakcji_chemicznych Równowaga reakcji chemicznych – Polish pl pl interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-pl display: none;
html
local
a
href title lang hreflang class
https://pt.wikipedia.org/wiki/Equil%C3%ADbrio_qu%C3%ADmico Equilíbrio químico – Portuguese pt pt interlanguage-link-target
html
local
li
class
interlanguage-link interwiki-pt
html
local
a
href title lang hreflang class
https://ro.wikipedia.org/wiki/Echilibru_chimic Echilibru chimic – Romanian ro ro interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-ro display: none;
html
local
a
href title lang hreflang class
https://qu.wikipedia.org/wiki/Chaqllisinchi_nankay Chaqllisinchi nankay – Quechua qu qu interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-qu display: none;
html
local
a
href title lang hreflang class
https://ru.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%D0%B2%D0%B5%D1%81%D0%B8%D0%B5 Химическое равновесие – Russian ru ru interlanguage-link-target
html
local
li
class
interlanguage-link interwiki-ru
html
local
a
href title lang hreflang class
https://sk.wikipedia.org/wiki/Chemick%C3%A1_rovnov%C3%A1ha Chemická rovnováha – Slovak sk sk interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-sk display: none;
html
local
a
href title lang hreflang class
https://ckb.wikipedia.org/wiki/%DA%BE%D8%A7%D9%88%D8%B3%DB%95%D9%86%DA%AF%DB%8C%DB%8C_%DA%A9%DB%8C%D9%85%DB%8C%D8%A7%DB%8C%DB%8C ھاوسەنگیی کیمیایی – Central Kurdish ckb ckb interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-ckb display: none;
html
local
a
href title lang hreflang class
https://sr.wikipedia.org/wiki/%D0%A5%D0%B5%D0%BC%D0%B8%D1%98%D1%81%D0%BA%D0%B0_%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%D1%82%D0%B5%D0%B6%D0%B0 Хемијска равнотежа – Serbian sr sr interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-sr display: none;
html
local
a
href title lang hreflang class
https://sh.wikipedia.org/wiki/Hemijska_ravnote%C5%BEa Hemijska ravnoteža – Serbo-Croatian sh sh interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-sh display: none;
html
local
a
href title lang hreflang class
https://fi.wikipedia.org/wiki/Kemiallinen_tasapaino Kemiallinen tasapaino – Finnish fi fi interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-fi display: none;
html
local
a
href title lang hreflang class
https://sv.wikipedia.org/wiki/Kemisk_j%C3%A4mvikt Kemisk jämvikt – Swedish sv sv interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-sv display: none;
html
local
a
href title lang hreflang class
https://tl.wikipedia.org/wiki/Ekilibriyong_kemikal Ekilibriyong kemikal – Tagalog tl tl interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-tl display: none;
html
local
a
href title lang hreflang class
https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AF%87%E0%AE%A4%E0%AE%BF%E0%AE%AF%E0%AE%BF%E0%AE%AF%E0%AE%B1%E0%AF%8D_%E0%AE%9A%E0%AE%AE%E0%AE%A8%E0%AE%BF%E0%AE%B2%E0%AF%88 வேதியியற் சமநிலை – Tamil ta ta interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-ta display: none;
html
local
a
href title lang hreflang class
https://th.wikipedia.org/wiki/%E0%B8%AA%E0%B8%A1%E0%B8%94%E0%B8%B8%E0%B8%A5%E0%B9%80%E0%B8%84%E0%B8%A1%E0%B8%B5 สมดุลเคมี – Thai th th interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-th display: none;
html
local
a
href title lang hreflang class
https://tr.wikipedia.org/wiki/Kimyasal_denge Kimyasal denge – Turkish tr tr interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-tr display: none;
html
local
a
href title lang hreflang class
https://uk.wikipedia.org/wiki/%D0%A5%D1%96%D0%BC%D1%96%D1%87%D0%BD%D0%B0_%D1%80%D1%96%D0%B2%D0%BD%D0%BE%D0%B2%D0%B0%D0%B3%D0%B0 Хімічна рівновага – Ukrainian uk uk interlanguage-link-target
html
local
li
class style
interlanguage-link interwiki-uk display: none;
html
local
a
href title lang hreflang class
https://zh.wikipedia.org/wiki/%E5%8C%96%E5%AD%A6%E5%B9%B3%E8%A1%A1 化学平衡 – Chinese zh zh interlanguage-link-target
html
local
li
class
interlanguage-link interwiki-zh
html
local
button
class title
mw-interlanguage-selector mw-ui-button All languages (initial selection from common choices by you and others)
html
local
ul
html
local
a
href title class
https://www.wikidata.org/wiki/Special:EntityPage/Q189520#sitelinks-wikipedia Edit interlanguage links wbc-editpage
html
local
span
class
wb-langlinks-edit wb-langlinks-link
html
local
div
class
after-portlet after-portlet-lang
html
local
div
class
body
html
local
div
class role id aria-labelledby
portal navigation p-lang p-lang-label
html
local
div
id
mw-panel
html
local
div
id
mw-navigation
html
local
li
id
footer-info-lastmod
html
local
a
rel href
license //en.wikipedia.org/wiki/Wikipedia:Text_of_Creative_Commons_Attribution-ShareAlike_3.0_Unported_License
html
local
a
rel href style
license //creativecommons.org/licenses/by-sa/3.0/ display:none;
html
local
a
href
//wikimediafoundation.org/wiki/Terms_of_Use
html
local
a
href
//wikimediafoundation.org/wiki/Privacy_policy
html
local
a
href
//www.wikimediafoundation.org/
html
local
li
id
footer-info-copyright
html
local
ul
id
footer-info
html
local
a
href class title
https://wikimediafoundation.org/wiki/Privacy_policy extiw wmf:Privacy policy
html
local
li
id
footer-places-privacy
html
local
a
href title
/wiki/Wikipedia:About Wikipedia:About
html
local
li
id
footer-places-about
html
local
a
href title
/wiki/Wikipedia:General_disclaimer Wikipedia:General disclaimer
html
local
li
id
footer-places-disclaimer
html
local
a
href
//en.wikipedia.org/wiki/Wikipedia:Contact_us
html
local
li
id
footer-places-contact
html
local
a
href
https://www.mediawiki.org/wiki/Special:MyLanguage/How_to_contribute
html
local
li
id
footer-places-developers
html
local
a
href
https://wikimediafoundation.org/wiki/Cookie_statement
html
local
li
id
footer-places-cookiestatement
html
local
a
href class
//en.m.wikipedia.org/w/index.php?title=Chemical_equilibrium&mobileaction=toggle_view_mobile noprint stopMobileRedirectToggle
html
local
li
id
footer-places-mobileview
html
local
a
href
#
html
local
li
style
display: none;
html
local
ul
id
footer-places
html
local
img
src srcset width height alt
/static/images/wikimedia-button.png /static/images/wikimedia-button-1.5x.png 1.5x, /static/images/wikimedia-button-2x.png 2x 88 31 Wikimedia Foundation
html
local
a
href
https://wikimediafoundation.org/
html
local
li
id
footer-copyrightico
html
local
img
src alt srcset width height
/static/images/poweredby_mediawiki_88x31.png Powered by MediaWiki /static/images/poweredby_mediawiki_132x47.png 1.5x, /static/images/poweredby_mediawiki_176x62.png 2x 88 31
html
local
a
href
//www.mediawiki.org/
html
local
li
id
footer-poweredbyico
html
local
ul
id class
footer-icons noprint
html
local
div
style
clear: both;
html
local
div
id role
footer contentinfo
html
local
polygon
points
0 8, 10 8, 18 0, 26 8, 1000 8, 1000 1000, 0 1000
html
local
clippath
id
mwe-popups-mask
html
local
polygon
points
0 8, 274 8, 282 0, 290 8, 1000 8, 1000 1000, 0 1000
html
local
clippath
id
mwe-popups-mask-flip
html
local
polygon
points
0 8, 174 8, 182 0, 190 8, 1000 8, 1000 1000, 0 1000
html
local
clippath
id
mwe-popups-landscape-mask
html
local
polygon
points
0 0, 1000 0, 1000 242, 190 242, 182 250, 174 242, 0 242
html
local
clippath
id
mwe-popups-landscape-mask-flip
html
local
defs
html
local
svg
xmlns width height
http://www.w3.org/2000/svg 0 0
html
local
div
id
mwe-popups-svg
html
local
div
class
suggestions-results
html
local
div
class
suggestions-special
html
local
div
class style
suggestions display: none; font-size: 13px;
html
local
body
class
mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Chemical_equilibrium rootpage-Chemical_equilibrium skin-vector action-view
html
local