# Short notes of Electro Chemistry for IIT-JEE Main and Advance Electro Chemistry is one of the most important chapter from IIT – JEE Main and Advance perspective. So make sure that you go through these short notes to score the most!

### ELECTROCHEMICAL CELLS

An electrochemical cell consists of two electrodes (metallic conductors) in contact with an electrolyte (an ionic conductor). An electrode and its electrolyte comprise an Electrode Compartment.

Electrochemical Cells can be classified as:

(i) Electrolytic Cells in which a non−spontaneous reaction is driven by an external source of current.

(ii) Galvanic Cells which produce electricity as a result of a spontaneous cell reaction

Note: In a galvanic cell, cathode is positive with respect to anode. In a electrolytic cell, anode is made positive with respect to cathode. ELECTROLYSIS The decomposition of electrolyte solution by passage of electric current, resulting into deposition of metals or liberation of gases at electrodes is known as electrolysis.

### ELECTROLYSIS

The decomposition of electrolyte solution by passage of electric current, resulting into deposition of metals or liberation of gases at electrodes is known as electrolysis.

### ELECTROLYTIC CELL

This cell converts electrical energy into chemical energy. The entire assembly except that of the external battery is known as the electrolytic cell ### ELECTRODES

The metal strip at which positive current enters is called anode; anode is positively charged in electrolytic cell. On the other hand, the electrode at which current leaves is called cathode. Cathodes are negatively charged.

Anode                         Positive                                  Loss of electron or oxidation takes place                     Positive current enters

Cathode                     Negative                               Gain of electron or reduction takes place                    Current leaves

### ELECTROLYSIS OF MOLTEN SODIUM CHLORIDE

The metal strip at which positive current enters is called anode; anode is positively charged in electrolytic cell. On the other hand, the electrode at which current leaves is called cathode. Cathodes are negatively charged.

Anode                   Positive                       Loss of electron or oxidation takes place                 Positive current  enters

Cathode              Negative                     Gain of electron or reduction takes place                Current  leaves

### ELECTROLYSIS OF MOLTEN SODIUM CHLORIDE

NaCl(molten)       —->     Na+ + Cl

Reactions at              anode (oxidation)         :       cathode (reduction)

Cl– → Cl2 (g) + 2e :                 2Na+ + 2e → 2Na(l)

There are two types of electrodes used in the electrolytic cell, namely attachable and non – attachable. The attachable electrodes participate in the electrode reaction. They are made up of reactive metals like Zn, Cu, Ag etc. In such electrodes, atom of the metal gets oxidized into the corresponding cation, which is passed into the solution. Thus, such anodes get dissolved and their mass decreases. On the other hand, non-attachable electrodes do not participate in the electrode reaction as they made up of nonreactive elements like Pt, graphite etc. Such electrodes do not dissolve and their mass remain same.

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##### (i) First law of electrolysis :

Amount of substance deposited or liberated at an electrode is directly proportional to amount of charge passed (utilized) through the solution.

w  ∝  Q

W = weight liberated, Q = charge in coulomb

w = ZQ

Z = electrochemical equivalent

when Q = 1 coulomb, then w = Z

Thus, weight deposited by 1 coulomb charge is called electrochemical equivalent. Let 1 ampere current is passed till ‘t’ seconds .

Then, Q = It ∴ w = ZIt 1 Faraday = 96500 coulomb = Charge of one mole electrons

One faraday is the charge required to liberate or deposit one gm equivalent of a substance at corresponding electrode.

Let ‘E’ is equivalent weight then ‘E’ gm will be liberated by 96500 coulomb.

∴ 1 Coulomb will liberate E / 96500  gm ;     By definition,  Z = E/  96500

W= ItE/ 96500

When a gas is evolved at an electrode, then above formula changes as,

V = ItV e / 96500

where V = volume of liberated gas,

Ve = equivalent volume of gas.

Equivalent volume may be defined as: The volume of gas liberated by 96500 coulomb at STP.

##### (ii) Second law of electrolysis

When same amount of charge is passed through different electrolyte solutions connected in series then weight of substances deposited or dissolved at anode or cathode are in ratio of their equivalent weights.

i.e. w1 /w2 = E1 /E2

### QUALITATIVE ASPECTS OF ELECTROLYSIS

In the electrolysis process we have discussed above, we have taken molten salt as electrolyte, which contains only one cation and anion. Now, if the electrolyte taken contains more than one cation and anion (for example, aqueous solution of the ionic electrolyte), then the cation and anion that will get discharged depends on the ability of cation to get reduced and the ability of anion to get oxidized. The ability of an ion to get oxidized or reduced depends upon the size, mass, positive charge, negative charge etc.

Thus, it is not possible to predict qualitatively that which ion would be discharged first, as one factor might enhance the ability to discharge while the other factor may hamper it. This can only be predicted on the basis of quantitative value assigned based on the cumulative effect of all the factors responsible for an ion’s ability to discharge.

The value is referred as standard potential, which is determined by keeping the concentration of ion as 1 M, pressure of gas at 1 atm, and the measurement done at 25°C. For a cation, the standard reduction potential (SRP) values are compared. The cation having higher standard reduction potential value is discharged in preference to cation with lower SRP value provided the ions are at 1 M concentration.

For an anion, the standard oxidation potential (SOP) values are compared and anion having higher SOP is preferentially discharged, if the concentration is 1 M for each of the ion. The SRP values at 25°C for some of the reduction half reactions are given in the table below. When solution of an electroyte contains more than one type of cations and anions at concentrations different than 1 M, the discharge of an ion does not depend solely on standard potentials but also depends on the concentration of ion in the solution. This value is refered as potential, called as reduction potential for cation and oxidation potential for anion. The relation between reduction potential and standard reduction potential is given by Nernst equation, as

ERP = E° RP – RT / nF In [concentration of product] / [concentration of reac tan t]

where ERP = Reduction potential of cation and E°RP = Standard reduction potential of cation. Thus, it is possible that a cation (A+ ) with lower standard reduction potential getting discharged in preference to cation (B+ ) having higher standard reduction potential because their concentration might be such that the reduction potential of A+ is higher than that of B+ . When two metal ions in the solution have identical values of their reduction potentials, the simultaneous deposition of both the metals will occur in the form of an alloy.

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### GALVANIC CELL

This cell converts chemical energy into electrical energy. Galvanic cell is made up of two half cells i.e., anodic and cathodic. The cell reaction is of redox kind. Oxidation takes place at anode and reduction at cathode. It is also known as voltaic cell. It may be represented as shown in Fig. Zinc rod immersed in ZnSO4 behaves as anode and copper rod immersed in CuSObehaves as cathode.

Oxidation takes place at anode:

Zn ⇌ Zn2+  +   2e  (loss of electron : oxidation)

Reduction takes place at cathode:

Cu2+ 2e–    ⇌   Cu (gain of electron ; reduction)

Over all process:

Zn(s) + Cu2+  ⇌  Cu(s) + Zn2+

In galvanic cell like Daniell cell; electrons flow from anode (zinc rod) to the cathode (copper rod) through external circuit; zinc dissolves as Zn2+  ;  Cu2+ ion in the cathode cell picks up two electron and become deposited at cathode.

### SALT BRIDGE

Two electrolyte solutions in galvanic cells are separated using salt bridge as represented in the Fig. salt bridge is a device to minimize or eliminate the liquid junction potential. Saturated solution of salt like KCI, KNO3 , NH4Cl and NH4NO3 etc. in agar-agar gel is used in salt bridge. Salt bridge contains high concentration of ions viz. K+ and NO3 − at the junction with electrolyte solution.

Thus, salt bridge carries whole of the current across the boundary ; more over the K+and NO3 − ions have same speed. Hence, salt bridge with uniform and same mobility of cations and anions minimize the liquid junction potential & completes the electrical circuit & permits the ions to migrate.

##### Representation of a cell (IUPAC conventions ): Let us illustrate the convention taking the example of Daniel cell.

(i) Anodic half cell is written on left and cathodic half cell on right hand side. Zn(s) | ZnSO4 (sol) || CuSO4 (sol) | Cu(s)

(ii) Two half cells are separated by double vertical lines: Double vertical lines indicate salt bridge or any type of porous partition.

(iii) EMF (electromotive force) may be written on the right hand side of the cell.

(iv) Single vertical lines indicate the phase separation between electrode and electrolyte solution. Zn | Zn2+ || Cu2+ | Cu (Illustration of Phase boundary)

(v) Inert electrodes are represented in the bracket Zn | ZnSO4 || H+ | H2 , Pt

### CONCEPT OF ELECTROMOTIVE FORCE (EMF) OF A CELL

Electron flows from anode to cathode in external circuit due to a pushing effect called or electromotic force (e.m.f.). E.m.f. is some times called as cell potential. Unit of e.m.f. of cell is volt. EMF of cell may be calculated as :

Ecell = reduction potential of cathode − Reduction potential of anode Similarly, standard e.m.f. of the cell (E°) may be calculated as

cell = Standard reduction potential of cathode − Standard reduction potential of anode.

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### SIGN CONVENTION OF EMF EMF

of cell should be positive other wise it will not be feasible in the given direction .

Zn | ZnSO4 || CuSO4 | Cu E = +1.10 volt (Feasible)

Cu | CuSO4 || ZnSO4 | Zn E = −1.10 volt (Not Feasible)

### NERNST EQUATION

Walter Nernst derived a relation between cell potential and concentration or Reaction quotient.

ΔG = ΔG° + RT ln Q

where ΔG and ΔG° are free energy and standard free energy change; ‘Q’ is reaction quotient. Let n, Faraday charge is taken out from a cell of e.m.f. (E) then electrical work done by the cell may be calculated as,

Work done = Charge x Potential = nFE

From thermodynamics we know that decrease in Gibbs free energy of a system is a measure of reversible or maximum obtainable work by the system if there is no work due to volume expansion

∴ −∆G = nFE and −∆G° = nFE°

Thus from Eq. (i),we get −nFE = -nFE° + RT lnQ

At 25°C, above equation may be written as E = E0 – 0.059 / n logQ

Where ‘n’ represents number of moles of electrons involved in process. E, E° are e.m.f. and standard e.m.f. of the cell respectively. In general , for a redox cell reaction involving the transference of n electrons aA + bB → cC + dD, the EMF can be calculated as:

ECell = E°Cell – 0.0591 / n log  [C]c [D]d / [A]a [B]b

### Prediction and feasibility of spontaniety of a cell reaction.

Work done by the cell = nFE; It is equivalent to decrease in free energy ∆G = –nFE Under standard state ∆ G0 = –nFE0

(i) From thermodynamics we know, ∆ G = negative for spontaneous process. Thus from eq.(i) it is clear that the EMF should be +ve for a cell process to be feasible or spontaneous.

(ii) When ∆G = positive, E = negative and the cell process will be non spontaneous.

(iii) When G = 0 , E = 0 and the cell will attain the equilibrium.

Reactions                                    ∆G                                            E

Spontaneous                             (–)                                            (+)

Non- spontaneous                  (+)                                           (–)

Equilibrium                                  0                                               0

Standard free energy change of a cell may be calculated by electrode potential data. Substituting the value of E0 (i.e., standard reduction potentialof cathode- standard reduction potential of anode) in eq. (i) we may get ∆G0 . Let us see whether the cell (Daniell) is feasible or not: i.e. whether Zinc will displace copper or not.

Zn | (s) | ZnSO4 (sol) || CuSO4 (sol) | Cu(s)

E0Zn2+ = 76.0 volt ; E0Cu2+/cu = +0.34volt

E0cell = E0cu2+ / Cu  -E0 zn2+/ Zn

=0.34 –(–0.76) = +1.10 volt

Since E0 = +ve , hence the cell will be feasible and zinc will displace copper from its salt solution. In the other words zinc will reduce copper.

### THERMODYNAMIC TREATMENT OF NERNST EQUATION

Determination of equilibrium constant : We know, that

E = E0 – 0.0591 / n logQ                                                       ….(i)

At equilibrium, the cell potential is zero because cell reactions are balanced, i.e. E = 0

∴ From Eq. (i), we have

0 = E0  – 0.0591 / n logKeq             or          Keq= antilog [nE0 / 0.0591 ]

Heat of Reaction inside the cell:  Let n Faraday charge flows out of a cell of e.m.f. E, then

−∆G = nFE                                                    (i)

Gibbs Helmholtz equation (from thermodynamics ) may be given as,

∆G = ∆H + T [ ∂∆G / ∂T ]p                       ………  (i)

From Eqs. (i) and (ii), we have

-nFE = ∆H = T[ ∂(-nFE) / ∂T]p   = ∆H-nFT [ ∂E /  ∂T ]p

∴  ∆H = nFE=nFT [  ∂E/  ∂T]p

Entropy change inside the cell : We know that G = H – TS or ∆G = ∆H − T∆S …(i) where ∆G = Free energy change ;

∆H = Enthalpy change and ∆S = entropy change. According to Gibbs Helmoholtz equation, Short Notes of Complex Numbers for IIT-JEE mains and advance

### DIFFERENT TYPES OF HALF-CELLS AND THEIR REDUCTION POTENTIAL ### CONCENTRATION CELL

The cells in which electrical current is produced due to transport of a substance from higher to lower concentration. Concentration gradient may arise either in electrode material or in electrolyte. Thus there are two types of concentration cell .

(i) Electrode concentration cell

(ii) Electrolyte concentration cell Important Questions Of Complex Numbers for IIT-JEE mains and advance

### SPECIFIC CONDUCTANCE IS CONDUCTANCE OF 1 CM3 OF AN ELECTROLYTE SOLUTION.

In case of electrolytic solution, the specific conductance is defined as the conductance of a solsution of definite concentration enclosed in a cell having two electrodes sof unit area separated by 1 cm apart.

1. Equivalent Conductance

Equivalent conductance is the conductance of an electrolyte solution containing 1 gm equivalent of electrolyte. It is densoted by ∧ .

∧ = K x V

(∧ = ohm−1 cm−1 x cm3 = ohm−1 cm2 )

Usually concen ration of electrolyte solution is expressed as C gm equivalent per litre.

Thus,  V= 1000 / C  {Volume having gm1 equivalent electrolyte in  the solution}Thus,  ∧=K   × 1000 / C

2. Molar Conductance

Molar conductance may be defined as conductance of an electrolyte solution having 1 gm mole electrolyte in a liter. It is denoted by ∧m .

m = K × V

Usually concentration of electrolyte solution is expressed as ‘M’ gm mole electrolyte per liter

Thus,  V= 1000 / M

Hence, ∧m=K x   1000 / M

Relation between ∧ and ∧m :              ∧m = n × ∧

DETERMINATION OF 0 ∧m0 OR ∧0 The ∧m vs √C plot of strong electrolyte being linear it can be extrapolated to zero concentration.

Thus, ∧m values of the solution of the test electrolyte are determined at various concentrations the concentrations should be as low as good.

m values are then plotted against √C when a straight line is obtained. This is the extrapolated to zero concentration. The point where the straight line intersects ∧m axis is 0 ∧m of the strong electrolyte.

However, the plot in the case weak electrolyte being non linear, shooting up suddenly at some low concentration and assuming the shape of a straight line parallel to ∧m axis. Hence extrapolation in this case is not possible. Thus, ∧0 of a weak electrolyte cannot be determined experimentally. It can, however, be done with the help of Kohlrausch’s law to be discussed later.

### Kohlrausch’s Law of Independent Migration of Ions ### Application of Kohlrausch’s law : Short Notes of Modern Physics for IIT-JEE mains and advance

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