is implicit. AH A− + H+ Water concentration is omitted from expressions defining equilibrium constants, except when solutions are very concentrated. (K defined as a dissociation constant) Similar considerations apply to metal ion hydrolysis reactions. Enthalpy and entropy: temperature dependence If both the equilibrium constant, and the standard enthalpy change, , for a reaction have been determined experimentally, the standard entropy change for the reaction is easily derived. Since and To a first approximation the standard enthalpy change is independent of temperature. Using this approximation, definite integration of the van 't Hoff equation gives This equation can be used to calculate the value of log K at a temperature, T2, knowing the value at temperature T1. The van 't Hoff equation also shows that, for an exothermic reaction (), when temperature increases K decreases and when temperature decreases K increases, in accordance with Le Chatelier's principle. The reverse applies when the reaction is endothermic. When K has been determined at more than two temperatures, a straight line fitting procedure may be applied to a plot of against to obtain a value for . Error propagation theory can be used to show that, with this procedure, the error on the calculated value is much greater than the error on individual log K values. Consequently, K needs to be determined to high precision when using this method. For example, with a silver ion-selective electrode each log K value was determined with a precision of ca. 0.001 and the method was applied successfully. Standard thermodynamic arguments can be used to show that, more generally, enthalpy will change with temperature. where Cp is the heat capacity at constant pressure. A more complex formulation The calculation of K at a particular temperature from a known K at another given temperature can be approached as follows if standard thermodynamic properties are available. The effect of temperature on equilibrium constant is equivalent to the effect of temperature on Gibbs energy because: where ΔrGo is the reaction standard Gibbs energy, which is the sum of the standard Gibbs energies of the reaction products minus the sum of standard Gibbs energies of reactants. Here, the term "standard" denotes the ideal behaviour (i.e., an infinite dilution) and a hypothetical standard concentration (typically 1 mol/kg). It does not imply any particular temperature or pressure because, although contrary to IUPAC recommendation, it is more convenient when describing aqueous systems over wide temperature