Page 92 - A Working Method Approach For Introductory Physical Chemistry Calculations

76 Chapter 6

Thermodynamics and the Determination of K, the Equilibrium Constant
for a Reaction
In Chapter 3 of this text, the idea of a spontaneous reaction was
related to AG, the Gibbs free energy change of a reaction.

In particular,
AG - ve spontaneous reaction
AG + ve non-spontaneous reaction
AG = 0 reaction at equilibrium

where AG was defined as:

AG= AH- TAS

AH = change in the enthalpy (measured in J mol-'), T = tempera-
ture (measured in K) and AS = change in the entropy (disorder)
(measured in J K - mol - ').
From physics, there is an expression for the voltage or potential, V:
V = w/Q + w = VQ, where w is the work done (i.e. the energy,
measured in joules, J) and Q is the charge (measured in coulombs, C).
In electrochemistry, one or multiple numbers of moles of reactants
are considered, and specifically for charge:
The Faraday constant is 96 500 C mol- '
i.e. the charge of 1 mole of electrons = F = 96 500 C mol-'
+ electrical energy = potential x charge (i.e. w = VQ)
+ AG = Ere" (- vfl, where AG, the change in Gibbs free energy is,
in fact, the change in electrical potential energy. This is normally
written as AG = - vFEre, where rev indicates reversibility.
This leads to a very useful expression, which connects thermody-
namics calculations to electrochemistry, and moreover to the determi-
nation of K, the equilibrium constant:
AG = I-vFEI
where v = the number of electrons participating in the reaction, as
defined by the equation describing the half-cell reaction (e.g. Fe2+(,
?
+ 2e + Fee(,>; u = 2); F = the Faraday constant = 96 500 C mol- ;
E = the electrode potential.
At standard state conditions, i.e. 25 "C and 1 bar pressure, the
expression becomes: