Page 93 - A Working Method Approach For Introductory Physical Chemistry Calculations

Electrochemistry I: Galvanic Cells 77

whereEo,ll = EORHE - EOLHE.
From this, one of the most important equations in electrochemistry,
the Nernst equation, can be derived:
AG = AGO + RTln K, where R = Universal Gas Constant = 8.314
J K-' mol-'.
But, AGO = -uFEO,II
+ -uFE = -uFEocell + RTlnK
Dividing across by - uF:

E = E',J - (RT/uF) lnK, the Nernst equation
I I
For the general reaction: uAA + vBB --+ ucC + uDD, where UA, uB,
uc and UD represent the stoichiometry factors, K, the equilibrium
constant can be written as follows:

i.e. of the form 'products/reactants'
e.g. for the reaction Fe"' + SCN-(aq) + Fe11(NCS)2+(aq),
(aq)III
K = [F~"(NCS)~ (aq)l/{ [~e (aq)~ [scN-(~~)II
+
As mentioned in Chapter 4, the activity, a, of a solid is unity, i.e. on
examination of the balanced chemical equation, any substance with an
(s) subscript implies the substance is in the solid state and therefore
has unit activity.
At equilibrium: AG = 0 + -vFE = 0 + E = 0
+ For the Nernst equation: E = Eocell - (RT/uF)ln K,
i.e. 0 = Eocell - (RT/uF)ln K
In
+- (RT/uF)ln K = Eocell j K = (uFE",II/RT),
from which K, the equilibrium constant can be determined.
In conclusion, three equations should be remembered: