Chemistry of Freshwaters - Principles of Environmental Chemistry - page 111

where {e } is small (pH is high where {H 1 } is small). pe is related to the
electrode potential, E H , by the expression
pe ¼ 16.9 E H (V) (3.67)

This relationship can be derived from the Nernst Equation
E H ¼ E H þ (2.303 RT n/F) log(P (oxidized species)/
P (reduced species)) (3.68)

where R is the universal gas constant, T the absolute temperature, F the
Faraday constant, and n the number of electrons.
Starting with the equilibrium expression
aA þ bB þ ne " cC þ dD (3.69)

we can write

K ¼ {C} c {D} d /{A} a {B} b {e } n (3.70)

Logarithmic expressions are then

log K ¼ log ð P ð reduced species Þ= P ð oxidized species ÞÞ n log f e g
pe ¼ð 1 = n Þ log K þð 1 = n Þ log ð P ð oxidized species Þ= P ð reduced species ÞÞ
Multiply by 2.303 RT/F to give

ð 2 : 303RT = F Þ pe ¼ð 2 : 303RT n = F Þ log K
þð 2 : 303RT n = F Þ log ð P ð oxidized species Þ= P ð reduced species ÞÞ
Now use the standard Gibbs free energy, DG 0 ¼ 2.303 RT logK
¼ -nFE H to give

ð 2 : 303RT = F Þ pe ¼ E H
þð 2 : 303RT n = F Þ log ð P ð oxidized species Þ= P ð reduced species ÞÞ
ð 3 : 71 Þ
The right hand side of Equation (3.71) is the same as that of the Nernst
Equation (3.68) and so the left hand side of Equation (3.71) must be
equal to the left hand side of the Nernst Equation (3.68), thus leading to
Equation (3.67). An additional definition is

pe 0 ¼ (1/n) log K (3.72)

and so

pe 0 ¼ (2.303 RT/F ) E H ¼ 16.9 E H (3.73)