Physical Chemistry , 1st ed.

need additional tools to determine the electromotive force at nonstandard

conditions.

Many complex biochemical reactions are electron-transfer processes, and as

such have a standard reduction potential. For example, nicotinamide adenine

dinucleotide (NAD^ ) accepts a proton and two electrons to become NADH:

NAD^ H^ 2e^ →NADH E°

0.105 V

under standard conditions. The potentials for one-electron reductions of iron

in myoglobin (E0.046 V) and cytochrome c(E0.254 V) listed here

are for biochemicalstandard states (that is, pH 7; 37°C). Thus, when con-

sidering biochemical processes, it is crucial to understand what the conditions

are for the reactions of interest.

8.5 Nonstandard Potentials and Equilibrium Constants

Example 8.3 assumed that the conditions of the reaction were standard ther-

modynamic conditions. However, in reality this is almost never the case.

Reactions occur in highly variable conditions of temperature, concentration,

and pressure. (Indeed, many electrochemically based reactions occur at tiny

concentrations of ions. Consider the rusting of your car.)

Standard and nonstandard E’s for electrochemical reactions follow the same

rules as energies: if it is a standard E, then the symbol Ehas the ° on it.

However, if the Eis simply some instantaneous electromotive force for any im-

mediate set of conditions, then the ° sign is left off:E.

The most well-known relationship between Eand E° is the Nernst equation,

derived by the German chemist Walther Hermann Nernst (Figure 8.6) in 1889.

(Among other achievements, Nernst was the principal enunciator of the third

law of thermodynamics, was the first to explain explosions in terms of branch-

ing chain reactions, and invented the Nernst glower, a useful source of infrared

radiation. He received the 1920 Nobel Prize in Chemistry for his contributions

in thermodynamics.) Having recognized the validity of the following two

equations:

G

nFE

GG° RTln Q

(these are equations 8.20 and 5.7, respectively), one can combine them to yield

nFE

nFE° RTln Q

Solving for E, the nonstandard electromotive force:

EE° 

R

nF

T

ln Q (8.25)

which is the Nernst equation. Recall that Qis the reaction quotient, which is

expressed in terms of the instantaneous (nonequilibrium) concentrations,

pressures, activities, or fugacities of reactants and products.

Example 8.4

Given the nonstandard concentrations for the following reaction, calculate

the instantaneous Eof the Daniell cell.

Zn Cu^2 (0.0333 M) →Zn^2 (0.00444 M) Cu

218 CHAPTER 8 Electrochemistry and Ionic Solutions

Figure 8.6 Walther Hermann von Nernst

(1864–1941), a German chemist who first formu-

lated an equation relating the potential of an elec-

trochemical reaction to the instantaneous condi-

tions of the products and reactants. His Nobel

Prize, however, was awarded in honor of his

pioneering work to establish the third law of

thermodynamics.

© CORBIS-Bettmann