The Foundations of Chemistry

EFFECT OF CONCENTRATIONS (OR PARTIAL PRESSURES)
ON ELECTRODE POTENTIALS

THE NERNST EQUATION

Standard electrode potentials, designated E^0 , refer to standard-state conditions. These
standard-state conditions are one molar solutions for ions, one atmosphere pressure for
gases, and all solids and liquids in their standard states at 25°C. (Remember that we refer
to thermodynamicstandard-state conditions, and not standard temperature and pressure as
in gas law calculations.) As any of the standard cells described earlier operates, and concen-
trations or pressures of reactants change, the observed cell voltage drops. Similarly, cells
constructed with solution concentrations different from one molar, or gas pressures
different from one atmosphere, cause the corresponding potentials to deviate from stan-
dard electrode potentials.
The Nernst equationis used to calculate electrode potentials and cell potentials for
concentrations and partial pressures other than standard-state values.

EE^0 

2.30

n

3

F

RT

log Q

where

E potential under the nonstandardconditions

E^0 standardpotential

R gas constant, 8.314 J/molK

T absolute temperature in K

n number of moles of electrons transferred in the reaction or half-reaction

F faraday, 96,485 C/mol e1 J/(VC)96,485 J/Vmol e

Q reaction quotient

The reaction quotient, Q,was introduced in Section 17-4. It involves a ratio of concen-
trations or pressures of products to those of reactants, each raised to the power indicated
by the coefficient in the balanced equation. The Qexpression that is used in the Nernst
equation is the thermodynamic reaction quotient; it can include bothconcentrations and
pressures. Substituting these values into the Nernst equation at 25°C gives

EE^0 

0.0

n

592

log Q (Note:in terms of base-10 log)

In general, half-reactions for standard reduction potentials are written

xOxne88nyRed

“Ox” refers to the oxidized species and “Red” to the reduced species; xand yare their
coefficients, respectively, in the balanced equation. The Nernst equation for any cathode
half-cell (reductionhalf-reaction) is

21-19

21-19 The Nernst Equation 877

In this equation the expression

following the minus sign represents

how much the nonstandardconditions

cause the electrode potential to deviate

from its standard value, E^0. The

Nernst equation is normally presented

in terms of base-10 logarithms, as we

will do in this text.

At 25°C, the value of 

2.30

F

3 RT

is

0.0592; at any other temperature, this

term must be recalculated. Can you

show that this term has the units

Vmol?