Thermodynamics and Chemistry

CHAPTER 14 GALVANIC CELLS

14.4 THENERNSTEQUATION 462

Finally, by combining Eqs.14.3.15and14.3.17withÅrGDÅrHTÅrS, we obtain
an expression for the standard molar reaction entropy:

ÅrSDzF

dEcell, eq

dT

(14.3.18)

(no solute standard states

based on concentration)

BecauseG,H, andSare state functions, the thermodynamic equilibrium constant
and the molar reaction quantities evaluated fromEcell, eqand dEcell, eq =dT are the same
quantities as those for the reaction when it takes place in a reaction vessel instead of in a
galvanic cell. However, the heats at constantTandpare not the same (page 318 ). During
a reversible cell reaction, dSmust equal∂q=T, and∂q=dis therefore equal toTÅrS
during a cell reaction taking place reversibly under standard state conditions at constantT
andp.

14.4 The Nernst Equation

The standard cell potentialEcell, eq of a cell reaction is the equilibrium cell potential of
the hypothetical galvanic cell in which each reactant and product of the cell reaction is
in its standard state and there is no liquid junction potential. The value ofEcell, eq for a
given cell reaction with given choices of standard states is a function only of temperature.
The measured equilibrium cell potentialEcell, eqof an actual cell, however, depends on the
activities of the reactants and products as well as on temperature and the liquid junction
potential, if present.
To derive a relation betweenEcell, eqand activities for a cell without liquid junction, or
with a liquid junction of negligible liquid junction potential, we substitute expressions for
ÅrGand forÅrGfrom Eqs.14.3.13and Eq.14.3.15intoÅrGDÅrGCRTlnQrxn
(Eq.11.8.8on page 351 ) and solve forEcell, eq:

Ecell, eqDEcell, eq 

RT

zF

lnQrxn (14.4.1)

(no liquid junction, orEjD 0 )

Equation14.4.1is theNernst equationfor the cell reaction. HereQrxnis the reaction
quotient for the cell reaction defined by Eq.11.8.6:QrxnD

Q

ia

i
i.
The rest of this section will assume that the cell reaction takes place in a cell without
liquid junction, or in one in whichEjis negligible.
If each reactant and product of the cell reaction is in its standard state, then each activity
is unity and lnQrxnis zero. We can see from the Nernst equation that the equilibrium cell
potentialEcell, eqin this case has its standard valueEcell, eq , as expected. A decrease in
product activities or an increase in reactant activities decreases the value of lnQrxnand
increasesEcell, eq, as we would expect sinceEcell, eqshould be greater when the forward cell
reaction has a greater tendency for spontaneity.
If the cell reaction comes to reaction equilibrium, as it will if we short-circuit the cell ter-
minals with an external wire, the value ofQrxnbecomes equal to the thermodynamic equi-
librium constantK, and the Nernst equation becomesEcell, eqDEcell, eq .RT=zF /lnK.