PHYSICAL CHEMISTRY IN BRIEF

CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 400

whereaiis the activity of substancei. Relation (11.111) is called theNernst equationfor
the equilibrium cell potential (electromotive force of the cell). The quantityE◦is called the
standard equilibrium cell potential. It is the potential of a cell in which reaction (11.110)
proceeds with the activities of all substances involved in the reaction being equal to one.
If the cell is in the state of thermodynamic equilibrium,E= 0 and we write

E◦=

RT

zF

lnK , (11.112)

whereKis the equilibrium constant of the reaction (11.110).

Note: For the activities of solids acting in the Nernst equation we choose the standard

state of a pure substance at the temperature and pressure of the system—thenai= 1.

For the activities of ions we choose the standard state of unit molality—thenai=miγ±[m].

For the activity of gaseous substances we choose the standard state of an ideal gas at a

given temperature and the pressurepst= 101 325 Pa—thenai=fi/pst.

Relation (11.111) applies on condition that the cell diffusion potential,Ed, is zero (either
the electrodes share an electrolyte or the diffusion potential is suppressed, e.g. by a salt bridge).
If it is not so, then

E=E◦−

RT

zF

ln

arRasS...

aaAabB...

+Ed. (11.113)

11.8.5 Electromotive force and thermodynamic quantities

From the relation between the cell potential and the reaction Gibbs energy (11.109) we have the
following relations for the reaction enthalpy ∆rH, the reaction entropy ∆rS, and the reaction
isobaric heat capacity ∆rCp

∆rH = zF



T

(

∂E

∂T

)

p

−E



, (11.114)

∆rS = zF

(

∂E

∂T

)

p

, (11.115)

∆rCp = zFT

(

∂^2 E

∂T^2

)

p

. (11.116)