CHEMISTRY TEXTBOOK

5.8 Thermodynamics of galvanic cells

5.8.1 Gibbs energy of cell reactions and
cell potential : The electrical work done in a
galvanic cell is the electricity (charge) passed
multiplied by the cell potential.

Electrical work
= amount of charge passed × cell potential.

Charge of one mole electrons is F
coulombs. For the cell reaction involving n
moles of electrons.

charge passed = nF coulombs
Hence, electrical work = nFEcell
W. Gibbs in 1878 concluded that
electrical work done in galvanic cell is equal
to the decrease in Gibbs energy, - ∆G, of cell
reaction. It then follows that

Electrical work = - ∆G

and thus - ∆G = nFEcell

or ∆G = -nFEcell (5.27)

Under standard state conditions, we write

∆G^0 = -nFE^0 cell (5.28)

The Eq. (5.28) explains why E^0 cell is an
intensive property.

We know that ∆G^0 is an extensive
property since its value depends on the
amount of substance. If the stoichiometric
equation of redox reaction is multiplied by
2 that is the amounts of substances oxidised
and reduced are doubled, ∆G^0 doubles. The
moles of electrons transferred also doubles.
The ratio,

E^0 cell = -

∆G^0

nF

then becomes

E^0 cell = -

2∆G^0

2 nF

= -

∆G^0

nF

Thus, E^0 cell remains the same by
multiplying the redox reaction by 2. It
means E^0 cell is independent of the amount of
substance and the intensive property.

5.8.2 Standard cell potential and equilibrium

constant : The relation between standard

Gibbs energy change of cell reaction and

standard cell potential is given by Eq. (5.27).

• ∆G^0 = nFE^0 cell
  The relation between standard Gibbs
  energy change of a chemical reaction
  and its equilibrium constant as given in
  thermodynamics is :
  ∆G^0 = - RT ln K^ (5.29)
  Combining Eq. (5.28) and Eq. (5.29), we
  have


• nFE^0 cell = - RT ln K

or E^0 cell =

RT

nF

ln K

= 2.303 RT

nF

log 10 K

=

0.0592

n

log 10 K at 25^0 C

(5.29)

Remember...

For chemical reaction to be

spontaneous, ∆G must be negative.

Because ∆G = - nFEcell, Ecell must be positive

for a cell reaction if it is spontaneous.

Try this...

Write expressions to calculate

equilibrium constant from

i. Concentration data

ii. Thermochemical data

iii. Electrochemical data