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Since the cell voltage
E0 determines if the reaction in a cell is spontaneous
or not, if clearly must be related to the DG, the change in the Gibbs free energy. The relationship
is
- DG = -nFE
where n is the number of
electrons that are exchanged during the balanced
redox reaction and F is the Faraday constant, 9.648*104 C/mol =
9.648*104 J/mol*V. At standard concentrations at 25oC,
this equation can be written as
- DG0 = -nFE0
Example: What is DG0 for the
reaction below?
- Cu(s) + 2Fe+3(aq) -> Cu+2(aq) +
2Fe+2(aq)
Solution: To determine , DG0 we
need to determine the voltage. Break the reaction up into two half reactions and
check the voltages of each
- Cu(s) -> Cu+2 + 2e- Eox =
-0.339 V
- Fe+3(aq) +e- -> Fe+2(aq)
Eox = +0.769 V
The cell voltage is thus E = Ered
+ Eox = -0.339 + 0.769 = +0.43 V.
In the balanced redox reaction, two electrons are exchanged- copper goes from
0 to +2 charge, and two iron ions gain 1 electron each. Thus, n=2. We can now
just plug in
- DG0 = -nFE0
- DG0 =
-2*9.648*104J/(mol*V)*0.43 V
- DG0 = -8.30*104 J/mol =
-83 kJ/mol
The reaction is spontaneous with a large value of
DG0. |