# Cell Potential and Free Energy Example Problem

Cell potentials are measured in volts or energy per unit charge. This energy can be related to the theoretical maximum free energy or Gibbs free energy of the total redox reaction driving the cell.

### Problem

For the following reaction:

Cu(s) + Zn2+(aq) ↔ Cu2+(aq) + Zn(s)

a. Calculate ΔG°.

b. Will zinc ions plate out onto the solid copper in the reaction?

### Solution

Free energy is related to cell EMF by the formula:

ΔG° = -nFE0cell

where

ΔG° is the free energy of the reaction

n is the number of moles of electrons exchanged in the reaction

F is Faraday's constant (9.648456 x 104 C/mol)

E0cell is the cell potential.​

Step 1: Break the redox reaction into oxidation and reduction half-reactions.

Cu → Cu2+ + 2 e- (oxidation)

Zn2+ + 2 e- → Zn (reduction)

Step 2: Find the E0cell of the cell.

Cu → Cu2+ + 2 e- E0 = -0.3419 V

Zn2+ + 2 e- → Zn E0 = -0.7618 V

E0cell = E0reduction + E0oxidation

E0cell = -0.4319 V + -0.7618 V

E0cell = -1.1937 V

Step 3: Find ΔG°.

There are 2 moles of electrons transferred in the reaction for every mole of reactant, therefore n=2.

Another important conversion is 1 volt = 1 Joule/Coulomb

ΔG° = -nFE0cell

ΔG° = -(2 mol)(9.648456 x 104 C/mol)(-1.1937 J/C)

ΔG° = 230347 J or 230.35 kJ

The zinc ions will plate out if the reaction is spontaneous. Since ΔG° > 0, the reaction is not spontaneous and the zinc ions will not plate out onto the copper at standard conditions.

### Answer

a. ΔG° = 230347 J or 230.35 kJ

b. Zinc ions will not plate out onto the solid copper.