In a common car battery, six identical cells each carry out the following reaction:
Pb + PbO₂ + 2HSO₄^- + 2H⁺ → 2PbSO₄ + 2H₂O
For such a cell, E° is 2.04 V. Calculate ΔG° at 25°C.

Question

In a common car battery, six identical cells each carry out the following reaction: Pb + PbO₂ + 2HSO₄^- + 2H⁺ → 2PbSO₄ + 2H₂O For such a cell, E° is 2.04 V. Calculate ΔG° at 25°C.

Quizplus · Accepted Answer

The formula to calculate ΔG° for a redox reaction based on E° is:

ΔG° = -nF E°

where n is the number of electrons exchanged in the reaction, F is the Faraday constant (96,485 C/mol), and E° is the standard reduction potential.

In this case, n = 2 since two electrons are exchanged in the reaction, and E° = 2.04 V. Therefore:

ΔG° = -2 x 96,485 C/mol x 2.04 V

ΔG° = -39,355 J/mol

To convert J/mol to kJ (as given in the answer choices), divide by 1000:

ΔG° = -39.355 kJ/mol

Since the reaction involves the oxidation of lead and the reduction of lead oxide, which are both solids, we can assume that their concentrations do not change during the reaction. Therefore, the standard state concentrations for the solids are 1 mol/L, and the activity of the solids is 1. Therefore, the value of ΔG° is the same as the value of the Gibbs free energy change under standard conditions. The answer is closest to -394 kJ, choice C.

In a Common Car Battery, Six Identical Cells Each Carry