Calculate the values of ΔG⁰ and K_eq for a copper / zinc voltaic cell at 25°C.

Data: E⁰ [Cu²⁺/Cu] = 0.340 V

E⁰ [Zn²⁺/Zn] = - 0.763 V

Question

Calculate the values of ΔG⁰ and K_eq for a copper / zinc voltaic cell at 25°C.

Data: E⁰ [Cu²⁺/Cu] = 0.340 V

E⁰ [Zn²⁺/Zn] = - 0.763 V

| General Chemistry 3

Accepted Answer

According to E⁰ values: copper preferentially reduced, zinc oxidized

Cu²⁺ (aq) + 2 e^- → Cu (s) (reduction à cathode)

Zn (s) → Zn²⁺ (aq) + 2 e^- (oxidation à anode)

ΔG⁰ = - ν_eFE_cell⁰

ν_e = stoichiometric coefficient of the electrons in the 2 half reaction equations = 2

F = Faraday’s constant = 96485 C.mol^-1

E_cell⁰ = electromotive force emf of the cell (in V)

E_cell⁰ = E⁰ (reduction) - E⁰ (oxydation)

E_cell⁰ = 0.340 – (-0.763) = 1.10 V

ΔG⁰ = - ν_eFE_cell⁰ = - 2 x 96485 x 1.10 = -212 kJ.mol^-1

ln K_eq = $\frac{ν_{e} F}{RT}$ E⁰_cell

K_eq = equilibrium constant

ν_e = stoichiometric coefficient of the electrons in the 2 half reaction equations = 2

F = Faraday’s constant = 96485 C.mol^-1

E⁰_cell = standard cell voltage (in V) = 1.10 V

R = ideal gas constant = 8.314 J.mol^-1.K^-1

T = temperature (in K) = 298 K

ln K_eq = $\frac{2 \times 96485 \times 1.10}{8.314 \times 298}$ = 85.7

K_eq = exp (85.7) = 1.61 x 10³⁷

Final - Question 2 | General Chemistry 3