What is the cell potential for this cell at 25 °C when [Zn²⁺] = 0.0143 M and [Cr³⁺] = 0.1556 M?

Question

Consider a galvanic electrochemical cell constructed using Cr/Cr³⁺ and Zn/Zn²⁺ at 25 °C. The following half-reactions are provided for each metal: Cr³⁺(aq) + 3 e⁻ → Cr(s) E°red = -0.744 V Zn²⁺(aq) + 2 e⁻ → Zn(s) E°red = -0.763 V Given that the standard cell potential is 0.019 V and the overall equation is 2 Cr³⁺ (aq) + 3 Zn (s) → 2 Cr (s) + 3 Zn²⁺ (aq), what is the cell potential for this cell at 25 °C when [Zn²⁺] = 0.0143 M and [Cr³⁺] = 0.1556 M?

Answer 1

As with you previous question, use the Arrhenius equation:

Ecell = Eºcell - 0.0592/n log Q

2 Cr³⁺ (aq) + 3 Zn (s) → 2 Cr (s) + 3 Zn²⁺ (aq)

Ecell = ?

Eºcell = 0.019 V

n = 6 moles electrons

Q = [Zn²⁺]³ / [Cr³⁺]² = (0.0143)³ / (0.1556)² = 1.208x10^-4

Plug in values and solve for Ecell

Ecell = 0.019 - 0.0592/6 log 1.208x10^-4

Ecell = 0.019 - 0.009867 x -3.92

Ecell = 0.019 + 0.0387

Ecell = 0.0577 V

(be sure to check all of the math)