The standard Gibbs energy of the following reaction is $-610\, kJ\, mol^{-1}$
$Mg(s) + 2Ag^+ (aq) → Mg^{2+}(aq) + 2Ag(s)$
What is the standard EMF for the cell corresponding to the above reaction?
Given: Faraday's constant = $96500\, C\, mol^{-1}$
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → +3.16 V
Use the relation between standard Gibbs energy change and standard EMF:
$\Delta G^\circ = -n F E^\circ_{\text{cell}}$
Given:
- $\Delta G^\circ = -610 \text{ kJ mol}^{-1} = -610000 \text{ J mol}^{-1}$
- n = 2 (Mg → Mg²⁺ + 2e⁻)
- $F = 96500 \text{ C mol}^{-1}$
Calculation:
$E^\circ_{\text{cell}} = \frac{-\Delta G^\circ}{nF} = \frac{610000}{2 \times 96500} \approx 3.16 \text{ V}$