Question

Standard electrode potentials for a few half-cells are mentioned below: \[ \begin{array}{|c|c|} \hline \text{Half-cell} & \text{Standard Electrode Potential}
\hline \text{Cu}^{2+} / \text{Cu} & +0.34 \, \text{V}
\text{Zn}^{2+} / \text{Zn} & -0.76 \, \text{V}
\text{Ag}^+ / \text{Ag} & +0.80 \, \text{V}
\text{Mg}^{2+} / \text{Mg} & -2.37 \, \text{V}
\hline \end{array} \] Which one of the following cells gives the most negative value of \( \Delta G^\circ \)?

• A. \( \text{Zn} | \text{Zn}^{2+} (1M) || \text{Ag}^+ (1M) | \text{Ag} \)
• B. \( \text{Zn} | \text{Zn}^{2+} (1M) || \text{Mg}^{2+} (1M) | \text{Mg} \)
• C. \( \text{Ag} | \text{Ag}^+ (1M) || \text{Mg}^{2+} (1M) | \text{Mg} \)
• D. \( \text{Cu} | \text{Cu}^{2+} (1M) || \text{Ag}^+ (1M) | \text{Ag} \)

Hint:

To determine the cell with the most negative \( \Delta G^\circ \), consider the cell with the largest difference in standard electrode potentials, where the anode has the most negative \( E^\circ \) and the cathode has the most positive \( E^\circ \).

Answer 1

The Correct Option is A

The standard Gibbs free energy change \( \Delta G^\circ \) is related to the standard electrode potential \( E^\circ \) by: \[ \Delta G^\circ = -n F E^\circ, \] where \( n \) is the number of electrons involved and \( F \) is Faraday's constant. The cell with the most negative \( \Delta G^\circ \) corresponds to the most positive \( E^\circ \). The cell that gives the most negative value of \( \Delta G^\circ \) is the one with the highest \( E^\circ \) for the cathode and lowest for the anode, which is option (1).