Question

Standard electrode potentials for a few half-cells are mentioned below: 

• 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

To determine the standard cell potential \( E^0_{\text{cell}} \) for each galvanic cell, we will utilize the formula: \(E^0_{\text{cell}} = E^0_{\text{cathode}} - E^0_{\text{anode}}\). The following standard electrode potentials will be used:

Half-cell	Standard Electrode Potential (V)
\(\text{Cu}^{2+} | \text{Cu}\)	+0.34
\(\text{Zn}^{2+} | \text{Zn}\)	-0.76
\(\text{Ag}^{+} | \text{Ag}\)	+0.80
\(\text{Mg}^{2+} | \text{Mg}\)	-2.37

1. Cell: \( \text{Zn} | \text{Zn}^{2+} (1M) || \text{Ag}^+ (1M) | \text{Ag} \)

In this cell, \(\text{Ag}^+\) acts as the cathode and \(\text{Zn}\) as the anode.

\(E^0_{\text{cell}} = E^0_{\text{Ag}^+/\text{Ag}} - E^0_{\text{Zn}^{2+}/\text{Zn}}\)

\(E^0_{\text{cell}} = (+0.80) - (-0.76) = +1.56 \, \text{V}\)

1. Cell: \( \text{Zn} | \text{Zn}^{2+} (1M) || \text{Mg}^{2+} (1M) | \text{Mg} \)

Here, \(\text{Mg}^{2+}\) is the cathode and \(\text{Zn}\) is the anode.

\(E^0_{\text{cell}} = E^0_{\text{Mg}^{2+}/\text{Mg}} - E^0_{\text{Zn}^{2+}/\text{Zn}}\)

\(E^0_{\text{cell}} = (-2.37) - (-0.76) = -1.61 \, \text{V}\)

1. Cell: \( \text{Ag} | \text{Ag}^+ (1M) || \text{Mg}^{2+} (1M) | \text{Mg} \)

The cathode is \(\text{Mg}^{2+}\) and the anode is \(\text{Ag}\).

\(E^0_{\text{cell}} = E^0_{\text{Mg}^{2+}/\text{Mg}} - E^0_{\text{Ag}^+/\text{Ag}}\)

\(E^0_{\text{cell}} = (-2.37) - (+0.80) = -3.17 \, \text{V}\)

1. Cell: \( \text{Cu} | \text{Cu}^{2+} (1M) || \text{Ag}^+ (1M) | \text{Ag} \)

In this cell, \(\text{Ag}^+\) is the cathode and \(\text{Cu}\) is the anode.

\(E^0_{\text{cell}} = E^0_{\text{Ag}^+/\text{Ag}} - E^0_{\text{Cu}^{2+}/\text{Cu}}\)

\(E^0_{\text{cell}} = (+0.80) - (+0.34) = +0.46 \, \text{V}\)

The cell exhibiting the highest positive standard cell potential is \( \text{Zn} | \text{Zn}^{2+} (1M) || \text{Ag}^+ (1M) | \text{Ag} \), with a value of \(+1.56 \, \text{V}\).

The correct answer is:

\( \text{Zn} | \text{Zn}^{2+} (1M) || \text{Ag}^+ (1M) | \text{Ag} \)