Question

What is the standard electrode potential of the half-reaction: \[ \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \, (\text{solid})? \] Given that the standard electrode potential for the half-reaction: \[ \text{Ag}^+ + e^- \rightarrow \text{Ag} \, (\text{solid}) \quad \text{is} \, +0.80 \, \text{V}. \] Also, the cell potential for the following reaction is: \[ \text{Cu}^{2+} + 2\text{Ag} \rightarrow \text{Cu} + 2\text{Ag}^+ \] is \( 0.46 \, \text{V} \).

• A. \( 1.26 \, \text{V} \)
• B. \( 0.50 \, \text{V} \)
• C. \( 0.46 \, \text{V} \)
• D. \( 1.0 \, \text{V} \)

Hint:

The cell potential can be determined by subtracting the electrode potential of the anode from that of the cathode. For a reduction half-reaction, the standard electrode potential is positive.

Answer 1

The Correct Option is A

Provided Information:

• Standard electrode potential for \( \text{Ag}^+ + e^- \rightarrow \text{Ag (solid)} \): \( +0.80 \, \text{V} \)
• Cell potential for \( \text{Cu}^{2+} + 2 \, \text{Ag} \rightarrow \text{Cu} + 2 \, \text{Ag}^+ \): \( 0.46 \, \text{V} \)

Step 1: Apply the Cell Potential Equation

The relationship between cell potential (\( E_{\text{cell}} \)) and standard electrode potentials of half-reactions is: \[ E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}} \] where \( E_{\text{cathode}} \) is the standard electrode potential of the reduction half-reaction, and \( E_{\text{anode}} \) is the standard electrode potential of the oxidation half-reaction.

Step 2: Determine the Half-Reactions

In the reaction \( \text{Cu}^{2+} + 2 \, \text{Ag} \rightarrow \text{Cu} + 2 \, \text{Ag}^+ \): - \( \text{Cu}^{2+} \) is reduced to \( \text{Cu (solid)} \) at the cathode. - \( \text{Ag} \) is oxidized to \( \text{Ag}^+ \) at the anode. Thus: \[ E_{\text{cathode}} = E_{\text{Cu}^{2+} / \text{Cu}} \quad \text{and} \quad E_{\text{anode}} = E_{\text{Ag}^+ / \text{Ag}} \]

Step 3: Calculate \( E_{\text{Cu}^{2+} / \text{Cu}} \)

Substitute known values into the equation: \[ E_{\text{cell}} = E_{\text{Cu}^{2+} / \text{Cu}} - E_{\text{Ag}^+ / \text{Ag}} \] \[ 0.46 \, \text{V} = E_{\text{Cu}^{2+} / \text{Cu}} - 0.80 \, \text{V} \] Solve for \( E_{\text{Cu}^{2+} / \text{Cu}} \): \[ E_{\text{Cu}^{2+} / \text{Cu}} = 0.46 \, \text{V} + 0.80 \, \text{V} = 1.26 \, \text{V} \]

✅ Final Result:

The standard electrode potential for the half-reaction \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu (solid)} \) is \( \boxed{1.26 \, \text{V}} \).