Question

What is the standard electrode potential at 298 K for the reaction:
\[ \text{Cu}^{2+} + \text{e}^- \rightarrow \text{Cu}^+ \] Given: \( E^0_{\text{Cu}^{+}/\text{Cu}} = 0.5 \, \text{V} \) and \( E^0_{\text{Cu}^{2+}/\text{Cu}} = 0.335 \, \text{V} \)

• A. 0.34 V
• B. 0.17 V
• C. 0.492 V
• D. 0.410 V

Hint:

When calculating electrode potentials, remember that the Nernst equation takes into account both the concentration of the ions involved and the temperature, which may affect the cell potential.

Answer 1

The Correct Option is B

Step 1: Understand the relationship between electrode potentials.
The electrode potential for the given reaction can be determined by using the formula derived from the Nernst equation:
\[ E = E^0 - \frac{0.0591}{n} \log \left( \frac{[\text{Cu}^{2+}]}{[\text{Cu}^+]} \right). \]
Here, \( n = 1 \) because the reaction involves the transfer of one electron.

Step 2: Use the known values to calculate the electrode potential.
The given standard electrode potentials are for the half-reactions:
- \( E^0_{\text{Cu}^{2+}/\text{Cu}} = 0.335 \, \text{V} \),
- \( E^0_{\text{Cu}^{+}/\text{Cu}} = 0.5 \, \text{V} \).
Now, using the relationship between these potentials, we can calculate the potential for the given reaction:
\[ E^0_{\text{Cu}^{2+}/\text{Cu}^+} = E^0_{\text{Cu}^{+}/\text{Cu}} - E^0_{\text{Cu}^{2+}/\text{Cu}} = 0.5 - 0.335 = 0.17 \, \text{V}. \]

Step 3: Conclusion.
The standard electrode potential for the reaction is 0.17 V, so the correct answer is option (B).