The standard reduction potentials of `Cu^(2+)//Cu` and `Cu^(2+)//Cu^(+)` are 0.337 V and 0.153V respectively. The standard electrode potential of `Cu^(+)//Cu` half-cell is

Options

A. 1.184V
B. 0.827V
C. 0.521V
D. 0.490V

Answer

To find the standard electrode potential of the half-cell reaction `Cu^+ // Cu`, we can use the given standard reduction potentials for the half-cells `Cu^2+ // Cu` and `Cu^2+ // Cu^+`.

### Step-by-Step Solution:

1. **Identify the Given Potentials**:
- The standard reduction potential for `Cu^2+ + 2e^- → Cu` is \( E_1 = 0.337 \, V \).
- The standard reduction potential for `Cu^2+ + e^- → Cu^+` is \( E_2 = 0.153 \, V \).

2. **Write the Reactions**:
- For the first reaction:
\[ Cu^{2+} + 2e^- \rightarrow Cu \quad (E_1 = 0.337 \, V) \]
- For the second reaction:
\[ Cu^{2+} + e^- \rightarrow Cu^+ \quad (E_2 = 0.153 \, V) \]

3. **Determine the Reaction for `Cu^+ // Cu`**:
- We want to find the standard reduction potential for the reaction:
\[ Cu^+ + e^- \rightarrow Cu \quad (E_3) \]

4. **Use Gibbs Free Energy Relationship**:
- The Gibbs free energy change for a reaction is related to the standard electrode potential by the equation:
\[ \Delta G = -nFE \]
- For the first reaction (2 electrons), the Gibbs free energy change is:
\[ \Delta G_1 = -2F \cdot E_1 = -2F \cdot 0.337 \]
- For the second reaction (1 electron), the Gibbs free energy change is:
\[ \Delta G_2 = -1F \cdot E_2 = -1F \cdot 0.153 \]

5. **Combine the Reactions**:
- To find \( E_3 \), we can use the relationship:
\[ \Delta G_3 = \Delta G_1 - \Delta G_2 \]
- Substituting the Gibbs free energy changes:
\[ \Delta G_3 = (-2F \cdot 0.337) - (-1F \cdot 0.153) \]
- Simplifying gives:
\[ \Delta G_3 = -2F \cdot 0.337 + F \cdot 0.153 \]

6. **Calculate \( E_3 \)**:
- Since \( \Delta G_3 = -F \cdot E_3 \), we can set up the equation:
\[ -F \cdot E_3 = -2F \cdot 0.337 + F \cdot 0.153 \]
- Dividing through by \( -F \) (and canceling \( F \)):
\[ E_3 = 2 \cdot 0.337 - 0.153 \]
- Now calculate:
\[ E_3 = 0.674 - 0.153 = 0.521 \, V \]

7. **Final Answer**:
- The standard electrode potential for the half-cell reaction `Cu^+ // Cu` is \( E_3 = 0.521 \, V \).