`E^@` values for the half cell reactions are given below :
`Cu^(2+) + e^(-) to Cu^(+) , E^@`=0.15 V
`Cu^(2+) + 2e^(-) to Cu, E^@`=0.34 V
What will be the `E^@` of the half-cell : `Cu^(+) + e^(-) to Cu` ?

Options

A. `+0.49 V`
B. `+0.19 V`
C. `+0.53V`
D. `+0.30V`

Explanation

To find the standard electrode potential (E°) for the half-cell reaction \( \text{Cu}^+ + e^- \rightarrow \text{Cu} \), we can use the given standard electrode potentials for the other half-cell reactions involving copper.

### Step-by-Step Solution:

1. **Identify the Given Reactions and Their E° Values:**
- Reaction 1: \( \text{Cu}^{2+} + e^- \rightarrow \text{Cu}^+ \), E° = 0.15 V
- Reaction 2: \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \), E° = 0.34 V

2. **Write the Equation for the Desired Half-Cell Reaction:**
- We want to find E° for the reaction: \( \text{Cu}^+ + e^- \rightarrow \text{Cu} \).

3. **Use the Relationship Between E° Values:**
- The relationship between the E° values can be derived from the Gibbs free energy change (ΔG°) for the reactions:
\[ \Delta G° = -nFE° \]
- Here, n is the number of moles of electrons transferred, F is Faraday's constant, and E° is the standard electrode potential.

4. **Calculate ΔG° for Each Reaction:**
- For Reaction 1:
\[ \Delta G°_1 = -1 \cdot F \cdot 0.15 \]
- For Reaction 2:
\[ \Delta G°_2 = -2 \cdot F \cdot 0.34 \]

5. **Combine the Reactions:**
- To find the desired reaction, we can manipulate the two reactions:
- Reverse Reaction 1:
\[ \text{Cu}^+ \rightarrow \text{Cu}^{2+} + e^- \]
This changes the sign of E°:
\[ E° = -0.15 \, \text{V} \]
- Add this to Reaction 2:
\[ \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \]
This gives:
\[ \text{Cu}^+ + e^- \rightarrow \text{Cu} \]

6. **Calculate the E° for the Desired Reaction:**
- The E° for the desired reaction can be calculated as follows:
\[ E°_{\text{desired}} = E°_2 + E°_1 \]
\[ E°_{\text{desired}} = 0.34 - 0.15 = 0.19 \, \text{V} \]

7. **Final Result:**
- Therefore, the standard electrode potential for the half-cell reaction \( \text{Cu}^+ + e^- \rightarrow \text{Cu} \) is:
\[ E° = 0.19 \, \text{V} \]