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

Options

A. `0.184V`
B. `0.827V`
C. `0.521V`
D. `0.490V`

Explanation

To find the standard electrode potential for the half-cell reaction \( \text{Cu}^+ + e^- \rightarrow \text{Cu} \), we can use the standard reduction potentials provided for the other half-cells. Here’s a step-by-step solution:

### Step 1: Write the half-cell reactions
We have the following half-cell reactions:
1. \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \) with a standard reduction potential \( E_1 = 0.337 \, \text{V} \)
2. \( \text{Cu}^{2+} + e^- \rightarrow \text{Cu}^+ \) with a standard reduction potential \( E_2 = 0.153 \, \text{V} \)

### Step 2: Determine the reaction for \( \text{Cu}^+ + e^- \rightarrow \text{Cu} \)
To find the standard reduction potential for the half-cell \( \text{Cu}^+ + e^- \rightarrow \text{Cu} \), we can subtract the second half-cell reaction from the first.

### Step 3: Write the equation for the Gibbs free energy
The Gibbs free energy change \( \Delta G \) for a reaction can be related to the standard electrode potentials by the equation:
\[ \Delta G = -nFE \]
where \( n \) is the number of moles of electrons transferred, \( F \) is Faraday's constant, and \( E \) is the standard electrode potential.

### Step 4: Apply the Gibbs free energy relation
For the reactions:
- For the first reaction (1): \( \Delta G_1 = -2F E_1 \)
- For the second reaction (2): \( \Delta G_2 = -1F E_2 \)
- For the third reaction (3): \( \Delta G_3 = -1F E_3 \)

From the relationship:
\[ \Delta G_3 = \Delta G_1 - \Delta G_2 \]
we can substitute:
\[ -1F E_3 = -2F E_1 + 1F E_2 \]

### Step 5: Cancel out Faraday's constant and rearrange
Canceling \( F \) from both sides gives:
\[ E_3 = 2E_1 - E_2 \]

### Step 6: Substitute the known values
Now, substituting the values of \( E_1 \) and \( E_2 \):
\[ E_3 = 2(0.337 \, \text{V}) - 0.153 \, \text{V} \]
Calculating this:
\[ E_3 = 0.674 \, \text{V} - 0.153 \, \text{V} = 0.521 \, \text{V} \]

### Final Answer
The standard electrode potential for the half-cell \( \text{Cu}^+ + e^- \rightarrow \text{Cu} \) is:
\[ \boxed{0.521 \, \text{V}} \]