`Cu^(2+)(aq.)` is unstable in solution and under goes simultaneous oxidation and reduction according to the reaction
`2Cu^(+)(aq.)hArr Cu^(2+)(aq.)+Cu(s)`
Choose the correct `E^(@)` for the above reaction if
`E_(Cu^(2+))^(@)//Cu = 0.34 V and E_(Cu^(2+))^(@)//Cu^(+) = 0.15 V`

Options

A. `-0.38 V`
B. `+0.49 V`
C. `+0.38 V`
D. `+0.19 V`

Explanation

To solve the problem, we need to determine the standard electrode potential (E°) for the reaction:

\[ 2Cu^+(aq) \rightleftharpoons Cu^{2+}(aq) + Cu(s) \]

We are given the following standard electrode potentials:
- \( E^\circ_{Cu^{2+}/Cu} = 0.34 \, V \)
- \( E^\circ_{Cu^{2+}/Cu^+} = 0.15 \, V \)

### Step 1: Write the half-reactions

1. The reduction half-reaction for \( Cu^{2+} \) to \( Cu^+ \):
\[ Cu^{2+} + 2e^- \rightarrow Cu^+ \quad (E^\circ = 0.15 \, V) \]

2. The oxidation half-reaction for \( Cu^+ \) to \( Cu \):
\[ Cu^+ + e^- \rightarrow Cu \quad (E^\circ = 0.34 \, V) \]

### Step 2: Reverse the oxidation half-reaction

To find the standard potential for the oxidation of \( Cu^+ \) to \( Cu^{2+} \), we reverse the first half-reaction:
\[ Cu^+ \rightarrow Cu^{2+} + e^- \quad (E^\circ = -0.15 \, V) \]

### Step 3: Combine the half-reactions

Now, we can add the two half-reactions together. The overall reaction will be:
\[ 2Cu^+ \rightarrow Cu^{2+} + Cu \]

### Step 4: Calculate the standard electrode potential for the overall reaction

To find the standard electrode potential for the overall reaction, we use the formula:
\[ E^\circ_{cell} = E^\circ_{reduction} - E^\circ_{oxidation} \]

Substituting the values we have:
\[ E^\circ_{cell} = E^\circ_{Cu^{2+}/Cu^+} - E^\circ_{Cu^+/Cu} \]
\[ E^\circ_{cell} = 0.15 \, V - 0.34 \, V \]
\[ E^\circ_{cell} = -0.19 \, V \]

### Step 5: Finalize the answer

The standard electrode potential for the reaction \( 2Cu^+ \rightleftharpoons Cu^{2+} + Cu \) is:
\[ E^\circ = -0.19 \, V \]

### Summary of the steps:
1. Write the half-reactions for the reduction and oxidation processes.
2. Reverse the oxidation half-reaction to find its potential.
3. Combine the half-reactions to form the overall reaction.
4. Calculate the standard electrode potential for the overall reaction using the potentials of the half-reactions.