`(CU^(+) ((aq))` is unstable in solution and undergoes simultaneous oxidation and reduction, according to the reaction
`2Cu_((aq))^(+)` `Cu_((aq))^(2+) +Cu_((s))` choose `E^(@)` for the above reaction if
`E_(Cu^(2+)//Cu^(@))= 0.34V` and `E_(Cu^(2+)//Cu^(+) )= 0.15V`

Options

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

Explanation

To find the standard cell potential \( E^\circ \) for the reaction

\[ 2 \text{Cu}^+ \rightarrow \text{Cu}^{2+} + \text{Cu} \]

we will follow these steps:

### Step 1: Identify the half-reactions and their standard potentials
The half-reactions involved are:

1. Reduction of copper(II) ion to copper:
\[ \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \quad E^\circ = 0.34 \, \text{V} \]

2. Reduction of copper(II) ion to copper(I) ion:
\[ \text{Cu}^{2+} + e^- \rightarrow \text{Cu}^+ \quad E^\circ = 0.15 \, \text{V} \]

### Step 2: Write the oxidation half-reaction
The oxidation half-reaction for the conversion of copper(I) to copper(II) is:
\[ \text{Cu}^+ \rightarrow \text{Cu}^{2+} + e^- \]

### Step 3: Determine the standard potential for the oxidation half-reaction
The standard potential for the oxidation half-reaction can be calculated from the reduction potential:
\[ E^\circ_{\text{oxidation}} = -E^\circ_{\text{reduction}} = -0.15 \, \text{V} \]

### Step 4: Calculate the overall cell potential
The overall cell reaction involves the reduction of copper(II) to copper and the oxidation of copper(I) to copper(II):
\[ 2 \text{Cu}^+ \rightarrow \text{Cu}^{2+} + \text{Cu} \]

Using the formula for the cell potential:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \]

Where:
- \( E^\circ_{\text{cathode}} = 0.34 \, \text{V} \) (reduction of Cu\(^{2+}\) to Cu)
- \( E^\circ_{\text{anode}} = 0.15 \, \text{V} \) (oxidation of Cu\(^{+}\) to Cu\(^{2+}\))

Substituting the values:
\[ E^\circ_{\text{cell}} = 0.34 \, \text{V} - 0.15 \, \text{V} = 0.19 \, \text{V} \]

### Final Answer
The standard cell potential \( E^\circ \) for the reaction is:
\[ E^\circ = 0.19 \, \text{V} \]