`Cu^(+)` ion is not stable in aqueous solution because because of dispropotionation reaction. `E^(@)` value of disproportionation of `Cu^(+)` is
`[E_(Cu^(2+)//Cu^(+))^(@)=+ 0.15 V, E_(Cu^(2+)//Cu)^(@)=0.34 V]`

Options

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

Explanation

To determine the stability of the `Cu^+` ion in aqueous solution and to calculate the `E^(@)` value for its disproportionation reaction, we can follow these steps:

### Step 1: Write the Disproportionation Reaction
The disproportionation reaction for `Cu^+` can be represented as:
\[ 2 \, Cu^+ \rightarrow Cu + Cu^{2+} \]
In this reaction, one `Cu^+` ion is reduced to `Cu`, while another `Cu^+` ion is oxidized to `Cu^{2+}`.

### Step 2: Identify the Standard Reduction Potentials
We are given the following standard reduction potentials:
- For the reduction of `Cu^{2+}` to `Cu^+`:
\[ E^0_{(Cu^{2+}/Cu^+)} = +0.15 \, V \]
- For the reduction of `Cu^{2+}` to `Cu`:
\[ E^0_{(Cu^{2+}/Cu)} = +0.34 \, V \]

### Step 3: Write the Half-Reactions
1. The reduction half-reaction for `Cu^{2+}` to `Cu^+`:
\[ Cu^{2+} + e^- \rightarrow Cu^+ \quad (E^0 = +0.15 \, V) \]
2. The oxidation half-reaction for `Cu^+` to `Cu^{2+}` (reverse the sign):
\[ Cu^+ \rightarrow Cu^{2+} + e^- \quad (E^0 = -0.15 \, V) \]

### Step 4: Calculate the Overall Cell Potential
To find the overall cell potential for the disproportionation reaction, we can add the potentials of the two half-reactions:
\[ E^0_{cell} = E^0_{reduction} + E^0_{oxidation} \]
Substituting the values:
\[ E^0_{cell} = (+0.34 \, V) + (-0.15 \, V) \]
\[ E^0_{cell} = +0.34 \, V - 0.15 \, V = +0.19 \, V \]

### Step 5: Conclusion on Stability
Since the overall cell potential for the disproportionation reaction is positive (`+0.19 V`), this indicates that the reaction is spontaneous. Therefore, the `Cu^+` ion is not stable in aqueous solution as it will tend to disproportionate into `Cu` and `Cu^{2+}`.

### Final Answer
The `Cu^+` ion is unstable in aqueous solution due to its tendency to undergo disproportionation, and the calculated standard cell potential for this reaction is `+0.19 V`.

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