If `E_(Cu^(2+)|Cu)^(@) = 0.34V` and `E_(Cu^(2+)|Cu^(+))^(@)= 0.15 V` then the value for disproportion for `Cu^(+)` is :

Options

A. `(-0.19V)`
B. `(-0.38V)`
C. `(0.94)`
D. `(0.38V)`

Explanation

To find the value for the disproportionation potential of \( Cu^+ \), we can follow these steps:

### Step 1: Understand the Disproportionation Reaction
The disproportionation reaction for \( Cu^+ \) can be represented as:
\[ 2 Cu^+ \rightarrow Cu^{2+} + Cu \]
In this reaction, \( Cu^+ \) is both oxidized to \( Cu^{2+} \) and reduced to \( Cu \).

### Step 2: Identify the Standard Electrode Potentials
From the question, we have the following standard electrode potentials:
- \( E^\circ (Cu^{2+}/Cu) = 0.34 \, V \)
- \( E^\circ (Cu^{2+}/Cu^+) = 0.15 \, V \)

### Step 3: Write the Half-Reactions
We can write the half-reactions based on the given potentials:
1. \( Cu^{2+} + 2e^- \rightarrow Cu \) with \( E^\circ = 0.34 \, V \) (Reduction)
2. \( Cu^{2+} + e^- \rightarrow Cu^+ \) with \( E^\circ = 0.15 \, V \) (Reduction)

### Step 4: Reverse the Second Half-Reaction
To find the oxidation potential of \( Cu^+ \) to \( Cu^{2+} \), we reverse the second half-reaction:
\[ Cu^+ \rightarrow Cu^{2+} + e^- \quad (E^\circ = -0.15 \, V) \]

### Step 5: Calculate the Overall Cell Potential
Now, we can combine the two half-reactions:
- The reduction of \( Cu^{2+} \) to \( Cu \) (first half-reaction)
- The oxidation of \( Cu^+ \) to \( Cu^{2+} \) (reversed second half-reaction)

The overall cell reaction is:
\[ Cu^+ + 2e^- \rightarrow Cu + Cu^{2+} \]

### Step 6: Use the Nernst Equation
The overall cell potential \( E^\circ_{cell} \) can be calculated using:
\[ E^\circ_{cell} = E^\circ_{reduction} + E^\circ_{oxidation} \]
Substituting the values:
\[ E^\circ_{cell} = 0.34 \, V + (-0.15 \, V) = 0.34 \, V - 0.15 \, V = 0.19 \, V \]

### Step 7: Calculate the Disproportionation Potential
The potential for the disproportionation of \( Cu^+ \) can be calculated as follows:
\[ E^\circ_{disproportionation} = E^\circ_{cell} = 0.19 \, V \]

### Final Answer
The value for the disproportionation potential for \( Cu^+ \) is:
\[ E^\circ_{disproportionation} = 0.19 \, V \]

---