For the disproportion of copper:
`2 Cu^(+) to Cu^(+2) + Cu E^(0)` is :- Given `E^(0)` for `Cu^(+2)//Cu` is 0.34 V & `E^(0)` for `Cu^(+2)//Cu^(+)` is 0.15 V:

Options

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

Answer

To solve the problem of calculating the standard cell potential (E°) for the disproportionation of copper, we will follow these steps:

### Step 1: Write the Half-Reactions
We have two half-reactions given:
1. \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \) with \( E^\circ = 0.34 \, \text{V} \) (Reduction)
2. \( \text{Cu}^{2+} + e^- \rightarrow \text{Cu}^+ \) with \( E^\circ = 0.15 \, \text{V} \) (Reduction)

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

### Step 3: Combine the Half-Reactions
Now we can add the two half-reactions together:
1. \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \) (from the first half-reaction)
2. \( \text{Cu}^+ \rightarrow \text{Cu}^{2+} + e^- \) (reversed second half-reaction)

When we add these:
\[ \text{Cu}^{2+} + 2e^- + \text{Cu}^+ \rightarrow \text{Cu} + \text{Cu}^{2+} + e^- \]
Cancelling out the common species gives:
\[ 2 \text{Cu}^+ + 2e^- \rightarrow \text{Cu}^{2+} + \text{Cu} \]

### Step 4: Calculate the Standard Cell Potential (E°)
Using the formula for the cell potential:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{reduction}} + E^\circ_{\text{oxidation}} \]
Where:
- \( E^\circ_{\text{oxidation}} \) is for \( \text{Cu}^+ \rightarrow \text{Cu}^{2+} + e^- \) which is \( -0.15 \, \text{V} \)
- \( E^\circ_{\text{reduction}} \) is for \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \) which is \( 0.34 \, \text{V} \)

So,
\[ E^\circ_{\text{cell}} = 0.34 \, \text{V} + (-0.15 \, \text{V}) = 0.34 \, \text{V} - 0.15 \, \text{V} = 0.19 \, \text{V} \]

### Step 5: Final Calculation
Thus, the standard cell potential for the disproportionation of copper is:
\[ E^\circ_{\text{cell}} = 0.19 \, \text{V} \]

### Summary
The standard cell potential for the disproportionation of copper is \( 0.19 \, \text{V} \).

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