The standard reduction potentials of `Cu^(2+)|Cu` and `Cu^(2+)|Cu^(o+)` are `0.337V` and `0.153V`, respectively. The standard electrode potential fo `Cu^(o+)|Cu` half cell in Volts is

Options

A. 1.184
B. 0.82
C. 0.521
D. 0.490

Explanation

To find the standard electrode potential for the half-cell reaction \( Cu^{+} | Cu \), we will follow these steps:

### Step 1: Write down the given standard reduction potentials
We are given:
- \( E^\circ (Cu^{2+} | Cu) = 0.337 \, V \)
- \( E^\circ (Cu^{2+} | Cu^{+}) = 0.153 \, V \)

### Step 2: Identify the half-cell reactions
1. For the first half-cell reaction:
\[ Cu^{2+} + 2e^- \rightarrow Cu \quad (E^\circ = 0.337 \, V) \]

2. For the second half-cell reaction:
\[ Cu^{2+} + e^- \rightarrow Cu^{+} \quad (E^\circ = 0.153 \, V) \]

### Step 3: Write the reaction for \( Cu^{+} | Cu \)
We want to find the standard reduction potential for the half-cell reaction:
\[ Cu^{+} + e^- \rightarrow Cu \quad (E^\circ = ?) \]

### Step 4: Use the relationship between the half-cell potentials
To find \( E^\circ (Cu^{+} | Cu) \), we can relate it to the other two half-cell reactions. We can derive it using the following relationship:
\[ E^\circ (Cu^{2+} | Cu) = E^\circ (Cu^{2+} | Cu^{+}) + E^\circ (Cu^{+} | Cu) \]

### Step 5: Rearranging the equation
Rearranging the equation gives us:
\[ E^\circ (Cu^{+} | Cu) = E^\circ (Cu^{2+} | Cu) - E^\circ (Cu^{2+} | Cu^{+}) \]

### Step 6: Substitute the values
Now, substituting the known values:
\[ E^\circ (Cu^{+} | Cu) = 0.337 \, V - 0.153 \, V \]

### Step 7: Calculate the value
Calculating the above expression:
\[ E^\circ (Cu^{+} | Cu) = 0.337 - 0.153 = 0.184 \, V \]

### Step 8: Conclusion
Thus, the standard electrode potential for the half-cell \( Cu^{+} | Cu \) is:
\[ E^\circ (Cu^{+} | Cu) = 0.184 \, V \]