Given that the standard oxidation potentials `(E^0)` of `A|A^(+3)` and `A^(+1)|a^(+3)` are 0.20V and -0.40V respectively, the `E^0` of `A^+//A` is

Options

A. -1.40V
B. -0.20V
C. -0.6
D. +0.20V

Explanation

To solve the problem, we need to find the standard oxidation potential \( E^0 \) for the half-reaction \( A^+ \rightarrow A \) given the standard oxidation potentials for the reactions \( A \rightarrow A^{+3} + 3e^- \) and \( A^{+1} \rightarrow A^{+3} + 2e^- \).

### Step-by-Step Solution:

1. **Identify the Given Potentials:**
- For the reaction \( A \rightarrow A^{+3} + 3e^- \), the standard oxidation potential \( E^0_1 = 0.20 \, \text{V} \).
- For the reaction \( A^{+1} \rightarrow A^{+3} + 2e^- \), the standard oxidation potential \( E^0_2 = -0.40 \, \text{V} \).

2. **Write the Reactions:**
- Reaction 1: \( A \rightarrow A^{+3} + 3e^- \) (with \( E^0_1 = 0.20 \, \text{V} \))
- Reaction 2: \( A^{+1} \rightarrow A^{+3} + 2e^- \) (with \( E^0_2 = -0.40 \, \text{V} \))

3. **Reverse Reaction 1 to Find \( E^0 \) for \( A^{+3} \rightarrow A \):**
- When we reverse Reaction 1, we get:
\[ A^{+3} + 3e^- \rightarrow A \quad (E^0 = -0.20 \, \text{V}) \]

4. **Combine Reactions to Find \( E^0 \) for \( A^{+1} \rightarrow A \):**
- We can express the desired reaction \( A^{+1} \rightarrow A \) by manipulating the two reactions:
- From Reaction 2: \( A^{+1} \rightarrow A^{+3} + 2e^- \) (with \( E^0_2 = -0.40 \, \text{V} \))
- From the reversed Reaction 1: \( A^{+3} + 3e^- \rightarrow A \) (with \( E^0 = -0.20 \, \text{V} \))

5. **Add the Reactions:**
- To find the reaction \( A^{+1} \rightarrow A \):
\[ A^{+1} \rightarrow A^{+3} + 2e^- \quad (E^0_2 = -0.40 \, \text{V}) \]
\[ A^{+3} + 3e^- \rightarrow A \quad (E^0 = -0.20 \, \text{V}) \]
- When we add these two reactions, we need to cancel out \( A^{+3} \):
\[ A^{+1} + e^- \rightarrow A \quad (E^0_3 = E^0_2 + E^0_1) \]

6. **Calculate \( E^0 \) for \( A^{+1} \rightarrow A \):**
- Using the values:
\[ E^0_3 = (-0.40 \, \text{V}) + (-0.20 \, \text{V}) = -0.60 \, \text{V} \]

7. **Final Calculation for \( E^0 \) of \( A^{+1} \rightarrow A \):**
- The final value for \( E^0 \) for the half-reaction \( A^{+1} \rightarrow A \) is:
\[ E^0 = -0.60 \, \text{V} \]

### Final Answer:
The standard oxidation potential \( E^0 \) of \( A^+ // A \) is \( -0.60 \, \text{V} \).