If `E^(c-)._(Fe^(3+)|Fe)` and `E^(c-)._(Fe^(2+)|Fe)` are `=-0.36 V` and `-0.439V`, respectively, then the value of `E^(c-)._(Fe^(3+)|Fe^(2+))`

Options

A. `3x_(2)-2x_(1)`
B. `x_(2)-x_(1)`
C. `x_(2)+x_(1)`
D. `2x_(2)+3x_(2)`

Explanation

To solve the problem of finding the standard electrode potential \( E^{\circ}_{Fe^{3+}/Fe^{2+}} \) given the values of \( E^{\circ}_{Fe^{3+}/Fe} \) and \( E^{\circ}_{Fe^{2+}/Fe} \), we can follow these steps:

### Step-by-Step Solution:

1. **Write down the given values:**
- \( E^{\circ}_{Fe^{3+}/Fe} = -0.36 \, V \)
- \( E^{\circ}_{Fe^{2+}/Fe} = -0.439 \, V \)

2. **Identify the half-reactions:**
- For the reduction of \( Fe^{3+} \) to \( Fe \):
\[ Fe^{3+} + 3e^- \rightarrow Fe \]
- For the reduction of \( Fe^{2+} \) to \( Fe \):
\[ Fe^{2+} + 2e^- \rightarrow Fe \]

3. **Write the equation for the desired reaction:**
- We want to find the potential for the reaction:
\[ Fe^{3+} + e^- \rightarrow Fe^{2+} \]

4. **Use the relationship between the potentials:**
- The relationship between the standard electrode potentials can be expressed as:
\[ E^{\circ}_{Fe^{3+}/Fe^{2+}} = E^{\circ}_{Fe^{3+}/Fe} - E^{\circ}_{Fe^{2+}/Fe} \]

5. **Substitute the known values:**
- Substitute the given values into the equation:
\[ E^{\circ}_{Fe^{3+}/Fe^{2+}} = (-0.36 \, V) - (-0.439 \, V) \]

6. **Calculate the result:**
- Perform the calculation:
\[ E^{\circ}_{Fe^{3+}/Fe^{2+}} = -0.36 \, V + 0.439 \, V = 0.079 \, V \]

### Final Answer:
\[ E^{\circ}_{Fe^{3+}/Fe^{2+}} = 0.079 \, V \]

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