Given, standard electrode potentials,
`{:(Fe^(3+)+3e^(-) rarr Fe,,,E^(@) = -0.036 " volt"),(Fe^(2+)+2e^(-)rarr Fe,,,E^(@) = - 0.440 " volt"):}`
The standard electrode potential `E^(@)` for `Fe^(3+) + e^(-) rarr Fe^(2+)` is :

Options

A. `-0.476 "volt"`
B. `-0.404 "volt"`
C. `0.440 "volt"`
D. `-0.772 "volt"`

Explanation

To find the standard electrode potential \( E^\circ \) for the reaction \( \text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+} \), we can use the given standard electrode potentials for the half-reactions involving iron.

### Step-by-Step Solution:

1. **Identify the Given Reactions and Their Potentials:**
- The first reaction is:
\[ \text{Fe}^{3+} + 3e^- \rightarrow \text{Fe} \quad E^\circ_1 = -0.036 \, \text{V} \]
- The second reaction is:
\[ \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \quad E^\circ_2 = -0.440 \, \text{V} \]

2. **Write the Desired Reaction:**
- We want to find the standard electrode potential for:
\[ \text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+} \]

3. **Reverse the Second Reaction:**
- To find the potential for the desired reaction, we need to reverse the second reaction:
\[ \text{Fe} \rightarrow \text{Fe}^{2+} + 2e^- \quad E^\circ = +0.440 \, \text{V} \]

4. **Combine the Reactions:**
- Now we can combine the first reaction and the reversed second reaction:
- First reaction:
\[ \text{Fe}^{3+} + 3e^- \rightarrow \text{Fe} \]
- Reversed second reaction:
\[ \text{Fe} \rightarrow \text{Fe}^{2+} + 2e^- \]
- Adding these reactions together:
\[ \text{Fe}^{3+} + 3e^- + \text{Fe} \rightarrow \text{Fe} + \text{Fe}^{2+} + 2e^- \]
- Canceling the common species (Fe):
\[ \text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+} \]

5. **Calculate the Standard Electrode Potential \( E^\circ \):**
- The overall standard electrode potential can be calculated using the formula:
\[ E^\circ = E^\circ_1 + E^\circ_2 \]
- Here, \( E^\circ_1 = -0.036 \, \text{V} \) and \( E^\circ_2 = +0.440 \, \text{V} \):
\[ E^\circ = (-0.036) + (0.440) = 0.404 \, \text{V} \]

### Final Answer:
The standard electrode potential \( E^\circ \) for the reaction \( \text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+} \) is:
\[ E^\circ = 0.404 \, \text{V} \]