The standard electrode potentials, `E^(@)` of `Fe^(3+)//Fe^(2+) and Fe^(2+)//Fe` at 300 K are `+0.77V and -0.44V`, respectively. The `E^(@)` of `Fe^(3+)//Fe` at the same temperature is

Options

A. 1.21 V
B. 0.33 V
C. `-0.036 V`
D. `0.036V`

Answer

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

### Step-by-Step Solution:

1. **Identify the given standard electrode potentials:**
- For the half-reaction \( \text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+} \), \( E^\circ_1 = +0.77 \, \text{V} \)
- For the half-reaction \( \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \), \( E^\circ_2 = -0.44 \, \text{V} \)

2. **Write the equations for the half-reactions:**
- Equation 1: \( \text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+} \) (with \( E^\circ_1 = +0.77 \, \text{V} \))
- Equation 2: \( \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \) (with \( E^\circ_2 = -0.44 \, \text{V} \))

3. **Combine the half-reactions to find the overall reaction:**
- To find \( \text{Fe}^{3+} + 3e^- \rightarrow \text{Fe} \), we can add the two half-reactions.
- First, we need to reverse Equation 2 to match the electrons:
\[ \text{Fe} \rightarrow \text{Fe}^{2+} + 2e^- \quad (E^\circ = +0.44 \, \text{V}) \]
- Now, we can add Equation 1 and the reversed Equation 2:
\[ \text{Fe}^{3+} + e^- + \text{Fe} \rightarrow \text{Fe}^{2+} + 2e^- + \text{Fe} \]
- This simplifies to:
\[ \text{Fe}^{3+} + 3e^- \rightarrow \text{Fe} \]

4. **Calculate the standard electrode potential \( E^\circ_3 \):**
- The relationship for the standard electrode potential when combining reactions is given by:
\[ E^\circ_3 = E^\circ_1 + E^\circ_2 \]
- Since we reversed Equation 2, we take the positive value:
\[ E^\circ_3 = E^\circ_1 + E^\circ_2 = 0.77 \, \text{V} + (-0.44 \, \text{V}) = 0.77 \, \text{V} - 0.44 \, \text{V} = 0.33 \, \text{V} \]

5. **Final Result:**
- The standard electrode potential \( E^\circ \) for the half-reaction \( \text{Fe}^{3+} + 3e^- \rightarrow \text{Fe} \) is \( +0.33 \, \text{V} \).