A solution contains `Fe^(2+), Fe^(3+)` and `T^(-)` ions. This solution was treated with iodine at `35^(@)C. E^(@)` for `Fe^(3+), Fe^(2+)` is `0.77 V` and `E^(@)` for `I_(2)//2I^(-)` = 0.536 V. The favourable redox reaction is:

Options

A. `Fe^(2+)` will be oxidized to `Fe^(3+)`
B. `I_(2)` will be the reduced to `I^(-)`
C. There will be no redox reaction
D. `I^(-)` will be oxidized to `I_(2)`

Explanation

To determine the favorable redox reaction in a solution containing \( \text{Fe}^{2+}, \text{Fe}^{3+}, \) and \( \text{I}^- \) ions, we will analyze the given standard reduction potentials and identify the reactions that can occur.

### Step-by-Step Solution:

1. **Identify the half-reactions and their standard potentials:**
- The reduction of \( \text{Fe}^{3+} \) to \( \text{Fe}^{2+} \):
\[ \text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+} \quad E^\circ = 0.77 \, \text{V} \]
- The reduction of \( \text{I}_2 \) to \( \text{I}^- \):
\[ \text{I}_2 + 2e^- \rightarrow 2\text{I}^- \quad E^\circ = 0.536 \, \text{V} \]

2. **Determine the oxidation half-reaction for iodine:**
- The oxidation of \( \text{I}^- \) to \( \text{I}_2 \):
\[ 2\text{I}^- \rightarrow \text{I}_2 + 2e^- \quad E^\circ = -0.536 \, \text{V} \]

3. **Set up the overall redox reaction:**
- The overall reaction involves \( \text{Fe}^{3+} \) being reduced to \( \text{Fe}^{2+} \) and \( \text{I}^- \) being oxidized to \( \text{I}_2 \).
- The balanced reaction can be written as:
\[ \text{Fe}^{3+} + 2\text{I}^- \rightarrow \text{Fe}^{2+} + \text{I}_2 \]

4. **Calculate the standard cell potential \( E^\circ_{\text{cell}} \):**
- The overall cell potential is calculated using the formula:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{reduction}} - E^\circ_{\text{oxidation}} \]
- Substituting the values:
\[ E^\circ_{\text{cell}} = 0.77 \, \text{V} - (-0.536 \, \text{V}) = 0.77 \, \text{V} + 0.536 \, \text{V} = 1.306 \, \text{V} \]

5. **Determine if the reaction is spontaneous:**
- Since \( E^\circ_{\text{cell}} > 0 \), the reaction is spontaneous.

6. **Conclusion:**
- The favorable redox reaction is:
\[ \text{Fe}^{3+} + 2\text{I}^- \rightarrow \text{Fe}^{2+} + \text{I}_2 \]