For `I_(2)+2e^(-) rarr 2I^(-)`, standard reduction potential `=+0.54 V.` For `2Br^(-) rarr Br_(2)+2e^(-)`, standard oxidation potential `=-1.09V.` For `Fe rarr Fe^(2+)+2e^(-)`, standard oxidation potential `=+0.44V`. Which of the following reactions is `(` are `)` spontaneous ?

Options

A. `Br_(2)+2I^(-) rarr 2Br^(c-)+I_(2)`
B. `Fe+Br_(2) rarr Fe^(2+)+2Br^(-)`
C. `Fe +I_(2) rarr Fe^(2+)+2I^(-)`
D. `I_(2)+2Br^(c-) rarr 2I^(-) +Br_(2)`

Explanation

To determine which of the given reactions are spontaneous, we will calculate the standard cell potential (E°cell) for each reaction and check if it is positive. A positive E°cell indicates that the reaction is spontaneous.

### Step 1: Understand the reactions and their potentials

1. **Reaction 1:**
\[ I_2 + 2e^- \rightarrow 2I^- \]
- Standard reduction potential (E°) = +0.54 V

2. **Reaction 2:**
\[ 2Br^- \rightarrow Br_2 + 2e^- \]
- Standard oxidation potential = -1.09 V (which means the reduction potential = +1.09 V)

3. **Reaction 3:**
\[ Fe \rightarrow Fe^{2+} + 2e^- \]
- Standard oxidation potential = +0.44 V (which means the reduction potential = -0.44 V)

### Step 2: Calculate E°cell for each reaction

**For each reaction, we will use the formula:**
\[ E°_{cell} = E°_{cathode} - E°_{anode} \]

#### Reaction 1: \( Br_2 + 2I^- \rightarrow 2Br^- + I_2 \)

- **At the cathode:** \( Br_2 + 2e^- \rightarrow 2Br^- \) (E° = +1.09 V)
- **At the anode:** \( 2I^- \rightarrow I_2 + 2e^- \) (E° = -0.54 V)

\[ E°_{cell} = 1.09 - (-0.54) = 1.09 + 0.54 = 1.63 \, V \]
**Spontaneous:** Yes (E°cell > 0)

#### Reaction 2: \( Fe + Br_2 \rightarrow Fe^{2+} + 2Br^- \)

- **At the cathode:** \( Br_2 + 2e^- \rightarrow 2Br^- \) (E° = +1.09 V)
- **At the anode:** \( Fe \rightarrow Fe^{2+} + 2e^- \) (E° = -0.44 V)

\[ E°_{cell} = 1.09 - 0.44 = 0.65 \, V \]
**Spontaneous:** Yes (E°cell > 0)

#### Reaction 3: \( Fe + I_2 \rightarrow Fe^{2+} + 2I^- \)

- **At the cathode:** \( I_2 + 2e^- \rightarrow 2I^- \) (E° = +0.54 V)
- **At the anode:** \( Fe \rightarrow Fe^{2+} + 2e^- \) (E° = -0.44 V)

\[ E°_{cell} = 0.54 - 0.44 = 0.10 \, V \]
**Spontaneous:** Yes (E°cell > 0)

#### Reaction 4: \( I_2 + 2Br^- \rightarrow 2I^- + Br_2 \)

- **At the cathode:** \( I_2 + 2e^- \rightarrow 2I^- \) (E° = +0.54 V)
- **At the anode:** \( 2Br^- \rightarrow Br_2 + 2e^- \) (E° = -1.09 V)

\[ E°_{cell} = 0.54 - (-1.09) = 0.54 + 1.09 = 1.63 \, V \]
**Spontaneous:** Yes (E°cell > 0)

### Conclusion
The reactions that are spontaneous are:
1. Reaction 1
2. Reaction 2
3. Reaction 3
4. Reaction 4