Which reaction has positive value of `DeltaG^(@)`?

Options

A. `F_(2)+H_(2)O overset(R.T.)to2HF+(1)/(2)O_(2)uarr`
B. `Cl_(2)+H_(2)O overset(R.T.)toHCl+HOCl`
C. `Br_(2)+H_(2)O overset(R.T.) to HBr+HOBr`
D. `I_(2)+H_(2)O overset(R.T.)toHI+HOI`

Explanation

To determine which reaction has a positive value of ΔG° (Gibbs free energy), we need to analyze the feasibility of each reaction based on the oxidation states of the reactants and products. A positive ΔG° indicates a non-spontaneous reaction.

### Step-by-Step Solution:

1. **Identify the Reactions**: We have four reactions to consider:
- Reaction A: F₂ + H₂O → 2HF + ½ O₂
- Reaction B: Cl₂ + H₂O → HCl + HOCl
- Reaction C: Br₂ + H₂O → HBr + HOBr
- Reaction D: I₂ + H₂O → HI + HOI

2. **Analyze Reaction A**:
- For F₂, the oxidation state is 0.
- For HF, the oxidation state of F is -1.
- Since fluorine is going from 0 to -1, this indicates a reduction, and the reaction is feasible (spontaneous). Therefore, ΔG° < 0.

3. **Analyze Reaction B**:
- For Cl₂, the oxidation state is 0.
- In HCl, the oxidation state of Cl is -1, and in HOCl, it is +1.
- This is a disproportionation reaction where Cl is both reduced and oxidized. The oxidation states are stable, indicating that this reaction is also feasible (spontaneous). Thus, ΔG° < 0.

4. **Analyze Reaction C**:
- For Br₂, the oxidation state is 0.
- In HBr, the oxidation state of Br is -1, and in HOBr, it is +1.
- Similar to reaction B, this is also a disproportionation reaction, and the oxidation states are stable. Therefore, this reaction is feasible (spontaneous), leading to ΔG° < 0.

5. **Analyze Reaction D**:
- For I₂, the oxidation state is 0.
- In HI, the oxidation state of I is -1, and in HOI, it is +1.
- Here, the oxidation states of iodine are less stable compared to its elemental form. The reaction does not favor the formation of products, indicating that it is not feasible (non-spontaneous). Therefore, ΔG° > 0.

6. **Conclusion**: The reaction that has a positive value of ΔG° is Reaction D: I₂ + H₂O → HI + HOI.

### Final Answer:
The reaction with a positive value of ΔG° is **I₂ + H₂O → HI + HOI**.