Consider the following reactions:
` I. C_(2)H_(5) - I + NH_(3) rarr C_(2) H_(5) N^(o+)H_(3) + I^(o-)`
II. `C_(2)H_(5) - I + ddot(P)H_(3) rarr C_(2)H_(5) P^(o+)H_(5)` +` I^(o-)`
III. `C_(2)H_(5) - I + EtO^(o-) rarr C_(2) H_(5) - OEt + I^(o-)`
IV. `Me - overset(o+)(S) - Me_(2) + O^(o-)H rarr Me-OH + Me_(2)S`
In which of the above reactions does the rate of `SN^(2)` reactions increases with increase in solvent polarity?

Options

A. `(I)`
B. `(II)`
C. `(III)`
D. `(IV)`

Explanation

To determine in which of the given reactions the rate of SN2 reactions increases with an increase in solvent polarity, we need to analyze each reaction based on the nature of the nucleophiles and the presence of charged species.

### Step-by-Step Solution:

1. **Understanding SN2 Reactions**:
- SN2 (Substitution Nucleophilic Bimolecular) reactions are characterized by a single transition state and involve a nucleophile attacking an electrophile, leading to the displacement of a leaving group.
- The rate of SN2 reactions is influenced by the polarity of the solvent, especially when charged species are involved.

2. **Analyzing Each Reaction**:
- **Reaction I**:
\[ C_2H_5 - I + NH_3 \rightarrow C_2H_5N^{o+}H_3 + I^{o-} \]
- Here, NH3 is a neutral nucleophile. Increasing solvent polarity will stabilize the transition state and potentially increase the reaction rate.

- **Reaction II**:
\[ C_2H_5 - I + PH_3 \rightarrow C_2H_5P^{o+}H_5 + I^{o-} \]
- Similar to Reaction I, PH3 is also a neutral nucleophile. Thus, increasing solvent polarity may also increase the reaction rate.

- **Reaction III**:
\[ C_2H_5 - I + EtO^{o-} \rightarrow C_2H_5 - OEt + I^{o-} \]
- Here, EtO^- is a charged nucleophile. Increasing solvent polarity would stabilize the charged species and decrease the reaction rate.

- **Reaction IV**:
\[ Me - (S) - Me_2 + O^{o-}H \rightarrow Me-OH + Me_2S \]
- In this reaction, O^- is also a charged nucleophile. Similar to Reaction III, increasing solvent polarity would decrease the reaction rate.

3. **Conclusion**:
- From the analysis, we find that the reactions where the nucleophile is neutral (Reactions I and II) would see an increase in the rate of SN2 reactions with increasing solvent polarity.
- Therefore, the reactions that fit the criteria are **Reaction I and Reaction II**.

### Final Answer:
The rate of SN2 reactions increases with an increase in solvent polarity in **Reactions I and II**.