In which of the following reactions, `SN^2` rate increases on changing the solvent from (95 % acetone + 5 % `H_2 O`) to (80 % acetone + 20 % `H_2O`) ?

Options

A. `Me_2 - overset (oplus) P- Me + NH_3 rarr Me overset (oplus) N H_3 + Me_2 P`
B. `MeI + PH_3 rarr Me overset (oplus) P H_3 + I^(Ө)`
C. `MeBr + overset (Ө) O H rarr MeOH + Br^(Ө)`
D. `Me_2 - overset (oplus) S - Me + overset (Ө)OH rarr MeOH + Me_2 S`

Answer

To determine in which of the following reactions the SN2 rate increases when changing the solvent from 95% acetone + 5% water to 80% acetone + 20% water, we need to analyze the effect of solvent polarity on the SN2 reaction mechanism.

### Step-by-Step Solution:

1. **Understanding SN2 Mechanism**:
- The SN2 (Substitution Nucleophilic Bimolecular) reaction involves a nucleophile attacking an electrophile, leading to the substitution of one group for another. The rate of an SN2 reaction depends on both the nucleophile and the substrate.

2. **Effect of Solvent on SN2 Reactions**:
- The solvent can affect the rate of the reaction by stabilizing or destabilizing the reactants and transition states.
- In a polar solvent, charged species (like nucleophiles or electrophiles) are stabilized due to solvation, which can slow down the reaction if the reactants are charged.

3. **Changing Solvent Composition**:
- By changing the solvent from 95% acetone (a polar aprotic solvent) + 5% water to 80% acetone + 20% water, we are increasing the polarity of the solvent mixture.
- Increasing the proportion of water (which is a polar protic solvent) increases the overall polarity of the solvent.

4. **Analyzing Reactants**:
- If the reactants are charged (e.g., a nucleophile like OH⁻), increasing solvent polarity will stabilize the charged reactants, thus decreasing the reaction rate.
- If the reactants are neutral, increasing the solvent polarity will stabilize the transition state, which can increase the reaction rate.

5. **Conclusion**:
- Based on the above analysis, the SN2 reaction rate will increase when the reactants are neutral and the solvent polarity is increased.
- Therefore, we need to identify the reaction among the options provided where the reactants are neutral.

### Final Answer:
The correct answer is **B**, where the SN2 reaction rate increases upon changing the solvent from 95% acetone + 5% water to 80% acetone + 20% water.