Consider the following reactions which are carried out at the same temperature
`CH_(3) -Br + OH^Theta overset(EtOH)rarr CH_(3) -OH + BrQ ...(i)`
` CH_(3) Br + OH^Theta overset(DMSO)rarr CH_(3) -OH + BrQ ...(ii)`
Which of the following statement is correct about these reactions

Options

A. Both the reactions take place at the same rate
B. The first reaction takes place faster than second reaction .
C. The second reaction takes place faster than first reaction .
D. Both the reactions take place by `S_(N)1` mechanism .

Explanation

To analyze the reactions provided and determine the correct statement regarding their rates, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Reactions**:
- The first reaction is:
\[ CH_3Br + OH^- \overset{(EtOH)}{\rightarrow} CH_3OH + Br^- \]
- The second reaction is:
\[ CH_3Br + OH^- \overset{(DMSO)}{\rightarrow} CH_3OH + Br^- \]

2. **Understand the Solvents**:
- The first reaction uses ethanol (EtOH), which is a polar protic solvent.
- The second reaction uses dimethyl sulfoxide (DMSO), which is a polar aprotic solvent.

3. **Determine the Mechanism**:
- In polar protic solvents like ethanol, the nucleophile (OH^-) is solvated, which can slow down the reaction rate.
- In polar aprotic solvents like DMSO, the nucleophile is less solvated, allowing it to be more reactive and thus facilitating a faster reaction.

4. **Compare the Reaction Rates**:
- Since DMSO is a polar aprotic solvent, it enhances the nucleophilicity of OH^-, leading to a faster reaction compared to the reaction in ethanol.
- Therefore, the reaction in DMSO (reaction ii) will proceed faster than the reaction in ethanol (reaction i).

5. **Conclusion**:
- The correct statement is that the second reaction (in DMSO) is faster than the first reaction (in ethanol).

### Final Answer:
The second reaction (using DMSO) is faster than the first reaction (using ethanol).

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