The mechanism of the reaction :
`Nu^(-)+R-X to R-Nu+X^(-)` is `Nu(-)+R-X to` [Transition state] (slow) [Transition state] `to Nu-R+X^(-)` (fast)
The rate of reaction can be increased by:

Options

A. Increasing the conc. of Nu– only
B. Increasing the conc. of R – X only
C. Increasing the conc. of both `Nu^–` and R – X
D. Decreasing the conc. of both `Nu^–` and R – X

Answer

To solve the question regarding how to increase the rate of the reaction `Nu^(-) + R-X → R-Nu + X^(-)`, we will analyze the given mechanism and determine which factors affect the rate of the reaction.

### Step-by-Step Solution:

1. **Identify the Mechanism**:
The reaction consists of two steps:
- The first step is the formation of a transition state from the nucleophile (Nu^(-)) and the alkyl halide (R-X). This step is labeled as slow, indicating that it is the rate-determining step (RDS).
- The second step involves the conversion of the transition state to the product (R-Nu + X^(-)), which is fast.

2. **Rate-Determining Step**:
Since the first step is the slow step, it controls the overall rate of the reaction. The rate of the reaction can be expressed in terms of the concentrations of the reactants involved in this step.

3. **Write the Rate Law**:
The rate law for the reaction can be expressed as:
\[ \text{Rate} = k[\text{Nu}^-][\text{R-X}] \]
where \( k \) is the rate constant, \([\text{Nu}^-]\) is the concentration of the nucleophile, and \([\text{R-X}]\) is the concentration of the alkyl halide.

4. **Effect of Concentrations on Rate**:
From the rate law, we can see that the rate of the reaction is directly proportional to both the concentration of the nucleophile and the concentration of the alkyl halide. This means that:
- Increasing the concentration of the nucleophile (\([\text{Nu}^-]\)) will increase the rate of reaction.
- Increasing the concentration of the alkyl halide (\([\text{R-X}]\)) will also increase the rate of reaction.

5. **Conclusion**:
To increase the rate of the reaction, we can increase the concentration of either the nucleophile, the alkyl halide, or both. Therefore, the best option to increase the rate of the reaction is to increase the concentration of both the nucleophile and the alkyl halide.

### Final Answer:
The rate of reaction can be increased by increasing the concentration of both the nucleophile and the alkyl halide.

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