Assertion (A): For the reaction
`RCl + NaOH(g) rarr ROH + NaCl`, the rate of reaction is reduced to half on reducing the cocentration of `RCl` to half.
Reason (R ): The rate of the reaction is represented by `k[RCl]`, i.e., it is a first order reaction.

Options

A. If both `(A)` and `(R )` are correct, and `(R )` is the correct explnation of `(A)`.
B. If both `(A)` and `(R )` are correct, but `(R )` is noth the correct explanation of `(A)`.
C. If `(A)` is correct, but `(R )` is incorrect.
D. If `(A)` is incorrect, but `(R )` is correct.

Explanation

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step 1: Understand the Reaction
The reaction given is:
\[ \text{RCl} + \text{NaOH} \rightarrow \text{ROH} + \text{NaCl} \]

This is a nucleophilic substitution reaction where an alkyl halide (RCl) reacts with sodium hydroxide (NaOH) to produce an alcohol (ROH) and sodium chloride (NaCl).

**Hint:** Identify the components of the reaction and the type of reaction taking place.

### Step 2: Analyze the Assertion (A)
The assertion states that the rate of the reaction is reduced to half when the concentration of RCl is reduced to half.

To understand this, we recognize that if the rate of reaction is directly proportional to the concentration of RCl, then halving the concentration of RCl would indeed halve the rate of reaction.

**Hint:** Consider how the rate of reaction changes with concentration in a first-order reaction.

### Step 3: Analyze the Reason (R)
The reason states that the rate of reaction is represented by \( k[\text{RCl}] \), indicating that it is a first-order reaction with respect to RCl.

In a first-order reaction, the rate is directly proportional to the concentration of the reactant. Therefore, if the concentration of RCl is halved, the rate will also be halved.

**Hint:** Recall the formula for the rate of a first-order reaction and how it relates to concentration.

### Step 4: Conclusion
Since both the assertion and the reason are correct and the reason correctly explains the assertion, we conclude that:

- Assertion (A) is true.
- Reason (R) is true and provides a correct explanation for (A).

Thus, the correct answer is that both A and R are correct, and R is the correct explanation of A.

**Final Answer:** Both Assertion (A) and Reason (R) are correct, and R is the correct explanation of A.