The rate law for the reaction
`RCl + NaOH(aq) to ROH + NaCl` is given by Rate `=K_1[RCl]`. The rate of the reaction will be

Options

A. Doubled on doubling the concentration of sodium hydroxide
B. Halved on reducing the concentration of alkyl halide to one half
C. Decreased on increasing the temperature of the reaction
D. Unaffected by decreasing the temperature of the reaction

Answer

To solve the problem, we need to analyze the given rate law for the reaction:

**Reaction:**
\[ \text{RCl} + \text{NaOH (aq)} \rightarrow \text{ROH} + \text{NaCl} \]

**Rate Law:**
\[ \text{Rate} = k_1 [\text{RCl}]^1 \]

### Step-by-Step Solution:

1. **Understanding the Rate Law:**
The rate law indicates that the rate of the reaction is directly proportional to the concentration of RCl raised to the power of 1. This means that the reaction is first order with respect to RCl.

**Hint:** The order of a reaction can be determined from the rate law equation.

2. **Effect of Concentration Changes:**
- **Doubling the Concentration of NaOH:**
Since NaOH does not appear in the rate law, changing its concentration will not affect the rate of the reaction. Therefore, the statement that the rate will double is incorrect.

**Hint:** Check if the reactant concentration is included in the rate law to determine its effect on the reaction rate.

3. **Halving the Concentration of RCl:**
- If the concentration of RCl is halved, the new rate can be calculated as follows:
\[ \text{New Rate} = k_1 \left( \frac{[\text{RCl}]}{2} \right)^1 = \frac{1}{2} k_1 [\text{RCl}]^1 \]
This shows that the rate will indeed be halved when the concentration of RCl is halved.

**Hint:** The rate of a first-order reaction is directly proportional to the concentration of the reactant.

4. **Effect of Temperature:**
- Increasing the temperature generally increases the rate of reaction because it increases the kinetic energy of the molecules, leading to more frequent and effective collisions. Therefore, the statement that the rate decreases with an increase in temperature is incorrect.

**Hint:** Remember that temperature typically affects the rate of reaction positively by increasing molecular collisions.

5. **Effect of Decreasing Temperature:**
- Similar to the previous point, decreasing the temperature would decrease the rate of reaction, as it would reduce the kinetic energy of the molecules. Thus, the statement that the rate is unaffected by decreasing the temperature is also incorrect.

**Hint:** Consider how temperature influences molecular motion and collision frequency.

### Conclusion:
From the analysis, the correct statement is that the rate of the reaction will be halved when the concentration of RCl is reduced to half.

### Final Answer:
The rate of the reaction will be halved on reducing the concentration of alkyl halide (RCl) to half.