The rate law for a reaction `A + B to C + D` is given by the expression k[A]. The rate of reaction will be

Options

A. doubled on doubling the concentration of B
B. halved on reducing the concentration of A to half
C. Decreased on increasing the temperature of the reaction
D. unaffected by any change in concentration or temperature.

Explanation

To solve the question regarding the rate law for the reaction \( A + B \to C + D \) given by the expression \( \text{Rate} = k[A] \), we will analyze how changes in the concentration of reactants affect the rate of the reaction.

### Step-by-Step Solution:

1. **Understand the Rate Law**: The rate law provided is \( \text{Rate} = k[A] \). This means that the rate of the reaction depends only on the concentration of reactant A and is independent of the concentration of reactant B.

2. **Consider the Effect of Concentration of A**: Let's denote the initial concentration of A as \([A]\). If we reduce the concentration of A to half, we denote this new concentration as \( A' = \frac{1}{2}[A] \).

3. **Calculate the New Rate**: Using the rate law with the new concentration:
\[ \text{Rate}' = k[A'] = k\left(\frac{1}{2}[A]\right) = \frac{1}{2}k[A] \]
This shows that the new rate of reaction \( \text{Rate}' \) is half of the original rate \( \text{Rate} \).

4. **Analyze the Options**:
- The first option states that the rate of reaction will be doubled on doubling the concentration of B. This is incorrect because the rate is independent of B.
- The second option states that the rate will be half on reducing the concentration of A to half. This is correct as we calculated.
- The third option suggests that the rate will decrease on increasing the temperature. This is also incorrect because increasing temperature generally increases the rate of reaction.

5. **Conclusion**: Based on our calculations and analysis of the options, the correct answer is that the rate of reaction will be half on reducing the concentration of A to half.

### Final Answer:
The rate of reaction will be half on reducing the concentration of A to half.

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