When the concentration of a reactant ,`A to` products , is doubled In first order reaction, the increase in the rate of reaction cannot be more than

Options

A. 2 times
B. 4 times
C. 6 times
D. 8 times

Answer

To solve the question, we will analyze the effect of doubling the concentration of a reactant \( A \) on the rate of a first-order reaction.

### Step-by-Step Solution:

1. **Understanding the Rate Law for a First-Order Reaction**:
The rate of a first-order reaction can be expressed using the rate law:
\[ R = k[A]^1 \]
where \( R \) is the rate of the reaction, \( k \) is the rate constant, and \( [A] \) is the concentration of reactant \( A \).

2. **Initial Rate Calculation**:
Let the initial concentration of \( A \) be \( [A] \). The initial rate of the reaction can be written as:
\[ R_1 = k[A] \]

3. **Doubling the Concentration**:
If the concentration of \( A \) is doubled, the new concentration becomes \( 2[A] \). The new rate of the reaction can be expressed as:
\[ R_2 = k[2A] = k \cdot 2[A] = 2k[A] \]

4. **Comparing the Rates**:
Now, we compare the new rate \( R_2 \) with the initial rate \( R_1 \):
\[ R_2 = 2R_1 \]
This indicates that when the concentration of \( A \) is doubled, the rate of the reaction also doubles.

5. **Conclusion**:
Therefore, the increase in the rate of reaction cannot be more than 2 times when the concentration of reactant \( A \) is doubled in a first-order reaction.

### Final Answer:
The increase in the rate of reaction cannot be more than 2 times.

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