The half-life of a reaction is halved as the initial concentration of the reaction is doubled. The order of the reaction is

Options

A. 0.5
B. 1
C. 2
D. 0

Explanation

To determine the order of the reaction based on the information provided, we can analyze the relationship between half-life and concentration for different orders of reactions.

### Step-by-Step Solution:

1. **Understanding Half-Life**:
The half-life (T₁/₂) of a reaction is the time required for the concentration of a reactant to decrease to half of its initial concentration.

2. **Given Information**:
We are told that when the initial concentration of the reactant is doubled, the half-life of the reaction is halved. This indicates a specific relationship between half-life and concentration.

3. **Analyzing Zero-Order Reactions**:
- For a zero-order reaction, the half-life is given by the formula:
\[ T_{1/2} = \frac{[A]_0}{2k} \]
- Here, T₁/₂ is directly proportional to the initial concentration \([A]_0\). If we double \([A]_0\), T₁/₂ would also double, which contradicts the given information. Therefore, the reaction cannot be zero-order.

4. **Analyzing First-Order Reactions**:
- For a first-order reaction, the half-life is given by:
\[ T_{1/2} = \frac{0.693}{k} \]
- The half-life for a first-order reaction is independent of the concentration. Doubling the concentration does not affect the half-life. Hence, this reaction cannot be first-order either.

5. **Analyzing Second-Order Reactions**:
- For a second-order reaction, the half-life is given by:
\[ T_{1/2} = \frac{1}{k[A]_0} \]
- In this case, the half-life is inversely proportional to the initial concentration. If we double the concentration, the half-life will be halved, which is consistent with the information given in the question.

6. **Conclusion**:
Since the only scenario that matches the condition where the half-life is halved when the concentration is doubled is the second-order reaction, we conclude that the order of the reaction is **second order**.

### Final Answer:
The order of the reaction is **second order**.