When initial concentration of a reactant is doubled in a reaction, its half-life period is not affected. The order of the reaction is

Options

A. second
B. more than zero but less than first
C. zero
D. first

Explanation

To determine the order of the reaction based on the information provided, we can follow these steps:

### Step 1: Understand the relationship between half-life and concentration
The half-life (\(T_{1/2}\)) of a reaction is the time required for the concentration of a reactant to decrease to half of its initial concentration. The relationship between half-life and initial concentration varies depending on the order of the reaction.

### Step 2: Analyze the effect of doubling the initial concentration
The problem states that when the initial concentration of a reactant is doubled, the half-life period remains unchanged. This indicates that the half-life is independent of the concentration of the reactant.

### Step 3: Recall the half-life formulas for different orders of reactions
- For a **zero-order reaction**:
\[ T_{1/2} = \frac{[A]_0}{2k} \]
(where \([A]_0\) is the initial concentration and \(k\) is the rate constant)

- For a **first-order reaction**:
\[ T_{1/2} = \frac{0.693}{k} \]
(independent of initial concentration)

- For a **second-order reaction**:
\[ T_{1/2} = \frac{1}{k[A]_0} \]
(depends on initial concentration)

### Step 4: Determine the order of the reaction
Since the half-life does not change when the initial concentration is doubled, we can conclude that the reaction must be of **first order**. This is because the half-life of a first-order reaction is constant and does not depend on the initial concentration.

### Conclusion
The order of the reaction is **1** (first order).

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