A reaction `P rarr Q` is completed 25 % in 25 min, 50 % completed in 25 min if [P] is halved, 25 % completed in 50 min if [P] is doubled. The order of reaction is

Options

A. 1
B. 2
C. 0
D. 3

Explanation

To determine the order of the reaction \( P \rightarrow Q \) based on the given data, we can analyze the information step by step.

### Step 1: Analyze the given data
- The reaction is 25% complete in 25 minutes.
- The reaction is 50% complete in 25 minutes if the concentration of \( [P] \) is halved.
- The reaction is 25% complete in 50 minutes if the concentration of \( [P] \) is doubled.

### Step 2: Understand the implications of the data
From the data:
- When the concentration of \( [P] \) is halved, the time taken to complete 25% of the reaction is 50 minutes, which is double the time taken when the concentration was at its original value (25 minutes).
- When the concentration of \( [P] \) is doubled, the time taken to complete 25% of the reaction is also 50 minutes, which indicates that the time taken is not decreasing as expected for a first-order or second-order reaction.

### Step 3: Identify the relationship between time and concentration
In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactant. Therefore, if the concentration is halved or doubled, the time taken for a certain percentage completion will change linearly:
- Original concentration \( [P] \) leads to 25% completion in 25 minutes.
- Halved concentration \( [P] \) leads to 25% completion in 50 minutes (double the time).
- Doubled concentration \( [P] \) leads to 25% completion in 50 minutes (time remains the same).

### Step 4: Conclude the order of the reaction
Since the time taken for 25% completion increases when the concentration is halved and does not decrease when the concentration is doubled, this behavior is characteristic of a zero-order reaction. In zero-order kinetics, the time taken is directly proportional to the concentration of the reactant.

Thus, the order of the reaction \( P \rightarrow Q \) is **zero-order**.

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

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