The concentration of a reactant in solution falls from (i) `0.5` M to `0.25` M in 5 hourse and from (ii) `1.0` M to `0.25` M in 10 hours The order of reaction is

Options

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

Answer

To determine the order of the reaction based on the given concentration changes, we will analyze the data provided in the question step by step.

### Step 1: Understand the Data
We have two cases:
1. The concentration of a reactant decreases from **0.5 M to 0.25 M** in **5 hours**.
2. The concentration of a reactant decreases from **1.0 M to 0.25 M** in **10 hours**.

### Step 2: Calculate the Change in Concentration
For the first case:
- Initial concentration (C1) = 0.5 M
- Final concentration (C2) = 0.25 M
- Change in concentration (ΔC) = C1 - C2 = 0.5 M - 0.25 M = 0.25 M
- Time taken (t1) = 5 hours

For the second case:
- Initial concentration (C1) = 1.0 M
- Final concentration (C2) = 0.25 M
- Change in concentration (ΔC) = C1 - C2 = 1.0 M - 0.25 M = 0.75 M
- Time taken (t2) = 10 hours

### Step 3: Determine the Half-Life
In the first case, the concentration decreases from 0.5 M to 0.25 M, which means it has reached half of its initial concentration. Therefore, the time taken for this half-life (t_half) is 5 hours.

In the second case, the concentration decreases from 1.0 M to 0.5 M in the first 5 hours (which is the first half-life), and then from 0.5 M to 0.25 M in the next 5 hours. Thus, the total time taken is 10 hours, confirming that two half-lives are involved.

### Step 4: Analyze the Order of Reaction
For a first-order reaction, the half-life is constant and does not depend on the initial concentration. In both cases, we observe that:
- The first case has a half-life of 5 hours.
- The second case has two half-lives (5 hours each) totaling 10 hours.

Since the half-life remains constant (5 hours for each half-life), we conclude that the reaction follows first-order kinetics.

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

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