Consider a reaction `A rarr B + C` . The initial concentration of `A` was reduced form `2 M `to `1 M` in `1 h` and form `1M` to `0.25 M` in `2h`, the order of the reaction is
(a) `1`
(b) `0`
(c) `2`
(d) `3`

Options

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

Explanation

To determine the order of the reaction \( A \rightarrow B + C \) based on the given concentration changes over time, we can analyze the data step by step.

### Step 1: Analyze the concentration changes
- The concentration of \( A \) decreases from \( 2 \, M \) to \( 1 \, M \) in \( 1 \, h \).
- The concentration of \( A \) decreases from \( 1 \, M \) to \( 0.25 \, M \) in \( 2 \, h \).

### Step 2: Calculate the change in concentration
1. From \( 2 \, M \) to \( 1 \, M \):
- Change in concentration: \( 2 \, M - 1 \, M = 1 \, M \)
- Time taken: \( 1 \, h \)

2. From \( 1 \, M \) to \( 0.25 \, M \):
- Change in concentration: \( 1 \, M - 0.25 \, M = 0.75 \, M \)
- Time taken: \( 2 \, h \)

### Step 3: Determine the fraction of the reaction completed
- For the first change (from \( 2 \, M \) to \( 1 \, M \)):
- Fraction reacted: \( \frac{1 \, M}{2 \, M} = \frac{1}{2} \) (50% of \( A \) reacted in \( 1 \, h \))

- For the second change (from \( 1 \, M \) to \( 0.25 \, M \)):
- Fraction reacted: \( \frac{0.75 \, M}{1 \, M} = \frac{3}{4} \) (75% of \( A \) reacted in \( 2 \, h \))

### Step 4: Relate the time taken to the order of the reaction
- For a first-order reaction, the time taken to reach \( \frac{1}{2} \) of the initial concentration (half-life, \( t_{1/2} \)) is constant.
- The time taken to reach \( \frac{3}{4} \) of the reaction completion (\( t_{3/4} \)) is related to \( t_{1/2} \) by the equation:
\[ t_{3/4} = 2 \times t_{1/2} \]

### Step 5: Verify the relationship
- From our data:
- \( t_{1/2} = 1 \, h \)
- \( t_{3/4} = 2 \, h \)

- Check the relationship:
\[ t_{3/4} = 2 \times t_{1/2} \implies 2 \, h = 2 \times 1 \, h \]
- This relationship holds true.

### Conclusion
Since the relationship between \( t_{1/2} \) and \( t_{3/4} \) satisfies the condition for a first-order reaction, we conclude that the order of the reaction is **1**.

### Final Answer
The order of the reaction is (a) **1**.

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