At `518^(@)C` the rate of decomposition of a smaple of gaseous acetaldehyde, initially at a pressure of 363 torr, was 1.00 torr `s^(-1)` when `5%` had reacted and `0.5"torr" s^(-1)` when `33%` had reacted. The order of the reaction is :

Options

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

Explanation

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

### Step 1: Understand the relationship between rate and concentration
The rate of a reaction can be expressed as:
\[ \text{Rate} = k \cdot [A]^{-\alpha} \]
where \( k \) is the rate constant, \( [A] \) is the concentration of the reactant, and \( \alpha \) is the order of the reaction.

### Step 2: Set up the equations for the two given conditions
We have two conditions given:
1. When 5% of acetaldehyde has reacted, the rate is \( 1.00 \, \text{torr/s} \).
2. When 33% of acetaldehyde has reacted, the rate is \( 0.5 \, \text{torr/s} \).

From the initial pressure of acetaldehyde, \( P_0 = 363 \, \text{torr} \):
- After 5% reaction: Remaining pressure \( P_1 = 363 \, \text{torr} \times (1 - 0.05) = 345.85 \, \text{torr} \)
- After 33% reaction: Remaining pressure \( P_2 = 363 \, \text{torr} \times (1 - 0.33) = 243.21 \, \text{torr} \)

### Step 3: Write the rate equations for both conditions
Using the rate equation:
1. For 5% reacted:
\[ 1.00 = k \cdot (345.85)^{-\alpha} \]
2. For 33% reacted:
\[ 0.5 = k \cdot (243.21)^{-\alpha} \]

### Step 4: Divide the two equations to eliminate \( k \)
\[ \frac{1.00}{0.5} = \frac{k \cdot (345.85)^{-\alpha}}{k \cdot (243.21)^{-\alpha}} \]
This simplifies to:
\[ 2 = \left(\frac{345.85}{243.21}\right)^{-\alpha} \]

### Step 5: Calculate the ratio
Calculating the ratio:
\[ \frac{345.85}{243.21} \approx 1.42 \]
So we have:
\[ 2 = (1.42)^{-\alpha} \]
Taking the logarithm on both sides:
\[ \log(2) = -\alpha \cdot \log(1.42) \]
Thus,
\[ \alpha = -\frac{\log(2)}{\log(1.42)} \]

### Step 6: Calculate \( \alpha \)
Using logarithm values:
- \( \log(2) \approx 0.301 \)
- \( \log(1.42) \approx 0.152 \)

Now substituting:
\[ \alpha \approx -\frac{0.301}{0.152} \approx 1.98 \approx 2 \]

### Conclusion
The order of the reaction is approximately 2.

### Final Answer
The order of the reaction is \( \alpha = 2 \).

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