Question

Which of the following is an example of fractional order reaction ?

• A. \(2\text{H}_2\text{O}_2\text{(g)}⟶2\text{H}_2\text{O}\text{(l)}+\text{O}_2\text{(g)}\)
• B. \(\text{H}_2\text{(g)}+\text{I}_2\text{(g)}⟶2\text{HI}\text{(g)}\)
• C. \(\text{CH}_3\text{CHO}\text{(g)}⟶\text{CH}_4\text{(g)}+\text{CO}\text{(g)}\)
• D. \(2\text{NO}\text{(g)}+2\text{H}_2\text{(g)}⟶\text{N}_2\text{(g)}+2\text{H}_2\text{O}\text{(l)}\)

Hint:

Acetaldehyde decomposition has an experimental rate law of order 3/2.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The order of a reaction is the sum of the powers of concentrations in the experimentally determined rate law. It need not be an integer and it cannot be read from the balanced equation.

Step 2: Key Formula or Approach:
Recall the known rate laws:
1. \(2\text{H}_2\text{O}_2 \to 2\text{H}_2\text{O} + \text{O}_2\): rate \(= k[\text{H}_2\text{O}_2]\), first order.
2. \(\text{H}_2 + \text{I}_2 \to 2\text{HI}\): rate \(= k[\text{H}_2][\text{I}_2]\), second order.
3. \(\text{CH}_3\text{CHO} \to \text{CH}_4 + \text{CO}\): rate \(= k[\text{CH}_3\text{CHO}]^{3/2}\).
4. \(2\text{NO} + 2\text{H}_2 \to \text{N}_2 + 2\text{H}_2\text{O}\): rate \(= k[\text{NO}]^2[\text{H}_2]\), third order.

Step 3: Detailed Explanation:
Reactions 1, 2 and 4 have whole-number orders 1, 2 and 3. Only the decomposition of acetaldehyde has the order \(3/2\), which is a fraction.
Its order differs from its molecularity (which is 1 for each elementary step) because the reaction proceeds through a chain mechanism.

Final Answer:
The thermal decomposition of acetaldehyde has order 1.5, so option (C) is the fractional order reaction. \[ \boxed{\text{CH}_3\text{CHO} \to \text{CH}_4 + \text{CO} \text{ (C)}} \]