Question

For the reaction A + B → C, the following data were obtained:

The order of reaction with respect to A and B are respectively

• A. 1, 2
• B. 2, 1
• C. 1.5, 1.5
• D. 0, 3

Hint:

Key steps: 1. Compare experiments where only one concentration changes 2. Solve for exponent that matches rate ratios 3. Verify with multiple data pairs when possible

Answer 1

The Correct Option is A

Let the rate law be: Rate = $k[A]^x[B]^y$ For order w.r.t B (y): Compare Expt 1 & 2 (constant [A]): \[ \frac{9.0 \times 10^{-4}}{1.0 \times 10^{-4}} = \left(\frac{0.3}{0.1}\right)^y \Rightarrow 9 = 3^y \Rightarrow y = 2 \] For order w.r.t A (x): Compare Expt 2 & 3 (constant [B]): \[ \frac{2.7 \times 10^{-3}}{9.0 \times 10^{-4}} = \left(\frac{0.3}{0.1}\right)^x \Rightarrow 3 = 3^x \Rightarrow x = 1 \] Thus, orders are 1 (A) and 2 (B). Answer: (1).

Answer 2

Assume the rate law:
Rate = k[A]^m[B]ⁿ

Step 1: Determine n (order w.r.t. B)
Compare Expt 1 and 2 (A is constant):

• [B] increases from 0.1 to 0.3 (3 times)
• Rate increases from 1.0×10⁻⁴ to 9.0×10⁻⁴ (9 times)

So, (Rate₂ / Rate₁) = ( [B]₂ / [B]₁ )ⁿ ⇒ 9 = 3ⁿ ⇒ n = 2

Step 2: Determine m (order w.r.t. A)
Compare Expt 2 and 3 (B is constant):

• [A] increases from 0.1 to 0.3 (3 times)
• Rate increases from 9.0×10⁻⁴ to 2.7×10⁻³ (3 times)

So, (Rate₃ / Rate₂) = ( [A]₃ / [A]₂ )ᵐ ⇒ 3 = 3ᵐ ⇒ m = 1

Final Answer:
The order of reaction with respect to A and B are 1 and 2 respectively.