Question

The rate of reaction \(\text{A}+\text{B}\rightarrow \text{P}\) is \(4\times 10^{-2} \text{mol dm}^{-3} \text{s}^{-1}\)
When \([A] = 0.2 \text{mole dm}^{-3}\) and \([B] = 0.1 \text{mole dm}^{-3}\), What is the rate constant of reaction, if it is first order with respect to A and second order with respect to B ?

• A. \(10 \text{mol}^{-2}\text{dm}^6 \text{s}^{-1}\)
• B. \(20 \text{mol}^{-2}\text{dm}^6 \text{s}^{-1}\)
• C. \(25 \text{mol}^{-2}\text{dm}^6 \text{s}^{-1}\)
• D. \(40 \text{mol}^{-2}\text{dm}^6 \text{s}^{-1}\)

Hint:

Rate = k [A][B]^2, so k = rate / ([A][B]^2).

Answer 1

The Correct Option is B

Step 1: Write the law
$r = k[A]^1[B]^2$.

Step 2: Substitute
Denominator: $0.2 \times 0.1^2 = 0.002$.

Step 3: Divide
$k = 0.04 / 0.002 = 20$ in units of $\text{mol}^{-2}\text{dm}^6\text{s}^{-1}$. Option (B).

Final Answer:
Option (B). \[ \boxed{20 \text{ mol}^{-2}\text{dm}^6\text{s}^{-1}} \]