For reaction $\mathrm{A}+\mathrm{B} \rightarrow$ product, rate of reaction is $3.6 \times 10^{-2}…

For reaction $\mathrm{A}+\mathrm{B} \rightarrow$ product, rate of reaction is $3.6 \times 10^{-2} \mathrm{sec}^{-1}$. When $\left[A^{\circ}\right]=0.2 \mathrm{moldm}^{-3}$ and $[B]=0.1 \mathrm{moldm}^{-3}$, calculate rate constant of reaction if reaction is first order in A and second order is B ?
  1. $3.6 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{sec}^{-1}$
  2. $1.8 \mathrm{~mol}^{-2} \mathrm{dm}^{-6} \mathrm{sec}^{-1}$
  3. $18 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{sec}^{-1}$
  4. $36 \mathrm{~mol}^{-2} \mathrm{dm}^{-6} \mathrm{sec}^{-1}$

Solution

$\begin{aligned} & \text { Rate }=\mathrm{k}[\mathrm{A}][\mathrm{B}]^2 \\ \therefore \quad & \mathrm{k}=\frac{\text { Rate }}{[\mathrm{A}][\mathrm{B}]^2}=\frac{3.6 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{sec}^{-1}}{\left(0.2 \mathrm{~mol} \mathrm{dm}^{-3}\right)\left(0.1 \mathrm{~mol} \mathrm{dm}^{-3}\right)^2} \\ \quad= & 18 \times 10^{-3} \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{sec}^{-1}\end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 2)

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