At $T(\mathrm{~K})$, the following data were obtained for a general reaction, $A+B+C \longrightarrow$…

At $T(\mathrm{~K})$, the following data were obtained for a general reaction, $A+B+C \longrightarrow$ products $ \begin{array}{ccccc} \hline \text{Expt.} & \begin{array}{c} \text{Initial} \\ {[A]} \end{array} & \begin{array}{c} \text{Initial} \\ {[B]} \end{array} & \begin{array}{c} \text{Initial} \\ {[C]} \end{array} & \text{Initial rate} \\ \hline 1. & 0.02 \, \text{M} & 0.1 \, \text{M} & 0.03 \, \text{M} & 2.4 \times 10^{-6} \, \text{ms}^{-1} \\ \hline 2. & 0.02 \, \text{M} & 0.2 \, \text{M} & 0.03 \, \text{M} & 4.8 \times 10^{-6} \, \text{ms}^{-1} \\ \hline 3. & 0.02 \, \text{M} & 0.2 \, \text{M} & 0.06 \, \text{M} & 9.6 \times 10^{-6} \, \text{ms}^{-1} \\ \hline 4. & 0.04 \, \text{M} & 0.2 \, \text{M} & 0.06 \, \text{M} & 9.6 \times 10^{-6} \, \text{ms}^{-1} \\ \hline \end{array} $ The rate constant for the above reaction is
  1. $8.0 \times 10^{-4} \mathrm{~s}^{-1}$
  2. $8.0 \times 10^{-4} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$
  3. $8.0 \times 10^4 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$
  4. $8.0 \times 10^{-4} \mathrm{~L}^2 \mathrm{~mol}^{-2} \mathrm{~s}^{-1}$

Solution

Comparing expt. (1) and expt. (2). When $[B]$ is doubled rate of reaction doubles. $\therefore$ Reaction is first order is $B$. Comparing expt. (2) and expt (3). When $[C]$ is doubled rate of reaction doubles. $\therefore$ Reaction is first order in $C$. Comparing expt. [3] and expt [4]. When $[A]$ is doubled rate of reaction remains unchanged. $\therefore$ Reaction is zero order in $A$. Rate law $=K[A]^0[B]^{\prime}[C]^{\prime}$ Using data of expt. (1) we get $ \begin{aligned} & 2.4 \times 10^{-6}=K[0.02]^0[0.1]^1[0.03]^1 \\ & 2.4 \times 10^{-6}=K \times 1 \times 0.1 \times 0.03 \\ & K=\frac{2.4 \times 10^{-6}}{3 \times 10^{-3}}=0.8 \times 10^{-3}=8.0 \times 10^{-4} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1} \end{aligned} $

Asked in: AP EAMCET 2018 (23 Apr Shift 2)

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