Rate of reaction for $2 \mathrm{X}+\mathrm{Y} \rightarrow 3 \mathrm{~W}+\mathrm{Z}$ is $1.2 \times 10^{-4}…

Rate of reaction for $2 \mathrm{X}+\mathrm{Y} \rightarrow 3 \mathrm{~W}+\mathrm{Z}$ is $1.2 \times 10^{-4} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{sec}^{-1}$ when $[\mathrm{X}]=[\mathrm{Y}]=0.6 \mathrm{~mol} \mathrm{dm}^{-3}$ Calculate value of rate constant if reaction is first order in $\mathrm{X}$ and zero order in Y
  1. $1.2 \times 10^{-4} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{sec}^{-1}$
  2. $6 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{sec}^{-1}$
  3. $2 \times 10^{-4} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{sec}^{-1}$
  4. $1.8 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{sec}^{-1}$

Solution

$\begin{aligned} & \mathrm{R}=-\frac{1}{2} \frac{\mathrm{d}[\mathrm{X}]}{\mathrm{dt}}=-\frac{\mathrm{d}[\mathrm{Y}]}{\mathrm{dt}}=\frac{1}{3} \frac{\mathrm{d}[\mathrm{W}]}{\mathrm{dt}}=\frac{\mathrm{d}[\mathrm{Z}]}{\mathrm{dt}} \\ & \mathrm{R}=\mathrm{k}[\mathrm{X}] \\ & 1.2 \times 10^{-4}=\mathrm{k}(0.6) \\ & \mathrm{k}=2 \times 10^{-4} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{sec}^{-1}\end{aligned}$

Asked in: MHT CET 2022 (07 Aug Shift 2)

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