For a reaction, $2 \mathrm{~A}+\mathrm{B} \rightarrow 2 \mathrm{C}$, rate of disappearance of $\mathrm{A}$…

For a reaction, $2 \mathrm{~A}+\mathrm{B} \rightarrow 2 \mathrm{C}$, rate of disappearance of $\mathrm{A}$ is $0.076 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$. What is the rate of disappearance of $\mathrm{B}$ ?
  1. $0.152 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$
  2. $0.114 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$
  3. $0.038 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$
  4. $0.076 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$

Solution

$\begin{aligned} & -\frac{1}{2} \frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}=-\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{d} t} \\ & \therefore-\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{d} t}=\frac{1}{2} \times 0.076 \\ & =0.038 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\end{aligned}$

Asked in: MHT CET 2022 (08 Aug Shift 2)

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