Consider the following reaction, the rate expression of which is given below \[ \begin{aligned} &…

Consider the following reaction, the rate expression of which is given below \[ \begin{aligned} & \mathrm{A}+\mathrm{B} \rightarrow \mathrm{C} \\ & \text { rate }=\mathrm{k}[\mathrm{A}]^{1 / 2}[\mathrm{~B}]^{1 / 2} \end{aligned} \] The reaction is initiated by taking \(1 \mathrm{M}\) concentration of \(\mathrm{A}\) and \(\mathrm{B}\) each. If the rate constant \((\mathrm{k})\) is \(4.6 \times 10^{-2} \mathrm{~s}^{-1}\), then the time taken for \(\mathrm{A}\) to become \(0.1 \mathrm{M}\) is ______ sec. (nearest integer)

Solution

$\begin{aligned} & \mathrm{K}=\frac{2.303}{\mathrm{t}} \log \frac{1}{0.1} \\ & 4.6 \times 10^{-2}=\frac{2.303}{\mathrm{t}} \\ & \mathrm{t}=50 \mathrm{sec} .\end{aligned}$

Asked in: JEE Main 2024 (04 Apr Shift 2)

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