What is half life time of a first order reaction if initial conc. of reactant is $0.01 \mathrm{~mol}…

What is half life time of a first order reaction if initial conc. of reactant is $0.01 \mathrm{~mol} \mathrm{~L}^{-1}$ and rate of reaction is $0.00352 \mathrm{~mol} \mathrm{~L}^{-1}$ minute ${ }^{-1}$ ?
  1. 1.969 minute
  2. 7.75 minute
  3. 16.69 minute
  4. 19.69 minute

Solution

For a first order reaction, rate $=\mathrm{k}[\mathrm{A}]$ $\begin{aligned} & \therefore \quad \begin{array}{l} 0.00352 \mathrm{~mol} \mathrm{~L}^{-1} \text { minute } \\ \mathrm{k}=0.352 \text { minute }^{-1} \end{array} \\ & \begin{aligned} \text { Half-life period, }\left(\mathrm{t}_{1 / 2}\right)=\frac{0.693}{\mathrm{k}} & =\frac{0.693}{0.352} \\ & =1.969 \text { minute } \end{aligned} \end{aligned}$

Asked in: MHT CET 2023 (11 May Shift 1)

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