Q55 / 160 · JIPMER 2007 · Chemistry

For a first order reaction $A \longrightarrow B$, the reaction rate at reactant concentration of 0.01 M is found to be $2.0 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$. The half-life period of the reaction is

  • A
    $220s$
  • B
    $30s$
  • C
    $300s$
  • Correct answer
    D
    $347s$

Solution

For first order reaction $A \longrightarrow B$ Given that rate $=k \times[A]$ Rate $=2.0 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ $[A]=$ Conc. of $A=0.01 \mathrm{M}$ So, $2.0 \times 10^{-5}=k \times 0.01$ $\begin{aligned} k & =\frac{2.0 \times 10^{-5}}{0.01} \mathrm{~s}^{-1} \\ & =2.0 \times 10^{-3} \mathrm{~s}^{-1}\end{aligned}$ For first order reaction $\begin{aligned} T_{1 / 2} & =\frac{0.693}{k}=\frac{0.693}{2.0 \times 10^{-3}} \\ & =346.5 \approx 347 \mathrm{~s}\end{aligned}$

Hence, the correct answer is option: 'D'.

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