The half life period of a first order chemical reaction is $6.93$ minutes. The time required for the…

The half life period of a first order chemical reaction is $6.93$ minutes. The time required for the completion of $99 \%$ of the chemical reaction will be $(\log 2=0.301)$ :
  1. $230.3$ minutes
  2. $23.03$ minutes
  3. $46.06$ minutes
  4. $460.6$ minutes

Solution

$ \begin{aligned} & \because \lambda=\frac{0.6932}{t_{1 / 2}}=\frac{0.6932}{6.93} \min ^{-1} \\ & \text { Also } t=\frac{2.303}{\lambda} \log \frac{\left[A_{\circ}\right]}{[A]} \\ & {\left[A_{\circ}\right]=\text { initial concentration (amount) }} \\ & {[A]=\text { final concentration (amount) }} \\ & \therefore t=\frac{2.303 \times 6.93}{0.6932} \log \frac{100}{1} \\ & =46.06 \text { minutes } \end{aligned} $

Asked in: JEE Main 2009

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