A first order reaction is half-completed in 45 minutes. How long does it need for $99.9 \%$ of the reaction…

A first order reaction is half-completed in 45 minutes. How long does it need for $99.9 \%$ of the reaction to be completed?
  1. 20 hours
  2. 10 hours
  3. $7 \frac{1}{2}$ hours
  4. 5 hours

Solution

$k=\frac{0.693}{45}$ further
$t=\frac{2.303}{0.693} \times 45 \log \frac{100}{100-99.9}$
$=\frac{2.303 \times 45 \times 3}{0.693}=7 \frac{1}{2}$ hours.

Asked in: JEE-TOPICTESTS-CHEMISTRY

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