The time taken for $90 \%$ of a first order reaction to complete is approximately

The time taken for $90 \%$ of a first order reaction to complete is approximately
  1. $1.1$ times that of half-life
  2. $2.2$ times that of half-life
  3. $3.3$ times that of half-life
  4. $4.4$ times that of half-life

Solution

$t_{90 \%}=\frac{2.303}{k} \log \frac{100}{100-90}$ (I)
$t_{50 \%}=\frac{2.303}{k} \log \frac{100}{100-50}$ (II)
Dividing $\frac{t_{90 \%}}{t_{50 \%}}=\frac{\log 10}{\log 2}$
$\therefore t_{90 \%}=3.3 t_{50 \%}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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