A first order reaction takes 40 min for 30% decomposition.

Question:

A first order reaction takes 40 min for 30% decomposition. Calculate t1/2.

Solution:

For a first order reaction,

$t=\frac{2.303}{k} \log \frac{[\mathrm{R}]_{0}}{[\mathrm{R}]}$

$k=\frac{2.303}{40 \mathrm{~min}} \log \frac{100}{100-30}$

$=\frac{2.303}{40 \mathrm{~min}} \log \frac{10}{7}$

$=8.918 \times 10^{-3} \mathrm{~min}^{-1}$

Therefore, t1/2 of the decomposition reaction is

$t_{1 / 2}=\frac{0.693}{k}$

$=\frac{0.693}{8.918 \times 10^{-3}} \mathrm{~min}$

= 77.7 min (approximately)

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