Ncert Exercises & Solutions

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

For a first order reaction,

$t = \frac{2.303}{K} \log \frac{{[R]}_{0}}{[R]}$
$K = \frac{2.303}{40 m i n} \log \frac{100}{100 - 30}$
$= \frac{2.303}{40 m i n} \log \frac{10}{7}$
$= 8.918 \times 10^{- 3} m i n^{- 1}$
$T h e r e f o r e, t_{1} = 2 t_{2}$ 2 of the decomposition reaction is

$t_{1 / 2} = \frac{0.693}{K}$
$= \frac{0.693}{8.918 \times 10^{- 3}} m i n$
$= 77.7 m i n (a p p r o x i m a t e l y)$

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