Question

A first order reaction takes $20$ minutes for $25$% decomposition. Calculate the time when $75$% of the reaction will be completed?
(Given: $\log 2=0.3010,\log 3=0.4771,\log 4=0.6021)$

Answer 1

A first order reaction takes 20 minutes for 25% decomposition.
$k=\frac{2.303}{t}log\frac{a}{a-x}$
$k=\frac{2.303}{20min}log\frac{a}{a-\left(0.25a\right)}$
$k=\frac{2.303}{20min}log\frac{1}{0.75}$
$k=0.0144/min$
When 75% of the reaction will be completed.
$t=\frac{2.303}{k}log\frac{a}{a-x}$
$t=\frac{2.303}{0.0144/min}log\frac{a}{a-\left(0.75a\right)}$
$t=\frac{2.303}{0.0144/min}log\frac{1}{0.25}$
$t=\frac{2.303}{0.0144/min}log4$
$t=\frac{2.303}{0.0144/min}\times 0.6021$
$t=96.4min$