Question

A first order reaction takes 20 minutes for 25% decomposition. Calculate the time when 75% of the reaction will be completed.
(Given: $log2=0.3010,log3=0.4771,log4=0.6021)$

Answer 1

$t=20\text{min,}{A}_0=100\%,A=100-25=75\%,k=?$
$k=\frac{1}{t}\times 2.303log\frac{A_0}{A}$
$=\frac{1}{20}\times 2.303log\frac{100}{75}=\frac{1}{20}\times 2.303log\left(1.33\right)$
$=\frac{1}{20}\times 2.303\times 0.1248$
$=0.0143mi{n}^{-1}$
So for 75% completion.
$t=\frac{1}{k}\times 2.303\times log\frac{A_0}{A}$
$=\frac{1}{0.0143}\times 2.303\times log\frac{100}{25}=96.96min$