Question

For a first order reaction $A→B$, the rate constant, $k=5.5×10^{−14}{s}^{−1}$. The time required for $67\%$ completion of reaction is $x×10^{−1}$ times the half life of reaction. The value of $x$ is ______(Nearest integer)
(Given : $\log 3=0.4771$ )

Answer 1

Answer: 16

$t_{67\%}=\frac{1}{k}\ln \left(\frac{1}{1−0.67}\right)=\frac{t_{1/2}}{\ln 2}×\ln \left(\frac{1}{1−\frac{2}{3}}\right)$
$t_{67\%}=\frac{t_{1/2}}{\log 2}×\log 3=\frac{t_{1/2}×0.4771}{0.301}$
$⇒t_{67\%}=1.585×t_{1/2}$
$X×10^{−1}=1.585$
$⇒X=15.85$
Ans.16