Question

The half life of two samples are $0.1$ and $0.4$ second. Their respective concentrations are $200$ and $50$ respectively. What is the order of the reaction?

Answer 1

Answer: 2

$t_{1/2}\propto a^{1-n}$
$\therefore \frac{0.1}{0.4}=\frac{(200{)}^{1-n}}{(50{)}^{1-n}}={\left(\frac{200}{50}\right)}^{1-n}$
$\therefore \frac{1}{4}=(4{)}^{1-n}$
or $(4{)}^{-1}=(4{)}^{1-4}$ of
or $(4{)}^{-1}=(4{)}^{1-n}$ or $-1=1-n$ or $n=2$