Question

At $300\text{K}$ and 1 atm pressure, the half-life of a sample of a gaseous compound is $100\text{sec}$. When the pressure is 0.5 atm the half-life is $50\text{sec}$. The order of reaction is:

Answer 1

we know,

$t_{\frac{1}{2}}\propto {\text{[initial concentration or initial pressure]}}^{1-\text{order}}$
Given,
$100\propto (1{)}^{1-n}....(i)$
$50\propto (0.5{)}^{1-n}...(ii)$
Dividing (i) by (ii)
$2=(2{)}^{1-n}=1-n=1$
$\Rightarrow n=0$
Hence the order of the reaction is zero