Question

For the reaction:
$2NO\left(g\right)+C{l}_2\left(g\right)\to 2NOCl\left(g\right)$, the mixture containing an equimolar mixture of $NO$ and $C{l}_2$ gases at 0.15 $atm$ was half consumed in 175 s. Another experiment, having an initial pressure of 0.35 atm, the mixture was half consumed in 75 s. Find the order of reaction.

Answer 1

Half-life is related to the initial concentration and to the order of the reaction as:
$\left(\frac{t_2}{t_1}\right)=(\frac{a_1}{a_2}{)}^{n-1}$
where, $a_1$ is the initial concentration, has the half-life $t_1$ and $a_2$ is the initial concentration has the half-life $t_2$ and $n$ is the order of reaction
so putting all the values in the above equation we get,
$\left(\frac{75}{175}\right)=(\frac{0.15}{0.35}{)}^{n-1}$
$(0.428{)}^1=(0.428{)}^{n-1}$
$\therefore n-1=1$
$n=2$