Question

The half-life period and the initial concentration for a reaction are as follows. What is order of reaction?

Initial concentration	$350$	$540$	$158$
$t_{1/2}$	$425$	$275$	$941$

Answer 1

For nth order reaction, the relationship between the half life period and initial concentration is as given below.

$\because t_{1/2}=(a{)}^{1-n}$ when n is order of reaction

$425\propto (350{)}^{1-n}$ ....(i)

$275\propto (540{)}^{1-n}$ ....(ii)

$941\propto (158{)}^{1-n}$ ....(iii)

Divide equation (ii) with equation (i) to obtain $\frac{425}{275}={\left[\frac{350}{540}\right]}^{1-n}$

Taking log,

$log\frac{425}{275}=(1-n)log\frac{350}{540}$

$n=2$

Hence, the reaction is of second order.