Question

The half-life period and initial concentration for a reaction are as follows

Initial concentration (M)	350	540	158
$t_{1/2}$ (hr)	425	275	941

What is order of reaction?

Answer 1

$t_{1 /2} \propto \left(a\right)^{1-n} $
For I $\Rightarrow 425 \propto\left(350\right)^{1-n}$ ____$\left(i\right)$
For II $\Rightarrow 275 \propto \left(540\right)^{1-n}$______ $\left(ii\right)$
For III $\Rightarrow 941 \propto\left(158\right)^{1-n}$______ $\left(iii\right)$
By Eqns. $\left(i\right)$ and $\left(ii\right)$ , $\frac{425}{275}=\left(\frac{350}{540}\right)^{1-n}$
Taking log $\Rightarrow log \frac{425}{275}$
$=\left(1-n\right)log \frac{350}{540} \Rightarrow n=2$