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

Answer: 2

$t_{1/2}\propto {\left(a\right)}^{1-n}$
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 $\Rightarrow log\frac{425}{275}$
$=\left(1-n\right)log\frac{350}{540}\Rightarrow n=2$