At certain temperature, the half life period in the thermal decomposition of a gaseous substance as follows:

$\mathrm{P}\left(\mathrm{mmHg}\right)$	$500$	$250$
${\mathrm{t}}_{1/2}$ (in min.)	$235$	$950$

Find the order of reaction [Given $\log (23.5)=1.37;\log \left(95\right)=1.97]$

A first order reaction is 50% completed in 20 minutes at 27°C and in 5 minutes at 47°C. The energy of activation of the reaction is :

Given that for a reaction of ${\mathrm{n}}^{\mathrm{th}}$ order, the integrated rate equation is: $\mathrm{k}=\frac{1}{\mathrm{t}(\mathrm{n}-1)}\left[\frac{1}{{\mathrm{C}}^{\mathrm{n}-1}}-\frac{1}{{\mathrm{C}}_0^{\mathrm{n}-1}}\right]$, where ${\mathrm{C}}_0$ and $\mathrm{C}$ are the values of the reactant concentration at the start and after time$\mathrm{t}$. What is the relationship between ${\mathrm{t}}_{\frac{3}{4}}$ and ${\mathrm{t}}_{\frac{1}{2}}$?

( ${\mathrm{t}}_{\frac{3}{4}}$ is the time required for $\mathrm{C}$ to become $\frac{1}{4}{\mathrm{C}}_0$)

$\mathrm{A}\to \mathrm{B}$      ${\mathrm{K}}_{\mathrm{A}}={10}^{15}{\mathrm{e}}^{-2000/\mathrm{T}}$

$\mathrm{C}\to \mathrm{D}$     ${\mathrm{K}}_{\mathrm{C}}={10}^{14}{\mathrm{e}}^{-1000/\mathrm{T}}$

Temperature $\mathrm{TK}$ at which $\left({\mathrm{K}}_{\mathrm{A}}={\mathrm{K}}_{\mathrm{C}}\right)$ is :

For the reaction $\mathrm{A}+2 \mathrm{B}\to$ products (started with concentrations taken in stoichiometric proportion), the experimentally determined rate law is :

 $-\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}=\mathrm{k} \sqrt{\left[\mathrm{A}\right] }\sqrt{\left[\mathrm{B}\right]}$

The half life time of the reaction would be: