Chemistry - Chemical Kinetics Question with Solution | TestHub

The gas phase decomposition of dimethylether follows first order kinetics
$\mathrm{C}{\mathrm{H}}_3-\mathrm{O}-\mathrm{C}{\mathrm{H}}_3\left(\mathrm{g}\right)\to \mathrm{C}{\mathrm{H}}_4\left(\mathrm{g}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)+\mathrm{C}{\mathrm{O}}_{\left(\mathrm{g}\right)}$
The reaction is carried out in constant volume container at${500}^{\mathrm{o}}\mathrm{C}$and has a half-life of$\text{14}\text{.5}\text{min}$. Initially only dimethylether is present at a pressure of$\text{0}\text{.40}\text{atm}$. The total pressure of the system after$\text{12}\text{min}$is$\frac{\text{x}}{\text{100}}\text{atm}$. The value of$\mathrm{x}$is
[Given${\text{10}}^{\text{0}\text{.25}}\text{=}\text{1}\text{.778}$]