A flask contains a mixture of compounds A and B . Both compounds decompose by first-order kinetics. The…

${\mathrm{C}}_{\mathrm{t}}={\mathrm{C}}_0{\mathrm{e}}^{-\mathrm{kt}}$

${\mathrm{k}}_{\mathrm{A}}=\frac{\ln 2}{300}$        $\left(\mathrm{k}=\frac{\ln 2}{{\mathrm{T}}_{1/2}}\right)$

${\mathrm{k}}_{\mathrm{B}}=\frac{\ln 2}{180}$

${\left({\mathrm{C}}_{\mathrm{t}}\right)}_{\mathrm{A}}={\left({\mathrm{C}}_0\right)}_{\mathrm{A}}{\mathrm{e}}^{-{\mathrm{k}}_{\mathrm{A}}\mathrm{t}}$        

${\left({\mathrm{C}}_{\mathrm{t}}\right)}_{\mathrm{B}}={\left({\mathrm{C}}_0\right)}_{\mathrm{B}}{\mathrm{e}}^{-{\mathrm{k}}_{\mathrm{B}}\mathrm{t}}$

$\frac{{\left({\mathrm{C}}_{\mathrm{t}}\right)}_{,\mathrm{B}}}{\left({\mathrm{C}}_{\mathrm{t}}\right),\mathrm{A}}=\frac{{\left({\mathrm{C}}_0\right)}_{,\mathrm{B}}}{\left({\mathrm{C}}_0\right),\mathrm{A}}\times {\mathrm{e}}^{\left({\mathrm{k}}_{\mathrm{A}}-{\mathrm{k}}_{\mathrm{B}}\right)\mathrm{t}}$

$\frac{1}{4}={\mathrm{e}}^{\left({\mathrm{k}}_{\mathrm{A}}-{\mathrm{k}}_{\mathrm{B}}\right)\mathrm{t}}$

$\ln \frac{1}{4}=\left[\frac{\ln 2}{300}-\frac{\ln 2}{180}\right]\mathrm{t}$

$-2\ln 2=\left[\frac{\ln 2}{300}-\frac{\ln 2}{180}\right]\mathrm{t}$

$2=\left(\frac{120}{180\times 300}\right)\mathrm{t}$

$\mathrm{t}=\frac{2\times 180\times 300}{120}=900 \sec$