The half life of the first order reaction ${\text{CH}}_{\text{3}}\text{.CHO}\left(\text{g}\right)\to {\text{\hspace{0.17em}CH}}_{\text{4}}\left(\text{g}\right)\text{+CO}\left(\text{g}\right)$If initial pressure of    ${\text{CH}}_{\text{3}}\text{CHO}\left(\text{g}\right)$is 80 mm Hg and the total pressure at the end of 20 minutes is 120 mm Hg

${\text{CH}}_{\text{3}}\text{CHO}\left(\text{g}\right)\to {\text{\hspace{0.17em}CH}}_{\text{4}}\left(\text{g}\right)\text{\hspace{0.17em}+\hspace{0.17em}CO}\left(\text{g}\right)$

${\text{When\hspace{0.17em}t\hspace{0.17em}=\hspace{0.17em}0 p}}^{\text{0}}\text{ 0 0}$

${\text{When\hspace{0.17em}t\hspace{0.17em}=\hspace{0.17em}t p}}^{\text{0}}\text{ -p p p}$

$\therefore {\text{p}}^{\text{0}}-\text{\hspace{0.17em}p\hspace{0.17em}+\hspace{0.17em}p\hspace{0.17em}+\hspace{0.17em}p\hspace{0.17em}=\hspace{0.17em}120\hspace{0.17em}mm\hspace{0.17em}Hg}$

${\text{or,\hspace{0.17em}p}}^{\text{0}}\text{+p\hspace{0.17em}=\hspace{0.17em}120\hspace{0.17em}mm\hspace{0.17em}Hg;}$

$\text{p\hspace{0.17em}=\hspace{0.17em}120\hspace{0.17em}-\hspace{0.17em}80\hspace{0.17em}=\hspace{0.17em}80\hspace{0.17em}=\hspace{0.17em}40\hspace{0.17em}mm\hspace{0.17em}Hg}$

$\text{k\hspace{0.17em}=\hspace{0.17em}}\frac{\text{1}}{\text{t}}\text{\hspace{0.17em}In\hspace{0.17em}}\frac{{\text{p}}^{\text{0}}}{{\text{p}}^{\text{0}}-\text{\hspace{0.17em}p}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{\text{1}}{\text{20}}\text{\hspace{0.17em}In\hspace{0.17em}}\frac{\text{80}}{\text{80\hspace{0.17em}}-\text{\hspace{0.17em}40}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{\text{1}}{\text{20}}\text{\hspace{0.17em}In\hspace{0.17em}2}$

${\text{Again\hspace{0.17em},\hspace{0.17em}t}}_{\text{1/2}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{\text{ln2}}{\text{k}}$

$\therefore {\text{\hspace{0.17em}t}}_{\text{1/2}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{\text{In2}}{\text{In2}}\text{\hspace{0.17em}×\hspace{0.17em}20\hspace{0.17em}=\hspace{0.17em}20\hspace{0.17em}min}$