${\mathrm{N}}_2{\mathrm{O}}_5$ decomposes to ${\mathrm{NO}}_2$ and ${\mathrm{O}}_2$ follows the first order kinetics. After $50$ minutes, the pressure inside the vessel increases from $50 \mathrm{mm} \mathrm{Hg}$ to $87.5 \mathrm{mm} \mathrm{Hg}$. The pressure of the gaseous mixture after $100$ minutes at constant temperature will be:

$\begin{array}{l} {\mathrm{N}}_2{\mathrm{O}}_5\to 2{\mathrm{NO}}_2+\frac{1}{2}{\mathrm{O}}_2\\ \mathrm{t}=0 50 0 0\\ \\ \mathrm{t}=50\mathrm{mins}\mathrm{\hspace{0.17em}} 50-{\mathrm{p}}_1\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{\hspace{0.17em}}2{\mathrm{p}}_1\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\frac{\mathrm{\hspace{0.17em}}{\mathrm{p}}_1}{2}\\ \\ \mathrm{t}=100\mathrm{mins}\hspace{0.17em}\hspace{0.17em}\mathrm{\hspace{0.17em}}50-{\mathrm{p}}_2\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}2{\mathrm{p}}_2\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{\hspace{0.17em}}\frac{\mathrm{\hspace{0.17em}}{\mathrm{p}}_2}{2}\end{array}$

$50-{\mathrm{p}}_1+2{\mathrm{p}}_1+\frac{{\mathrm{p}}_1}{2}=87.5$

$50+\frac{3{\mathrm{p}}_1}{2}=87.5$

$\frac{3{\mathrm{p}}_1}{2}=37.5$

${\mathrm{p}}_1=\frac{37.5\times 2}{3}=25$

$50$ minutes is half-life period.

For $100$ minutes ( half-life $2$)

$50-{\mathrm{p}}_2=12.5$

${\mathrm{p}}_2=37.5\mathrm{ }\mathrm{mm}\mathrm{ }\mathrm{Hg}$

Total pressure at $100$ minutes.

$=50-{\mathrm{p}}_2+2\mathrm{ }{\mathrm{p}}_2+\frac{{\mathrm{p}}_2}{2}$ $$

$50+\frac{3{\mathrm{p}}_2}{2}=50+\frac{3}{2}\times 37.5$

$=50+56.25$

$=106.25 \mathrm{mm} \mathrm{of} \mathrm{Hg}$.