JEE Main 2018 — Chemical Kinetics Question with Solution

${\mathrm{N}}_2{\mathrm{O}}_5\to 2{\mathrm{NO}}_2+\frac{1}{2}{\mathrm{O}}_2$ $\begin{array}{llll}\text{ At }\mathrm{t}=0& 50& 0& 0\\ \text{ At }\mathrm{t}=50\min & 50-{\mathrm{p}}_1& 2{\mathrm{p}}_1& \frac{{\mathrm{p}}_1}{2}\end{array}$ Total pressure at $50$ minutes $\begin{aligned} &=50-\mathrm{p}_1+2 \mathrm{p}_1+\frac{\mathrm{p}_1}{2}=87.5 \\ &50+\frac{3 \mathrm{p}_1}{2}=87.5 \\ &\frac{3 \mathrm{p}_1}{2}=37.5 \\ &\therefore \quad \mathrm{p}_1=\frac{37.5 \times 2}{3}=25 \end{aligned}$ At $\mathrm{t}=100\min 50-{\mathrm{p}}_{2}2{\mathrm{p}}_2\frac{{\mathrm{p}}_2}{2}$ $50$ minutes is half life period For $100$ minutes i.e. for $2$ half lives $50-p_2=12.5$ $\therefore {\mathrm{p}}_2=37.5\mathrm{mm}\text{ of }\mathrm{Hg}$ Total pressure at $100$ minutes $=50-{\mathrm{p}}_2+2{\mathrm{p}}_2+\frac{{\mathrm{p}}_2}{2}$ $=50+\frac{3{\mathrm{p}}_2}{2}=50+\frac{3}{2}\times 37.5$ $=50+56.25$ $=106.25\mathrm{mm}$ of $\mathrm{Hg}$