b
\({N_2}{O_5}\, \to \,2N{O_2}\, + \,\frac{1}{2}{O_2}\)

At    \(t=0\)                     \(50\)              \(0\)               \(0\)

At    \(t=50\,min\)         \(50-p_1\)        \(2p_1\)      \(\frac {p_1}{2}\)

Total pressure at \(50\,\min\)

\(=\,50-p_1+2p_1+\frac {p_1}{2}=87.5\)

\(50+\frac {3p_1}{2}=87.5\)

\(\frac{{3{p_1}}}{2}\, = \,37.5\)

\(\therefore \,\,{p_1}\, = \frac{{\,37.5\, \times 2}}{3}\, = \,25\)

At \(t=100\,min\)  \(50-p_2\)   \(2p_2\)  \(\frac {p_2}{2}\)

\(50\,\min\) is half life period

For \(100\,\min\) i.e., for \(2\) half lives \(50-p_2=12.5\)

\(\therefore \,\,{p_2}\, = 37.5\,mm\) of \(Hg\)

Total pressure at \(100\,\min\)

\( = {\mkern 1mu} 50 - {p_2} + 2{p_2} + \frac{{{p_2}}}{2}\)

\( = {\mkern 1mu} 50 + \frac{{3{p_2}}}{2}\, = \,50 + \frac{3}{2} \times 37.5\)

\(=\,50\,+\,56.25\)

\(=\,106.25\,mm\) of \(Hg\)