A(g)$\to$ B(g) + C(g) follows first order kinetics. Initial pressure of ‘A’ 108 mm of Hg.  After 100 minutes the total pressure was found to be 189 mm of Hg. Half-life of the reaction (in seconds) is 

$\begin{array}{l}\mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{A}\left(\mathrm{g}\right)\to \mathrm{B}\left(\mathrm{g}\right)+\mathrm{c}\left(\mathrm{g}\right)\\ \mathrm{At}\mathrm{\hspace{0.17em}\hspace{0.17em}}\mathrm{t}=0\mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\mathrm{P}}_0\\ \mathrm{At}\mathrm{\hspace{0.17em}\hspace{0.17em}}\mathrm{t}=100\mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\mathrm{P}}_0-\mathrm{x}\mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{x}\mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{x}\\ \mathrm{\hspace{0.17em}}\mathrm{At}\mathrm{\hspace{0.17em}\hspace{0.17em}}\mathrm{t}=\infty \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-\mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\mathrm{P}}_0\mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\mathrm{P}}_0\end{array}$

          $P_t=P_0-x+x+x=189$

          ${\mathrm{P}}^{\mathrm{\infty }}=2{\mathrm{P}}_0=2\times 108=216$

          $\mathrm{Kt}=2.303\log \frac{{\mathrm{P}}^{\mathrm{\infty }}-{\mathrm{P}}^0}{{\mathrm{P}}^{\mathrm{\infty }}-{\mathrm{P}}_{\mathrm{t}}}$

          $K\times 100=2.303\log \frac{216-108}{216-189}$

          $\mathrm{k}=\frac{2.303}{100}\log \frac{108}{27}=\frac{2.303}{100}=\log 4$

          $k=\frac{2.303\times 2\log 2}{100}=0.0138{\min }^{-1}$

          ${\mathrm{t}}_{1/2}=\frac{0.693}{\mathrm{k}}=\frac{0.693}{0.0138}\simeq 50$min = 3000 sec