Sol. $$ \begin{aligned} & \quad A_{(\mathrm{g})} \quad \rightarrow \quad \mathrm{B}_{(\mathrm{g})}+\mathrm{C}_{(\mathrm{g})} \\ & \mathrm{t}=0 \quad P^{\circ} \\ & \mathrm{t}=\mathrm{t} \quad \mathrm{P}^{\circ}-\mathrm{x} \\ & \mathrm{t}=\infty \quad 0 \quad \mathrm{x} \quad \mathrm{x} \\ & P_t=P^{\circ}+x \Rightarrow x=P_t-P^{\circ}=P_t-\frac{P_{\infty}}{2} \\ & P_{\infty}=2 P^{\circ} \Rightarrow P^{\circ}=\frac{P_{\infty}}{2} \\ & k=\frac{1}{t} \ln \frac{P^{\circ}}{P^{\circ}-x} \\ & k=\frac{1}{t} \ln \frac{P_{\infty}}{2\left(P_{\infty}-P_t\right)} \end{aligned} $$