$\begin{aligned}
& \begin{array}{lllll}
& A_{(g)} & \rightarrow & B_{(g)} & +
C_{(g)} \
t=0 & P^o & & 0 & 0 \
t=t & P^o-x & & x & x \
t=\infty & 0 & & P^o & P^o
\end{array} \
& \mathrm{P}{\mathrm{t}}=\mathrm{P}^{\mathrm{o}}+\mathrm{x} \Rightarrow \mathrm{x}=\mathrm{P}{\mathrm{t}}-\mathrm{P}^{\mathrm{o}}=\mathrm{P}{\mathrm{t}}-\frac{\mathrm{P}{\infty}}{2} \
& \mathrm{P}_{\infty}=2 \mathrm{P}^{\mathrm{o}} \Rightarrow \mathrm{P}^0=\frac{\mathrm{P} \infty}{2} \
& \mathrm{k}=\frac{1}{\mathrm{t}} \ell \ln \frac{\mathrm{P}^{\mathrm{o}}}{\mathrm{P}^{\mathrm{o}}-\mathrm{x}} \
& k=\frac{1}{t} \ell n \frac{P_{\infty}}{2\left(P_{\infty}-P_t\right)}
\end{aligned}$