• # question_answer For a homogeneous gaseous reaction $\operatorname{A}\xrightarrow{{}}3B,$, if pressure after time t was ${{\operatorname{P}}_{t}}$ and after completion of reaction, pressure was ${{\operatorname{P}}_{\infty }}$ then select correct relation A) $\operatorname{k}=\frac{1}{t}ln\left( \frac{{{P}_{\infty }}}{3\left( {{P}_{\infty }}-{{P}_{t}} \right)} \right)$ B) $\operatorname{k}=\frac{1}{t}ln\left( \frac{2{{P}_{\infty }}}{\left( {{P}_{\infty }}-{{P}_{t}} \right)} \right)$ C) $\operatorname{k}=\frac{1}{t}ln\left( \frac{3{{P}_{\infty }}}{2{{P}_{\infty }}-{{P}_{\operatorname{t}}}} \right)$ D) $\operatorname{k}=\frac{1}{t}ln\left( \frac{2{{P}_{\infty }}}{3\left( {{P}_{\infty }}-{{P}_{\operatorname{t}}} \right)} \right)$

 ${{P}_{T}}={{P}_{0}}+2x$ $x=\frac{{{P}_{T}}{{P}_{0}}}{2}$ $k=\frac{1}{t}\ln \left( \frac{{{P}_{0}}}{{{P}_{0}}-x} \right)$ After long time, $x=\frac{{{P}_{T}}-\frac{{{P}_{\infty }}}{3}}{2}$
 $k=\frac{1}{t}\ln \left( \frac{\frac{{{P}_{\infty }}}{3}}{\frac{{{P}_{\infty }}}{3}-\left( \frac{3{{P}_{T}}-{{P}_{\infty }}}{6} \right)} \right)$ ${{P}_{\infty }}=3{{P}_{O}},x=\frac{3{{P}_{T}}-{{P}_{\infty }}}{6}$ $k=\frac{1}{t}\ln \left( \frac{{{P}_{\infty }}/3}{\frac{{{P}_{\infty }}}{2}-\frac{{{P}_{T}}}{2}} \right)$ $k=\frac{1}{t}\ln \left( \frac{2{{P}_{\infty }}}{3\left( {{P}_{\infty }}-{{P}_{T}} \right)} \right)$