Question

In a homogenous reaction $A \longrightarrow B+C+D$ the initial pressure was $P_{0}$ and after time $t$ it was $P$. Expression for rate constant $k$ in terms of $P_{\alpha}$ $P$ and $t$ will be

• A. $k=\frac{2.303}{t}\log \frac{2P_{0}}{3P_{0}-P}$
• B. $k=\frac{2.303}{t}\log \frac{2P_{0}}{P_{0}-P}$
• C. $k=\frac{2.303}{t}\log \frac{3P_{0}-P}{2P_{0}}$
• D. $k=\frac{2.303}{t}\log \frac{2P_{0}}{3P_{0}-2P}$

Answer 1

Answer: (A)

$\begin{matrix}&A&\rightarrow&B&+&C&+&D\\ {\text{Initial}}&a&&0&&0&&0\\ {\text{After time t}} &a- x&&x&&x&&x\end{matrix}$

It is given that $a=P_{0}\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)$

$a-x+x+x+x=P$

or $\,\,\,\,\,a+2 x=P\,\,\,\,\,\,\,,\,\,\,....(ii)$

From (i),

$P_{0}+2 x=P$

or $x=\frac{P-P_{0}}{2}$

From rate equation

$k=\frac{2.303}{t} \log \frac{a}{a-x}$

$=\frac{2.303}{t} \,\log \frac{P_{0}}{P_{0}-\left(\frac{P-P_{0}}{2}\right)}=\frac{2.303}{t}\, \log \frac{2 P_{0}}{3 P_{0}-P}$