Question

In a homogenous reaction $A⟶B+C+D$ 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)

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

It is given that $a=P_0...(i)$

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

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

From (i),

$P_0+2x=P$

or $x=\frac{P-P_0}{2}$

From rate equation

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

$=\frac{2.303}{t}\log \frac{P_0}{P_0-\left(\frac{P-P_0}{2}\right)}=\frac{2.303}{t}\log \frac{2P_0}{3P_0-P}$