Question

For a homogeneous gaseous reaction, $A\to B+C+D$, the initial pressure was $P_0$ while pressure after time $t$ was $P$. Expression for rate constant $K$ in terms of $P_0$, $P$ and $t$ is:

• A. $K=\frac{2.303}{t}log\frac{\left[2P_0\right]}{[3P_0-P]}$
• B. $K=\frac{2.303}{t}log\frac{\left[4P_0\right]}{[2P_0-P]}$
  
• C. $K=\frac{2.303}{t}log\frac{\left[3P_0\right]}{[P_0-P]}$
• D. none of these

Answer 1

The correct option is A $K=\frac{2.303}{t}log\frac{\left[2P_0\right]}{[3P_0-P]}$

Initial pressure $=P_0$

From reaction,
Total pressure at time t $=P=P_0-x+x+x+x=P_0+2x$

$2x=P-P_0$

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

$P_0-x=P_0-\frac{P-P_0}{2}=\frac{3P_0-P}{2}$

$\frac{P_0}{P_0-x}=\frac{2P_0}{3P_0-P}$

The expression for rate constant is $K=\frac{2.303}{t}log\frac{\left[2P_0\right]}{[3P_0-P]}$