Question

For $A\left(g\right)\rightleftharpoons 2B\left(g\right)$, equilibrium constant at total equilibrium pressure $p_1$ is $K_{P_1}\text{and for C(g)}\rightleftharpoons D\left(g\right)+E\left(g\right),$
equilibrium constant at total equilibrium pressure $P_2$ is $K_{p2}.$ If degree of dissociation of A and C are same, then the ratio $K_{P_1}/K_{P_2},$ if $2P_1=P_2,$ is:

• A. 2
• B. $\frac{1}{8}$
• C. $\frac{1}{2}$
• D. 8

Answer 1

The correct option is A 2

For $A\left(g\right)\rightleftharpoons 2B\left(g\right)\text{initial}1\text{at eqb}1-\alpha 2\alpha$,
$K_{P_1}=\frac{4{\alpha }^2{P}_1}{1-{\alpha }^2}$

$\text{and similarly for C(g)}\rightleftharpoons D\left(g\right)+E\left(g\right),$
$K_{P_2}=\frac{{\alpha }^2{P}_2}{1-{\alpha }^2}$

$\text{Given,}2P_1=P_2$
$\Rightarrow \frac{P_1}{P_2}=\frac{1}{2}$
$\Rightarrow \frac{K_{P_1}}{K_{P_2}}=\frac{4P_1}{P_2}$
$\Rightarrow \frac{K_{P_1}}{K_{P_2}}=4\times \frac{1}{2}=2$