Question

The equilibrium constants $K_{p1}$ and $K_{p2}$ for the reactions $X\rightleftharpoons 2Y$ and $Z\rightleftharpoons P+Q$, respectively are in the ratio of $1:9$. If degree of dissociation of $X$ and $Z$ be equal then the ratio if total pressures at these equlibria is

• A. $1:9$
• B. $1:36$
• C. $1:1$
• D. $1:3$

Answer 1

The correct option is B $1:36$

$X\rightleftharpoons 2Y,Z\rightleftharpoons P+Q$
$\text{Initial moles}10100$
$\text{at equilibrium}1-\alpha 2\alpha 1-\alpha \alpha \alpha$
$K_{p1}=\frac{P_Y^2}{P_X}=\frac{(\frac{2\alpha }{1+\alpha }{P}_1{)}^2}{\left(\frac{1-\alpha }{1+\alpha }{P}_1\right)}$
$K_{p2}=\frac{P_P{P}_Q}{P_Z}=\frac{\left(\frac{\alpha }{1+\alpha }{P}_2\right)\left(\frac{\alpha }{1+\alpha }{P}_2\right)}{\frac{1-\alpha }{1+\alpha }{P}_2})...(i)$
$\Rightarrow K_{P1}=\frac{4{\alpha }^2{P}_1}{1-{\alpha }^2}...\left(ii\right)$
Given,
$\frac{K_{P1}}{K_{P2}}=\frac{1}{9}...\left(iii\right)$
Substituting values from equation (i) and (ii) into (iii), we get
$\frac{\frac{4{\alpha }^2{P}_1}{1-{\alpha }^2}}{\frac{{\alpha }^2{P}_2}{1-{\alpha }^2}}=\frac{1}{9}$
$\Rightarrow \frac{4P_1}{P_2}=\frac{1}{9}$
$\Rightarrow \frac{P_1}{P_2}=\frac{1}{36}$