Question

The equilibrium constants $K_{P1}$ and $K_{P2}$ for the reaction $X\rightleftharpoons 2Y$ and $Z\rightleftharpoons P+Q$, respectively are in the ratio of $1:9$. If the degree of dissociation of $X$ and $Z$ be equal then the ratio of total pressure at these equilibria is:

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

Answer 1

The correct option is A $1:36$

Let us consider the problem.

$\underset{\stackrel{1}{\left(1-x\right)}}{X}\rightleftharpoons \underset{\underset{2x}{0}}{2}Y$

For,

$K{p}_1=\frac{{\left(2x\right)}^2}{\left(1-x\right)}\left(\frac{P_1}{1+x}\right)$

Hence,

$\underset{\left(1-x\right)}{Z}\rightleftharpoons \underset{\underset{x}{0}}{P}+\underset{\underset{x}{0}}{Q}$

For,

$K{p}_2=\frac{{\left(x\right)}^2}{\left(1-x\right)}{\left(\frac{P_1}{1+x}\right)}^1$

$\frac{4\times P_1}{P_2}=\frac{1}{36}$

$\frac{P_1}{P_2}=\frac{1}{36}$