Question

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

• A. 1:1
• B. 1:3
• C. 1:9
• D. 1:36

Answer 1

Answer: (D)

1:36

let the initial pressure of X and Z be $P_1$ and $P_2$ respectively

$X\rightleftharpoons 2Y$

$P_1(1-\alpha )2P_1\alpha$

$K_1=\frac{4P_1{\alpha }^2}{1-\alpha }$

$Z\rightleftharpoons P+Q$

$P_2(1-\alpha )P_2\alpha P_2\alpha$

$K_2=\frac{P_2{\alpha }^2}{1-\alpha }$

$\frac{K_1}{K_2}=\frac{4P_1}{P_2}=\frac{1}{9}$

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

ratio of total pressures $=\frac{P_1(1+\alpha )}{P_2(1+\alpha )}=\frac{P_1}{P_2}=\frac{1}{36}$

So, the correct option is $D$