The equilibrium constants $K_{P_{1}}$ and $K_{P_{2}}$ for the reactions $X \rightleftharpoons 2 Y$ 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

JEE Main · 2008 · 27 Apr 2008 · Offline · Equilibrium

The equilibrium constants

K_{P_{1}}

and

K_{P_{2}}

for the reactions

X ⇌ 2 Y

and

Z ⇌ 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

Answer: (A)

For

X ⇌ 2 Y

the equilibrium constant in terms of the degree of dissociation and total pressure is

K_{p_{1}} = \frac{4 α ^{2} P _{1}}{1 - α ^{2}}

, while for

Z ⇌ P + Q

it is

K_{p_{2}} = \frac{α ^{2} P _{2}}{1 - α ^{2}}

, the factor of four coming from the two moles of

Y

produced. With equal degrees of dissociation their ratio is

\frac{K _{p_{1}}}{K _{p_{2}}} = \frac{4 P _{1}}{P _{2}}

, and setting this equal to

\frac{1}{9}

gives

\frac{P _{1}}{P _{2}} = \frac{1}{36}

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option