Question

The values of $ K_{p_1} $ and $ K_{p_2} $ for the reactions
$X \rightleftharpoons Y + Z .......(i) $
and $ A \rightleftharpoons 2B .......(ii) $
are in ratio of $9 : 1$. If degree of dissociation of $X$ and $A$ be equal, then total pressure at equilibrium (i) and (ii) are in the ratio

• A. 3:1
• B. 1:9
• C. 36:1
• D. 1:1

Answer 1

Answer: (C)

$\frac{ K _{ P _{1}}}{ K _{ I _{2}}}=\frac{\frac{ P _{1}^{2} \alpha^{2}}{ P _{1}(1+a)}}{\frac{\left(2 P _{2} a\right)^{2}}{ P _{2}(1+a)}} \Rightarrow \frac{ P _{1}^{2} \alpha^{2} \times P _{2}}{ P _{1} \times 4 P _{1}^{2} \alpha^{2} P _{2}}$
$\frac{ K _{ P _{1}}}{ K _{ P _{2}}}=\frac{ P _{1}}{4 P _{2}}=\frac{9}{1}$
$P _{1}=36 P _{2}$
Total pressure $(1)= P _{1}+ P _{1} \alpha $
Total pressure $(2)= P _{2}+ P _{2} \alpha$
$\frac{P_{1}+P_{1} \alpha}{P_{2}+P_{2} \alpha}=\frac{P_{1}(1+\alpha)}{P_{2}(1+\alpha)} \Rightarrow \frac{P_{1}}{P_{2}}=36: 1$