Question

(i) $ X ( g ) \rightleftharpoons Y ( g )+ Z$ (g) $ K _{ p 1}=3$
(ii) $A ( g ) \rightleftharpoons 2 B ( g )\,\, K _{ p 2}=1$
If the degree of dissociation and initial concentration of both the reactants $X ( g )$ and $A ( g )$ are equal, then the ratio of the total pressure at equilibrium $\left(\frac{p_1}{p_2}\right)$ is equal to $x : 1$. The value of $x$ is _________ (Nearest integer)

Answer 1

$k_{ p _1}=\frac{\left(\frac{\alpha}{1+\alpha} \times p _1\right)^2}{\frac{1-\alpha}{1+\alpha} p _1} $
$ 3=\frac{\alpha^2 \times p _1}{1-\alpha^2}$

$ k _{ p _2}=\frac{\left(\frac{2 \alpha}{1+\alpha} \times p _2\right)^2}{\frac{1-\alpha}{1+\alpha} \times p _2} $
$ 1=\frac{4 \alpha^2 \times p _2}{1-\alpha^2} $
$ \frac{ k _{ p _1}}{ k _{ p _2}}=\frac{ p _1}{4 p _2} $
$\frac{3}{1}=\frac{ p _1}{4 p _2} $
$\therefore p _1: p _2=12: 1$
$ x =12$