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

We have

$$\begin{gathered} \mathrm{X}\rightleftharpoons 2\mathrm{Y} \\ {p}_{\mathrm{X}}(1-\alpha ) p_{\mathrm{X}}\left(2\alpha \right) p_{\text{eql }}=p_{\mathrm{X}}(1-\alpha )+p_{\mathrm{X}}\left(2\alpha \right)=p_{\mathrm{X}}(1+\alpha ) \end{gathered}$$

$K_{p1}=\left(\frac{p_{\mathrm{Y}}^2}{p_{\mathrm{X}}}\right)=\frac{{\left\{p_{\mathrm{X}}\left(2\alpha \right)\right\}}^2}{p_{\mathrm{X}}(1-\alpha )}=\frac{4p_{\mathrm{X}}{\alpha }^2}{1-\alpha }$

$Z\rightleftharpoons P+Q$

$p_{\mathrm{Z}}(1-\alpha ) p_{\mathrm{Z}}\alpha p_{\mathrm{Z}}\alpha p_{\text{eq }2}=p_{\mathrm{Z}}(1-\alpha )+p_{\mathrm{Z}}\alpha +p_{\mathrm{Z}}\alpha =p_{\mathrm{Z}}(1+\alpha )$

$K_{p2}=\left(\frac{p_{\mathrm{P}}{p}_{\mathrm{Q}}}{p_{\mathrm{Z}}}\right)=\frac{\left(p_{\mathrm{Z}}\alpha \right)\left(p_{\mathrm{Z}}\alpha \right)}{p_{\mathrm{Z}}(1-\alpha )}=\frac{p_{\mathrm{Z}}{\alpha }^2}{1-\alpha }$. Now $\frac{K_{p1}}{K_{p2}}=\frac{4p_{\mathrm{X}}{\alpha }^2/(1-\alpha )}{p_{\mathrm{Z}}{\alpha }^2/(1-\alpha )}=\frac{4p_{\mathrm{X}}}{p_{\mathrm{Z}}}$

It is given $K_{p1}/K_{p2}$ that= 1/9. Hence $\frac{p_{\mathrm{X}}}{p_{\mathrm{Z}}}=\frac{1}{36}$ Also $\frac{p_{\mathrm{eq}1}}{p_{\mathrm{eq}2}}=\frac{p_{\mathrm{X}}}{p_{\mathrm{Z}}}=\frac{1}{36}$