a
In equation, \(\quad X \rightleftharpoons Y+Z\)

Initial moles \(\quad 0\quad \quad 0 \; \quad 0\)

At equil. \(\;\;\;\;(1-\alpha) \quad \alpha \quad \alpha\)

where, \(\alpha=\) degree of dissociation

Total number of moles

\(=1-\alpha+\alpha+\alpha=(1+\alpha)\)

\(P_{x}=\left(\frac{1-\alpha}{1+\alpha}\right) P_{1}\)

\(P_{y}=\left(\frac{\alpha}{1+\alpha}\right) P_{1}\)

\(P_{z}=\frac{\alpha}{1-\alpha} P_{1}\)

\(K_{p 1}=\frac{[p y][p z]}{[p x]}=\frac{\left(\frac{a}{1+\alpha}\right) p 1 \times\left(\frac{a}{1+\alpha}\right) p 1}{\left(\frac{1-\alpha}{1+\alpha}\right) p 1}\)

\(=\frac{\left(\frac{\alpha}{1+\alpha}\right)^{2} p 1}{\left(\frac{1-\alpha}{1+\alpha}\right)} \quad \cdots(i)\)

For equation, \(A \rightleftharpoons 2 B\)

Initial moles \(\;\;1 \;\;\;\quad 0\)

At equil. \(\;\;(1-\alpha) \;\;\;2 \alpha\)

Total number of moles at equilibrium \(=(1+\alpha)\) \(p_{B}=\left(\frac{2 \alpha}{1+\alpha}\right) p_{2}\)

\(p_{A}=\left(\frac{1-\alpha}{1+\alpha}\right) p_{2}\)

\(K_{p 2}=\frac{\left[p_{B}\right]^{2}}{\left[p_{A}\right]}\)\(=\frac{\left[\left(\frac{2 a}{1+\alpha}\right) p_{2}\right]^{2}}{\left(\frac{1-\alpha}{1+\alpha}\right)} \quad \cdots (i i)\)

Eq. \((i)\) divide by Eq. \((ii)\)

\(\frac{K_{\mathrm{pl}}}{K_{\mathrm{p} 2}}=\frac{\alpha^{2} \times p_{1}}{4 \alpha^{2} \times p_{2}}\)

\(\frac{9}{1}=\frac{p_{1}}{4 p_{2}}\)

\(\frac{p_{1}}{p_{2}}=\frac{36}{1}=36: 1\)