a
Let the initial moles of \(X\) be \(^{\prime} a^{\prime}\)

and that of \(Z\) be \(^{\prime} b^{\prime}\) the for the given reactions,

we have \(X \quad \rightleftharpoons \quad 2 Y\)

Initial        \(a\, moles \quad \quad 0\)

At equi. \(\quad a(1-\alpha) \quad 2 a \alpha\)

\(a(1-\alpha) \quad 2 a \alpha\)

Total no. of moles \(=a(1-\alpha)+2 a \alpha\)

\(=a-a \alpha+2 a \alpha=a(1+\alpha)\)

Now, \(\quad K_{p_{1}}=\frac{\left(n_{y}\right)^{2}}{n_{x}} \times\left(\frac{P_{r_{1}}}{\sum n}\right)^{\Delta n}\)

or, \(\quad K_{p_{1}}=\frac{(2 a \alpha)^{2} \cdot P_{T_{1}}}{[a(1-\alpha)][a(1+\alpha)]}\)

\(Z \rightleftharpoons P+Q\)

Initial \(\quad\) \(b \,moles\) \(\quad 0 \quad 0\)

Ar equi. \(\quad b(1-\alpha) \quad b \alpha \quad b \alpha\)

Total no. of moles

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

\(=b-b \alpha+b \alpha+b \alpha\)

\(=b(1+\alpha)\)

Now \(\quad K_{P_{2}}=\frac{n_{Q} \times n_{P}}{n_{z}} \times\left[\frac{P_{r_{2}}}{\Sigma_{n}}\right]^{\Delta n}\)

 \(\quad K_{P_{2}}=\frac{(b \alpha)(b \alpha) \cdot P_{T_{2}}}{|b(1-\alpha)||b(1+\alpha)|}\)

or \(\quad \frac{K_{P_{1}}}{K_{P_{2}}}=\frac{4 \alpha^{2} \cdot P_{T_{1}}}{\left(1-\alpha^{2}\right)} \times \frac{(1-\alpha)^{2}}{P_{T_{2}} \cdot \alpha^{2}}\)

\(=\frac{4 P r_{1}}{P r_{2}}\)

\(\frac{P_{T_{1}}}{P_{F_{2}}}=\frac{1}{9} \quad[\) as

\(\left.\frac{K_{P_{1}}}{K_{P_{1}}}=\frac{1}{9} \text { given }\right]\)

\(\frac{P_{T_{1}}}{P_{T 2}}=\frac{1}{36}\)

\(1: 36\)