b
\(\quad\quad\quad\quad A ( g ) \rightleftharpoons B ( g )+\frac{1}{2} C ( g )\)

Initial \(:\quad \, P _{ i } \quad\quad\quad0\quad\quad\quad 0\)

At eq.\(: \,P _{ i }(1-\alpha)\quad P _{ i } \cdot \alpha \quad P _{ i } \frac{\alpha}{2}\)

Now, equilibrium pressure (p),

\(P = P _{ i } \times\left(1+\frac{\alpha}{2}\right)\)

\(\therefore P _{ A }=\left(\frac{1-\alpha}{1+\frac{\alpha}{2}}\right) P\)

\(P _{ B }=\left(\frac{\alpha}{1+\frac{\alpha}{2}}\right) P\)

\(P _{ C }=\left(\frac{\frac{\alpha}{2}}{1+\frac{\alpha}{2}}\right) P\)

\(\therefore K =\frac{ P _{ c }^{\frac{1}{2}} \times P _{ B }}{ P _{ A }}\)

\(K =\frac{\alpha^{\frac{3}{2}} p ^{\frac{1}{2}}}{(2+\alpha)^{\frac{1}{2}}(1-\alpha)}\)