Question

A(g) $\rightleftharpoons$ nB(g)

Initial mole 1(say) 0

Equilibrium mole 1 –$\alpha$ n$\alpha$

Total moles = 1–$\alpha$ + n$\alpha$ = 1 + $\alpha$ (n – 1)

Now, $K_{P} = \frac{P_{B}^{n}}{P_{A}} = \frac{\left\lbrack \frac{n\alpha}{1 + \alpha(n - 1)}.P \right\rbrack^{n}}{\left\lbrack \frac{1 - \alpha}{1 + \alpha(n - 1)}.P \right\rbrack} = \frac{(n\alpha)^{n}.P^{n - 1}}{(1 - \alpha).\left\lbrack 1 + \alpha(n - 1) \right\rbrack^{n - 1}}$