The equilibrium constant, K_p for the gaseous reaction A$\rightleftharpoons$2B  is related to degree of dissociation ($\mathrm{\alpha }$) of A and total pressure P as

Given

Degree of dissociation of 'A' = α

Equilibrium pressure = P

Stoichimetry
Initial moles	1		-
Moles at equilibrium	1 - α		2α

Total moles at equilibrium = 1 - α + 2α = 1 + α

Mole fraction of A at equilibrium,  ${\mathrm{X}}_{\mathrm{A}}=\frac{1-\mathrm{\alpha }}{1+\mathrm{\alpha }}$

${\mathrm{P}}_{\mathrm{A}}={\mathrm{X}}_{\mathrm{A}}\times \mathrm{Total} \mathrm{pressure}$

${\mathrm{P}}_{\mathrm{A}}=\left(\frac{1-\mathrm{\alpha }}{1+\mathrm{\alpha }}\right)\times \mathrm{P}$

Similarly ${\mathrm{X}}_{\mathrm{B}}=\frac{2\mathrm{\alpha }}{1+\mathrm{\alpha }}$

${\mathrm{P}}_{\mathrm{B}}={\mathrm{X}}_{\mathrm{B}}\times \mathrm{Total} \mathrm{pressure}$

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