For which of the following reaction, the degree of dissociation (α) and equilibrium constant (K_p) are related as ${\mathrm{K}}_{\mathrm{p}}=\frac{4{\mathrm{\alpha }}^2\mathrm{P}}{\left(1-{\mathrm{\alpha }}^2\right)}$?
(1) ${\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right) \rightleftharpoons 2{\mathrm{NO}}_2\left(\mathrm{g}\right)$
(2) ${\mathrm{H}}_2\left(\mathrm{g}\right) + {\mathrm{I}}_2\left(\mathrm{g}\right) \rightleftharpoons 2\mathrm{HI}\left(\mathrm{g}\right)$
(3) ${\mathrm{N}}_2\left(\mathrm{g}\right) + 3{\mathrm{H}}_2\left(\mathrm{g}\right) \rightleftharpoons 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$
(4) ${\mathrm{PCl}}_3\left(\mathrm{g}\right) + {\mathrm{Cl}}_2\left(\mathrm{g}\right) \rightleftharpoons {\mathrm{PCl}}_5\left(\mathrm{g}\right)$

Solution

Thanks yaar

The equilibrium constant up for the gaseous reaction A-->2B is related to degree of dissociation alpha of A and total pressure P as

Thanks for clearing

                         N2O4(g) ⇌ 2NO2(g) Initially:                    1                  0 Finally:                   1-α                2α Let х = mole fraction = number of moles/ total moles ; P= total pressure Now, total moles = 1-α+2α = 1+α We know, Kp= (PNO2)²/PN2O4 =  (хNO2 * P)²/(хN2O4 * P) = (2αP/(1+α))²/((1-α)P/(1+α)) = 4α²P/((1+α)(1-α)) = 4α²P/(1-α²) Hence, option (1) N2O4(g) ⇌ 2NO2(g) is correct