# For which of the following reaction, the degree of dissociation (α) and equilibrium constant (Kp) are related as ${\mathrm{K}}_{\mathrm{p}}=\frac{4{\mathrm{\alpha }}^{2}\mathrm{P}}{\left(1-{\mathrm{\alpha }}^{2}\right)}$? (1)  (2)  (3)  (4)

Answer is 1) because it is a decomposition reaction and it is a general formula for a decomposition reaction. You just have to cram it, no other choice
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Solution

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

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Thanks for clearing
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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
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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
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