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NEET CHEMISTRYEquilibriumHard

Question

The value of Kp1K_{p_1} and Kp2K_{p_2} for the reactions XY+ZX \rightleftharpoons Y + Z ...(i) and A2BA \rightleftharpoons 2B ...(ii) are in the ratio of 9:19 : 1. If the degree of dissociation of X and A is equal, then the total pressure at equilibrium (i) and (ii) are in the ratio:

A

3 : 1

B

1 : 9

C

36 : 1

D

1 : 1

Step-by-Step Solution

For the reaction XY+ZX \rightleftharpoons Y + Z: Initial moles: 1, 0, 0 Moles at equilibrium: 1α1-\alpha, α\alpha, α\alpha Total moles at equilibrium = 1α+α+α=1+α1 - \alpha + \alpha + \alpha = 1 + \alpha Partial pressures: pX=1α1+αP1p_X = \frac{1-\alpha}{1+\alpha} P_1, pY=α1+αP1p_Y = \frac{\alpha}{1+\alpha} P_1, pZ=α1+αP1p_Z = \frac{\alpha}{1+\alpha} P_1 Kp1=pYpZpX=(α1+αP1)(α1+αP1)1α1+αP1=α21α2P1K_{p_1} = \frac{p_Y p_Z}{p_X} = \frac{(\frac{\alpha}{1+\alpha} P_1)(\frac{\alpha}{1+\alpha} P_1)}{\frac{1-\alpha}{1+\alpha} P_1} = \frac{\alpha^2}{1-\alpha^2} P_1

For the reaction A2BA \rightleftharpoons 2B: Initial moles: 1, 0 Moles at equilibrium: 1α1-\alpha, 2α2\alpha Total moles at equilibrium = 1α+2α=1+α1 - \alpha + 2\alpha = 1 + \alpha Partial pressures: pA=1α1+αP2p_A = \frac{1-\alpha}{1+\alpha} P_2, pB=2α1+αP2p_B = \frac{2\alpha}{1+\alpha} P_2 Kp2=pB2pA=(2α1+αP2)21α1+αP2=4α21α2P2K_{p_2} = \frac{p_B^2}{p_A} = \frac{(\frac{2\alpha}{1+\alpha} P_2)^2}{\frac{1-\alpha}{1+\alpha} P_2} = \frac{4\alpha^2}{1-\alpha^2} P_2

Given Kp1Kp2=91\frac{K_{p_1}}{K_{p_2}} = \frac{9}{1} α21α2P14α21α2P2=P14P2=91\frac{\frac{\alpha^2}{1-\alpha^2} P_1}{\frac{4\alpha^2}{1-\alpha^2} P_2} = \frac{P_1}{4P_2} = \frac{9}{1} P1P2=361\frac{P_1}{P_2} = \frac{36}{1} Therefore, the ratio of total pressures at equilibrium is 36:136 : 1.

Exam Context & Concepts Covered

This question aligns with the NEET CHEMISTRY syllabus, specifically targeting concepts from Equilibrium. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

CHEMISTRYEquilibriumreactionsrightleftharpoonsrightleftharpoonsdegreedissociation

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