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NEET CHEMISTRYEquilibriumMedium

Question

The reaction 2A+B(g)⇌3C(g)+D(g)2\text{A} + \text{B}(g) \rightleftharpoons 3\text{C}(g) + \text{D}(g) begins with the concentrations of A and B both at an initial value of 1.00 M1.00 \text{ M}. When equilibrium is reached, the concentration of D is measured and found to be 0.25 M0.25 \text{ M}. The value for the equilibrium constant for this reaction is given by the expression:

A

[(0.75)3(0.25)][(0.50)2(0.75)]\frac{[(0.75)^3(0.25)]}{[(0.50)^2(0.75)]}

B

[(0.75)3(0.25)][(0.50)2(0.25)]\frac{[(0.75)^3(0.25)]}{[(0.50)^2(0.25)]}

C

[(0.75)3(0.25)][(0.75)2(0.25)]\frac{[(0.75)^3(0.25)]}{[(0.75)^2(0.25)]}

D

[(0.75)3(0.25)][(1.00)2(1.00)]\frac{[(0.75)^3(0.25)]}{[(1.00)^2(1.00)]}

Step-by-Step Solution

Reaction: 2A+B⇌3C+D2\text{A} + \text{B} \rightleftharpoons 3\text{C} + \text{D}

Initial concentrations: [A]0=1.00 M[\text{A}]_0 = 1.00 \text{ M} [B]0=1.00 M[\text{B}]_0 = 1.00 \text{ M} [C]0=0 M[\text{C}]_0 = 0 \text{ M} [D]0=0 M[\text{D}]_0 = 0 \text{ M}

At equilibrium, [D]=0.25 M[\text{D}] = 0.25 \text{ M}. From the stoichiometry of the reaction, if xx is the concentration of D formed at equilibrium, then x=0.25 Mx = 0.25 \text{ M}. The change in concentrations will be: Change in [D]=+x=+0.25 M[\text{D}] = +x = +0.25 \text{ M} Change in [C]=+3x=+3(0.25)=+0.75 M[\text{C}] = +3x = +3(0.25) = +0.75 \text{ M} Change in [A]=−2x=−2(0.25)=−0.50 M[\text{A}] = -2x = -2(0.25) = -0.50 \text{ M} Change in [B]=−x=−0.25 M[\text{B}] = -x = -0.25 \text{ M}

Therefore, the equilibrium concentrations are: [A]=1.00−0.50=0.50 M[\text{A}] = 1.00 - 0.50 = 0.50 \text{ M} [B]=1.00−0.25=0.75 M[\text{B}] = 1.00 - 0.25 = 0.75 \text{ M} [C]=0+0.75=0.75 M[\text{C}] = 0 + 0.75 = 0.75 \text{ M} [D]=0.25 M[\text{D}] = 0.25 \text{ M}

The equilibrium constant KcK_c is given by the expression: Kc=[C]3[D][A]2[B]K_c = \frac{[\text{C}]^3[\text{D}]}{[\text{A}]^2[\text{B}]}

Substituting the equilibrium values into the expression: Kc=(0.75)3(0.25)(0.50)2(0.75)K_c = \frac{(0.75)^3(0.25)}{(0.50)^2(0.75)}

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.

CHEMISTRYEquilibriumreactiontextbgrightleftharpoonstextcgtextdg

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