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NEET CHEMISTRYEquilibriumMedium

Question

For the reaction 3O2(g)2O3(g)3\text{O}_2(g) \rightleftharpoons 2\text{O}_3(g) at 298 K298\text{ K}, KcK_c is found to be 3.0×10593.0 \times 10^{-59}. If the concentration of O2\text{O}_2 at equilibrium is 0.040 M0.040\text{ M}, then the concentration of O3\text{O}_3 in M\text{M} is:

A

1.2×10211.2 \times 10^{21}

B

4.38×10324.38 \times 10^{-32}

C

1.9×10631.9 \times 10^{-63}

D

2.4×10312.4 \times 10^{31}

Step-by-Step Solution

The given balanced chemical equation is: 3O2(g)2O3(g)3\text{O}_2(g) \rightleftharpoons 2\text{O}_3(g)

For this reaction, the equilibrium constant expression (KcK_c) is written as the ratio of the concentration of the product raised to its stoichiometric coefficient to the concentration of the reactant raised to its stoichiometric coefficient: Kc=[O3]2[O2]3K_c = \frac{[\text{O}_3]^2}{[\text{O}_2]^3}

Given the values at equilibrium: Kc=3.0×1059K_c = 3.0 \times 10^{-59} [O2]=0.040 M=4×102 M[\text{O}_2] = 0.040\text{ M} = 4 \times 10^{-2}\text{ M}

Substituting these values into the equilibrium constant expression: 3.0×1059=[O3]2(4×102)33.0 \times 10^{-59} = \frac{[\text{O}_3]^2}{(4 \times 10^{-2})^3} [O3]2=3.0×1059×(4×102)3[\text{O}_3]^2 = 3.0 \times 10^{-59} \times (4 \times 10^{-2})^3 [O3]2=3.0×1059×64×106[\text{O}_3]^2 = 3.0 \times 10^{-59} \times 64 \times 10^{-6} [O3]2=192×1065[\text{O}_3]^2 = 192 \times 10^{-65} [O3]2=19.2×1064[\text{O}_3]^2 = 19.2 \times 10^{-64}

Taking the square root on both sides to find the concentration of ozone: [O3]=19.2×1064=19.2×1032[\text{O}_3] = \sqrt{19.2 \times 10^{-64}} = \sqrt{19.2} \times 10^{-32} Since 16=4\sqrt{16} = 4 and 25=5\sqrt{25} = 5, 19.2\sqrt{19.2} is approximately 4.384.38. [O3]4.38×1032 M[\text{O}_3] \approx 4.38 \times 10^{-32}\text{ M}

Thus, the concentration of O3\text{O}_3 is 4.38×1032 M4.38 \times 10^{-32}\text{ M}.

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.

CHEMISTRYEquilibriumreactiontextogrightleftharpoonstextogconcentration

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