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NEET CHEMISTRYEquilibriumMedium

Question

Given that the equilibrium constant for the reaction 2SO2(g)+O2(g)2SO3(g)2\text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2\text{SO}_3(g) has a value of 278278 at a particular temperature, the value of the equilibrium constant for the following reaction at the same temperature will be: SO3(g)SO2(g)+12O2(g)\text{SO}_3(g) \rightleftharpoons \text{SO}_2(g) + \frac{1}{2} \text{O}_2(g)

A

3.6×1033.6 \times 10^{-3}

B

6.0×1026.0 \times 10^{-2}

C

1.3×1051.3 \times 10^{-5}

D

1.8×1031.8 \times 10^{-3}

Step-by-Step Solution

Let the given reaction be: (i) 2SO2(g)+O2(g)2SO3(g)2\text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2\text{SO}_3(g); K1=278K_1 = 278

The target reaction is: (ii) SO3(g)SO2(g)+12O2(g)\text{SO}_3(g) \rightleftharpoons \text{SO}_2(g) + \frac{1}{2}\text{O}_2(g)

Reaction (ii) is obtained by reversing reaction (i) and dividing it by 22 (or multiplying by 12\frac{1}{2}). When a reaction is reversed, its equilibrium constant becomes the inverse of the original . When a reaction is multiplied by a factor nn, the new equilibrium constant is the original equilibrium constant raised to the power nn . Therefore, the equilibrium constant K2K_2 for reaction (ii) will be: K2=(1K1)12=1K1K_2 = \left(\frac{1}{K_1}\right)^{\frac{1}{2}} = \frac{1}{\sqrt{K_1}} K2=1278=116.670.05996.0×102K_2 = \frac{1}{\sqrt{278}} = \frac{1}{16.67} \approx 0.0599 \approx 6.0 \times 10^{-2}.

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.

CHEMISTRYEquilibriumequilibriumconstantreactiontextsogtextog

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Consider the following reaction: $\text{A}_2(g) + \text{B}_2(g) \rightleftharpoons 2\text{AB}(g)$. At equilibrium, the concentrations of $[\text{A}_2] = 3.0 \times 10^{–3} \text{ M}$; $[\text{B}_2] = 4.2 \times 10^{–3} \text{ M}$ and $[\text{AB}] = 2.8 \times 10^{–3} \text{ M}$. The value of $K_c$ for the above-given reaction in a sealed container at $527^\circ\text{C}$ is:

A.3.9
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