For the following three reactions $\mathrm{a}, \mathrm{b}$ and c , equilibrium constants are given: a. $\quad \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) ; \quad \mathrm{K}_{1}$ b. $\mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g}) ; \quad \mathrm{K}_{2}$ c. $\mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2}(\mathrm{~g}) ; \mathrm{K}_{3}$ Which of the following relations is correct?

(C) $\mathrm{K}_{3}=\mathrm{K}_{1} \mathrm{~K}_{2}$

(A) $\mathrm{K}_{1} \sqrt{\mathrm{~K}_{2}}=\mathrm{K}_{3}$

(B) $\mathrm{K}_{2} \mathrm{~K}_{3}=\mathrm{K}_{1}$

(D) $\mathrm{K}_{3} \cdot \mathrm{~K}_{2}^{3}=\mathrm{K}_{1}^{2}$

JEE Main · 2008 · 27 Apr 2008 · Offline · Equilibrium

For the following three reactions

a, b

and c , equilibrium constants are given:
a.

CO (g) + H_{2} O (g) ⇌ CO_{2} (g) + H_{2} (g); K_{1}

CH_{4} (g) + H_{2} O (g) ⇌ CO (g) + 3 H_{2} (g); K_{2}

CH_{4} (g) + 2 H_{2} O (g) ⇌ CO_{2} (g) + 4 H_{2} (g); K_{3}

Which of the following relations is correct?

(A) $K_{1} K_{2} = K_{3}$
(B) $K_{2} K_{3} = K_{1}$
(C) $K_{3} = K_{1} K_{2}$ ✓ Correct
(D) $K_{3} \cdot K_{2}^{3} = K_{1}^{2}$

Answer: (C)

Solution

Reaction (c) is just the sum of reactions (a) and (b): adding the conversion of carbon monoxide and water into carbon dioxide and hydrogen to the conversion of methane and water into carbon monoxide and hydrogen gives the net conversion of methane and water into carbon dioxide and hydrogen. When equilibria are added their equilibrium constants multiply, so

K_{3} = K_{1} K_{2}

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option

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JEE Main · 2008 · 27 Apr 2008 · Offline · Equilibrium

Solution

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