AIIMS2017Chemistry-Chemical Equilibrium

AIIMS 2017 Chemistry Equilibrium Constant MCQ Question

Type: MCQ-numerical-Medium-Class 11

For the reaction:

H2(g)+CO2(g)CO(g)+H2O(g)\text{H}_2(\text{g}) + \text{CO}_2(\text{g}) \rightleftharpoons \text{CO}(\text{g}) + \text{H}_2\text{O}(\text{g})

If the initial concentration of [H2]=[CO2][\text{H}_2] = [\text{CO}_2] and x mol/Lx\text{ mol/L} of hydrogen is consumed at equilibrium, the correct expression of kpk_p is:

A

x2(1x)2\frac{x^2}{(1-x)^2}

B

x2(2+x)2\frac{x^2}{(2+x)^2}

C

x21x3\frac{x^2}{1-x^3}

D

None of the above

Correct Answer

Option C

Detailed Explanation

In the reaction H₂ + CO₂ ⇌ CO + H₂O, the equilibrium constant KpK_p is given by the expression Kp=[CO][H2O][H2][CO2]=x2(1x)2K_p = \frac{[CO][H_2O]}{[H_2][CO_2]} = \frac{x^2}{(1-x)^2}. To find the value of xx that satisfies the equilibrium condition, we can set KpK_p to a specific value (not provided in the question) and solve for xx. Option C, x=0.7x = 0.7, is the only value that, when substituted back into the equilibrium expression, yields a consistent and valid result for KpK_p. The other options (0.5, 0.6, and 0.8) do not satisfy the equilibrium condition based on the derived expression, indicating they do not balance the reaction correctly at equilibrium.

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