For the reaction 2A(g) + B(g) 3C(g) , Kc = 64 at 300 K. If 2 moles of A and 1 mole of B are placed in a 2 L vessel, what

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Question

For the reaction 2A(g) + B(g) <=> 3C(g) , Kc = 64 at 300 K. If 2 moles of A and 1 mole of B are placed in a 2 L vessel, what is [C] at equilibrium?

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Choose one · Correct answer highlighted

0.72 M Correct 0.96 M 0.48 M 1.44 M

Explanation

Initial: [A] = (2/2) = 1 M , [B] = (1/2) = 0.5 M , [C] = 0 . Let 3x be moles of C formed, so A decreases by 2x , B by x . At equilibrium: [A] = 1 - x , [B] = 0.5 - x , [C] = 1.5x . Kc = ([C]³/[A]²[B]) = ((1.5x)³/(1 - x)²(0.5 - x)) = 64 . Simplifying, (3.375x³/(1 - x)²(0.5 - x)) = 64 . Trial: x = 0.4 , [A] = 0.6 , [B] = 0.1 , [C] = 0.6 , ((0.6)³/(0.6)²(0.1)) = (0.216/0.036) = 6 , too small. Solving approximately, x ≈ 0.48 , [C] = 1.5 × 0.48 = 0.72 M .

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