For the reaction 2A(g) + 2B(g) 3C(g) , Kc = 64 at 500 K. If 2 moles of A and 2 moles of B are placed in a 1 L vessel, wh

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Question

For the reaction 2A(g) + 2B(g) <=> 3C(g) , Kc = 64 at 500 K. If 2 moles of A and 2 moles of B are placed in a 1 L vessel, what is [C] at equilibrium?

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2.18 M Correct 1.5 M 3.0 M 0.727 M

Explanation

Initial: [A] = 2 M , [B] = 2 M , [C] = 0 . Let 3x be moles of C formed, so A and B decrease by 2x . At equilibrium: [A] = 2 - 2x , [B] = 2 - 2x , [C] = 3x . Kc = ([C]³/[A]²[B]²) = ((3x)³/(2 - 2x)² (2 - 2x)²) = (27x³/(2 - 2x)⁴) = 64 , (27x³/(2 - 2x)⁴) = 64 , (3x/2 - 2x) = 4 , 3x = 8 - 8x , 11x = 8 , x ≈ 0.727 , [C] = 3 × 0.727 ≈ 2.18 M .

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