Equilibrium concentration of C in A + 3B ⇌ 2C reaction

Practice question

Question

For the reaction A(g) + 3B(g) <=> 2C(g) , Kc = 125 at 400 K. If 1 mole of A and 4 moles of B are placed in a 2 L vessel, what is [C] at equilibrium?

Options

Choose one · Correct answer highlighted

0.38 M Correct 0.5 M 0.76 M 1.0 M

Explanation

Initial: [A] = (1/2) = 0.5 M , [B] = (4/2) = 2 M , [C] = 0 . Let 2x be moles of C formed, so A decreases by x , B by 3x . At equilibrium: [A] = 0.5 - x , [B] = 2 - 3x , [C] = x . Kc = ([C]²/[A][B]³) = ((x)²/(0.5 - x)(2 - 3x)³) = 125 . Solving, test x = 0.4 : ((0.4)²/(0.1)(0.2)³) = (0.16/0.0008) = 200 (too high), x = 0.35 , ((0.35)²/(0.15)(0.35)³) = (0.1225/0.0064) ≈ 19 (too low), x ≈ 0.38 , [C] = 0.38 M .

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