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Calculating Equilibrium Concentrations

AP Chemistry· difficulty 4/5

For A ⇌ B + C with K = 0.10, starting from [A] = 1.0 M, [B] = [C] = 0. At equilibrium, [B] is approximately (xx NOT negligible)

  • A

    0.27 M (solve x2/(1.0−x)=0.10x^2/(1.0-x) = 0.10)

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  • B

    0.50 M

  • C

    0.10 M

  • D

    1.0 M

Explanation

x2=0.10(1.0−x)=0.10−0.10xx^2 = 0.10(1.0 - x) = 0.10 - 0.10x. Quadratic: x2+0.10x−0.10=0x^2 + 0.10x - 0.10 = 0. x=(−0.10+0.01+0.40)/2=(−0.10+0.640)/2=0.270x = (-0.10 + \sqrt{0.01 + 0.40})/2 = (-0.10 + 0.640)/2 = 0.270.

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