For the reaction 2A(g) + B(g) ⇌ 2C(g), the equilibrium constant Kc is 0.50 at a certain temperature. If the equilibrium concentrations are [A] = 0.20 M and [B] = 0.10 M, what is the equilibrium concentration of C?
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Correct answer
C. 0.045 M
Principle or equation
The equilibrium constant expression for the reaction 2A + B ⇌ 2C is Kc = [C]^2 / ([A]^2 [B]). Given Kc, [A], and [B], solve for [C].
Why this answer is correct
Substitute the given values into the equilibrium expression: 0.50 = [C]^2 / (0.20^2 × 0.10) = [C]^2 / 0.0040. Multiply both sides by 0.0040: [C]^2 = 0.0020. Taking the square root gives [C] ≈ 0.045 M.
Example
For N2 + 3H2 ⇌ 2NH3, Kc = [NH3]^2 / ([N2][H2]^3). If Kc = 4.0, [N2] = 0.50, [H2] = 0.25, then [NH3]^2 = 4.0 × 0.50 × 0.25^3 = 0.03125, so [NH3] = 0.177 M.
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