In the reaction X2 (g) + 2Y(g) ⇌ 2Z (g). 12.00 moles of Z are placed in an evacuated 2.00-liter flask. After equilibrium, the flask contains 6.00 moles of Y. What is the equilibrium constant, K, for the reaction?

• A. 0.333
• B. 0.667
• C. 1.50
• D. 3.00

Answer: (B)

This question tests how to apply the equilibrium-constant expression for a gas-phase reaction and extract equilibrium concentrations from the data. The reaction is X2 + 2 Y ⇌ 2 Z. Initially, only Z is present: 12.00 moles in 2.00 L gives [Z]0 = 6.0 M, while [X2]0 and [Y]0 are zero.

The system shifts toward products, but we’re told at equilibrium there are 6.00 moles of Y. Since Y increases by 2 per extent of the reverse reaction, 2ξ = 6, so ξ = 3 moles. This means Z decreases by 2ξ = 6, giving Z_eq = 12 − 6 = 6 moles; X2 increases by ξ = 3 moles, giving X2_eq = 3 moles. All species are in 2.00 L, so concentrations are [X2] = 3/2 = 1.5 M, [Y] = 6/2 = 3.0 M, [Z] = 6/2 = 3.0 M.

Now use the equilibrium-constant expression: Kc = [Z]^2 / ([X2][Y]^2) = (3.0)^2 / (1.5 × (3.0)^2) = 9 / 13.5 ≈ 0.6667, which is 0.667.