Equilibrium Constant Calculation for Gas-Phase Reaction Steps:

• Reaction stoichiometry: 0.100 mol SO₃ formed consumes 0.100 mol SO₂ and 0.050 mol O₂.
• Equilibrium moles: SO₂ = 0.200 - 0.100 = 0.100 mol; O₂ = 0.200 - 0.050 = 0.150 mol; SO₃ = 0.100 mol.
• Concentrations (1 dm³ volume): [SO₂] = 0.100 mol dm⁻³; [O₂] = 0.150 mol dm⁻³; [SO₃] = 0.100 mol dm⁻³.
• Kc = [SO₃]² / ([SO₂]² [O₂]) = (0.100)² / ((0.100)² × 0.150) = 0.01 / 0.0015 = 6.67 dm³ mol⁻¹.

Why D is correct:

• D equals the Kc value from the equilibrium expression Kc = [SO₃]² / ([SO₂]² [O₂]).

Why the others are wrong:

• A: Equals 1/Kc, inverting the expression.
• B: From using initial instead of equilibrium concentrations.
• C: From halving SO₃ consumption incorrectly.

Final answer: D