Calculating Kc from equilibrium moles

Steps:

• From 0.100 mol SO₃ produced, use stoichiometry: 2y = 0.100 mol SO₃, so y = 0.050 mol (O₂ consumed) and 2y = 0.100 mol (SO₂ consumed).
• Equilibrium moles: SO₂ = 0.200 - 0.100 = 0.100 mol; O₂ = 0.200 - 0.050 = 0.150 mol; SO₃ = 0.100 mol.
• In 1.00 dm³, concentrations equal moles: [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) = 0.0100 / 0.00150 = 6.67 dm³ mol⁻¹.

Why D is correct:

• Matches Kc formula for reaction with Δn = -1, yielding units dm³ mol⁻¹.

Why the others are wrong:

• A: From inverting Kc or wrong stoichiometry.
• B: From using initial moles without equilibrium adjustment.
• C: From partial consumption error, like assuming equal reactant depletion.

Final answer: D