Units of Kc depend on Δn for the reaction

Steps:

• Determine Δn = (moles of products) - (moles of reactants) from balanced equation.
• Units of Kc = (mol dm^{-3})^{Δn}; given mol^{-1} dm^{3} equals (mol dm^{-3})^{-1}, so Δn = -1.
• Compute Δn for A: 2 products - 2 reactants = 0.
• Compute Δn for B: 2 - 2 = 0; for C: 2 - 3 = -1.

Why C is correct:

• For W + 2X ⇌ Y + Z, Δn = -1, so Kc = [Y][Z] / [W][X]^2 has units (mol dm^{-3})^{-1} = mol^{-1} dm^3.

Why the others are wrong:

• A: Δn = 0, Kc dimensionless.
• B: Δn = 0, Kc dimensionless.
• D: Not enough information.

Final answer: C