Equilibrium constant for reverse dissociation of XY

Steps:

• Reaction 1 is X + Y ⇌ 2XY, so K1 = [XY]^2 / ([X][Y]) = 0.002.
• The formation constant for the single molecule reaction X + Y ⇌ XY is K_f = √K1 = √0.002 ≈ 0.0447.
• Reaction 2 is the reverse of the single formation: XY ⇌ X + Y.
• Thus, K2 = 1 / K_f = 1 / √0.002 ≈ 22.36 (matches option B in problem context).

Why B is correct:

• B follows the formula for reverse K of halved stoichiometry reaction: K2 = 1 / √K1, per equilibrium constant power rule for multiplied reactions.

Why the others are wrong:

• A is approximately K1, ignoring the reverse.
• C is approximately 1/K1 for a different K1 value (~0.0052), not adjusted for coefficient 2.
• D is roughly twice C, possibly from doubling without basis.

Final answer: B