Solubility and complexation dictate Ksp and Kf order

Steps:

• Equilibria lie left, so K1 and K2 (Ksp values) are small; AgCl dissolves in NH3 but AgI does not, indicating AgCl more soluble, thus K1 > K2.
• Complexation Ag⁺ + 2NH3 ⇌ [Ag(NH3)2]⁺ with K3 removes free Ag⁺, shifting dissolution right for AgCl but not AgI.
• Smaller K2 means less Ag⁺ from AgI, so even large K3 insufficient to dissolve AgI, while K1 allows effective complexation.
• Thus, K2 < K1 < K3 in magnitude.

Why C is correct:

• K2 < K1 reflects AgI's lower solubility (smaller Ksp); K3 > K1 as complex stability constant enables AgCl dissolution per Le Chatelier's principle.

Why the others are wrong:

• A: Places K3 smallest, but large K3 drives AgCl solubility via complexation.
• B: Suggests K1 < K3 < K2, contradicting K2 < K1 from solubility difference.
• D: Implies K1 < K2, but AgCl's greater solubility means K1 > K2.

Final answer: C