The relationships linking the generic solubility '' and the solubility product '' vary by the stoich — Ionic Equilibrium Chemistry Question
Question
The relationships linking the generic solubility '$S$' and the solubility product '$K_{sp}$' vary by the stoichiometric ratios of the salt. Which of the following pairings of empirical salt formulas and their corresponding $K_{sp}$ expressions are rigorously accurate?
💡 Solution & Explanation
For an $A_xB_y$ salt, $K_{sp} = x^x y^y S^{x+y}$. For $A_2B_3$, $x=2, y=3$, so $K_{sp} = 2^2 \cdot 3^3 \cdot S^5 = 4 \cdot 27 \cdot S^5 = 108 S^5$. For $AB_3$, $x=1, y=3$, so $K_{sp} = 1^1 \cdot 3^3 \cdot S^4 = 27 S^4$. For $A_3B$, $x=3, y=1$, so $K_{sp} = 3^3 \cdot 1^1 \cdot S^4 = 27 S^4$. For $A_2B$, $x=2, y=1$, so $K_{sp} = 2^2 \cdot 1^1 \cdot S^3 = 4 S^3$ (making D incorrect).