Solubility product constants () of three sparingly soluble salts of types , , and at temperature '' — Ionic Equilibrium Chemistry Question
Question
Solubility product constants ($K_{sp}$) of three sparingly soluble salts of types $MX$, $MX_2$, and $M_3X$ at temperature '$T$' are $4.0 \times 10^{-8}$, $3.2 \times 10^{-14}$, and $2.7 \times 10^{-15}$, respectively. Which of the following statements correctly compare their molar solubilities ($S$) at temperature '$T$'?
💡 Solution & Explanation
For $MX$: $S^2 = 4 \times 10^{-8} \implies S_1 = 2 \times 10^{-4} \text{ M}$. For $MX_2$: $4S^3 = 3.2 \times 10^{-14} = 32 \times 10^{-15} \implies S^3 = 8 \times 10^{-15} \implies S_2 = 2 \times 10^{-5} \text{ M}$. For $M_3X$: $27S^4 = 2.7 \times 10^{-15} = 27 \times 10^{-16} \implies S^4 = 10^{-16} \implies S_3 = 10^{-4} \text{ M}$. Comparing them: $2 \times 10^{-4} > 10^{-4} > 2 \times 10^{-5}$, which means $S_1 > S_3 > S_2$, or $MX > M_3X > MX_2$.