Which compound has the highest molar solubility in water given the following Ksp values: AgI 8.52 × 10^−17; BaCO3 2.58 × 10^−9; Fe(OH)3 2.79 × 10^−39; ZnS 3.00 × 10^−23?

Which compound has the highest molar solubility in water given the following Ksp values: AgI 8.52 × 10^−17; BaCO3 2.58 × 10^−9; Fe(OH)3 2.79 × 10^−39; ZnS 3.00 × 10^−23?

• A. AgI, Ksp = 8.52 × 10^−17
• B. BaCO3, Ksp = 2.58 × 10^−9
• C. Fe(OH)3, Ksp = 2.79 × 10^−39
• D. ZnS, Ksp = 3.00 × 10^−23

Answer: (B)

Solubility is governed by the solubility product constant, Ksp, and the dissolution stoichiometry. For a 1:1 salt, Ksp = s^2, so the molar solubility is s = sqrt(Ksp). The larger the Ksp, the higher the solubility, with the caveat that differing stoichiometries change how s relates to Ksp. - AgI dissolves as 1:1 (Ag+ and I−), so s ≈ sqrt(8.52×10−17) ≈ 9×10−9 M. - BaCO3 also dissolves 1:1 (Ba2+ and CO3^2−), so s ≈ sqrt(2.58×10−9) ≈ 5×10−5 M. - Fe(OH)3 has Fe3+ and OH− in a 1:3 ratio, giving Ksp = [Fe3+][OH−]^3 = s(3s)^3 = 27s^4, so s ≈ (2.79×10−39/27)^(1/4) ≈ 1×10−10 M. - ZnS dissolves 1:1, so s ≈ sqrt(3.00×10−23) ≈ 5×10−12 M. BaCO3 stands out with the largest molar solubility, about 5×10−5 M, making it the compound with the highest solubility in water among the given options. The markedly smaller solubility of Fe(OH)3 reflects the extra exponent on OH− in its dissolution expression, which pushes s down even though Ksp is tiny.

Solubility is governed by the solubility product constant, Ksp, and the dissolution stoichiometry. For a 1:1 salt, Ksp = s^2, so the molar solubility is s = sqrt(Ksp). The larger the Ksp, the higher the solubility, with the caveat that differing stoichiometries change how s relates to Ksp.

• AgI dissolves as 1:1 (Ag+ and I−), so s ≈ sqrt(8.52×10−17) ≈ 9×10−9 M.

• BaCO3 also dissolves 1:1 (Ba2+ and CO3^2−), so s ≈ sqrt(2.58×10−9) ≈ 5×10−5 M.

• Fe(OH)3 has Fe3+ and OH− in a 1:3 ratio, giving Ksp = [Fe3+][OH−]^3 = s(3s)^3 = 27s^4, so s ≈ (2.79×10−39/27)^(1/4) ≈ 1×10−10 M.

• ZnS dissolves 1:1, so s ≈ sqrt(3.00×10−23) ≈ 5×10−12 M.

BaCO3 stands out with the largest molar solubility, about 5×10−5 M, making it the compound with the highest solubility in water among the given options. The markedly smaller solubility of Fe(OH)3 reflects the extra exponent on OH− in its dissolution expression, which pushes s down even though Ksp is tiny.