Salt X has the formula MX (1:1 stoichiometry, like AgCl) with Ksp = 1.0 × 10⁻¹⁰. Salt Y has the formula MY₂ (1:2 stoichiometry, like CaF₂) with Ksp = 1.0 × 10⁻¹⁰. Which salt has the greater molar solubility?
ASalt X, because lower molar solubility always corresponds to smaller Ksp
BSalt Y, because the 1:2 stoichiometry increases the number of ions produced
CSalt Y, because Ksp = 4s³ for 1:2 salts — solving gives a higher s than for Ksp = s² in 1:1 salts
DThey are equal, because they have the same Ksp
For salt X (MX): Ksp = s² = 1.0 × 10⁻¹⁰, so s = 1.0 × 10⁻⁵ M. For salt Y (MY₂): Ksp = s(2s)² = 4s³ = 1.0 × 10⁻¹⁰, so s = (2.5 × 10⁻¹¹)^(1/3) ≈ 2.9 × 10⁻⁴ M. Salt Y is roughly 30 times more soluble despite having the same Ksp! This is the key insight: identical Ksp values do not mean identical solubilities when stoichiometries differ. The stoichiometric coefficient becomes an exponent in Ksp and a multiplier in the ion concentration, making the relationship between Ksp and molar solubility highly dependent on the formula.
Question 2 Multiple Choice
You mix 50 mL of 0.010 M AgNO₃ with 50 mL of 0.010 M NaCl. Ksp for AgCl = 1.8 × 10⁻¹⁰. What happens?
ANo precipitate forms because both solutions are dilute
BA precipitate of AgCl forms because Q > Ksp after mixing
CNo precipitate forms because Q < Ksp after mixing
DA precipitate forms only if the temperature is above 25°C
After mixing equal volumes, concentrations are halved: [Ag⁺] = [Cl⁻] = 0.0050 M. The reaction quotient Q = [Ag⁺][Cl⁻] = (0.0050)(0.0050) = 2.5 × 10⁻⁵. Since Q = 2.5 × 10⁻⁵ >> Ksp = 1.8 × 10⁻¹⁰, the solution is far supersaturated and AgCl will precipitate until the ion product equals Ksp. This is precisely how Q vs. Ksp comparison works: Q > Ksp means the system must shift left (precipitation) to reach equilibrium. Temperature (option D) affects the value of Ksp but is not the determining factor here.
Question 3 True / False
Two salts can have identical Ksp values but very different molar solubilities if their dissolution stoichiometries differ.
TTrue
FFalse
Answer: True
This is a critical point that students frequently miss. Ksp is a product of ion concentrations raised to stoichiometric powers. For AgCl, Ksp = s². For CaF₂, Ksp = 4s³. If both had Ksp = 1.0 × 10⁻¹⁰, AgCl would have s = 1.0 × 10⁻⁵ M while CaF₂ would have s ≈ 2.9 × 10⁻⁴ M — nearly 30 times more soluble. You cannot rank solubilities simply by comparing Ksp values across salts with different formulas; you must solve for s in each case.
Question 4 True / False
A salt with a smaller Ksp generally has a lower molar solubility than a salt with a larger Ksp.
TTrue
FFalse
Answer: False
This is false when the salts have different dissolution stoichiometries. The relationship between Ksp and molar solubility s depends on the formula: for MX (1:1), Ksp = s²; for MX₂ (1:2), Ksp = 4s³. A salt with formula MX₂ and Ksp = 1 × 10⁻¹⁰ has s ≈ 2.9 × 10⁻⁴ M, while a salt with formula MX and Ksp = 1 × 10⁻⁸ (a larger Ksp) has s = 1 × 10⁻⁴ M. The 1:2 salt is actually more soluble despite having the smaller Ksp. Direct Ksp comparison is only valid for salts with the same stoichiometry.
Question 5 Short Answer
A solution contains 0.050 M Ca²⁺ ions. You slowly add fluoride ions. Using Ksp for CaF₂ = 3.9 × 10⁻¹¹, explain how you would determine the fluoride concentration at which CaF₂ begins to precipitate.
Think about your answer, then reveal below.
Model answer: Precipitation begins when the ion product Q exceeds Ksp. For CaF₂: Q = [Ca²⁺][F⁻]². Set Q = Ksp to find the threshold fluoride concentration: 3.9 × 10⁻¹¹ = (0.050)[F⁻]², so [F⁻]² = 7.8 × 10⁻¹⁰, giving [F⁻] = 2.8 × 10⁻⁵ M. When the fluoride concentration exceeds 2.8 × 10⁻⁵ M, Q > Ksp and precipitation begins.
The reaction quotient Q is evaluated using the actual (current) ion concentrations, while Ksp is the equilibrium value. As long as Q < Ksp, the solution is unsaturated and no precipitation occurs. The moment Q > Ksp, the system is supersaturated and will precipitate until equilibrium is restored. Notice that the fluoride concentration appears squared because of the 1:2 stoichiometry — forgetting this exponent is one of the most common calculation errors with Ksp.