The questions are on the solubility product Ksp test. Take it under real conditions before reading the mark scheme.
Quick answer: The solubility product Ksp is the equilibrium constant for a sparingly soluble ionic solid dissolving, such as AgCl(s) ⇌ Ag⁺ + Cl⁻, with Ksp = [Ag⁺][Cl⁻]. This mark scheme gives the model answers and the marks for the 8 questions of the AP Chemistry test on solubility product Ksp, from writing Ksp to comparing salts, with the equivalent answers to accept.
Each model answer is followed by a marking guide. Allow follow-through marks when a later step correctly uses an earlier wrong value.
Level: AP Chemistry · Curriculum: AP Chem Unit 7
Question 1 Writing Ksp (2 marks)
Ca₃(PO₄)₂ ⇌ 3Ca²⁺ + 2PO₄³⁻. Ksp = [Ca²⁺]³[PO₄³⁻]² = (3s)³(2s)² = 108s⁵.Marking: 1 mark for the expression, 1 mark for 108s⁵.
Question 2 Molar solubility (3 marks)
PbF₂ ⇌ Pb²⁺ + 2F⁻, Ksp = 4s³. s = ³√(3.3 × 10⁻⁸ / 4) = ³√(8.25 × 10⁻⁹) = 2.02 × 10⁻³ mol/dm³; [F⁻] = 2s = 4.04 × 10⁻³ mol/dm³.Marking: 1 mark for 4s³, 1 for s, 1 for [F⁻].
Question 3 Ksp from mass solubility (3 marks)
s = 0.62 / 175.3 = 3.537 × 10⁻³ mol/dm³. [Ba²⁺] = s and [F⁻] = 2s, so Ksp = 4s³ = 4 × (3.537 × 10⁻³)³ = 1.77 × 10⁻⁷.Marking: 1 mark for s, 1 for 4s³, 1 for the answer.
Question 4 Common ion calculation (3 marks)
[Ag⁺] ≈ 0.020 mol/dm³, so s = [Cl⁻] = 1.8 × 10⁻¹⁰ / 0.020 = 9.00 × 10⁻⁹ mol/dm³. The extra Ag⁺ pushes the equilibrium AgCl ⇌ Ag⁺ + Cl⁻ to the left (common ion effect), so less dissolves.Marking: 1 mark for the substitution, 1 for the value, 1 for the explanation.
Question 5 Precipitation test (3 marks)
Total volume 100.0 cm³. [Ba²⁺] = 1.0 × 10⁻³ × 40.0 / 100.0 = 4.0 × 10⁻⁴; [SO₄²⁻] = 2.0 × 10⁻⁴ × 60.0 / 100.0 = 1.2 × 10⁻⁴ mol/dm³. Q = 4.80 × 10⁻⁸, which is greater than Ksp, so BaSO₄ precipitates.Marking: 1 mark for dilution, 1 for Q, 1 for the conclusion.
Question 6 Solubility in acid (2 marks)
CO₃²⁻ is a base: it reacts with H₃O⁺ to give CO₂ and water, which pulls the CaCO₃ equilibrium to the right so the solid dissolves. Cl⁻ is a negligible base, so acid does not remove it.Marking: 1 mark for the basic anion argument, 1 for the contrast with Cl⁻.
Question 7 Saturated solution diagram (2 marks)
The two rates are equal (dynamic equilibrium), so the concentrations of M⁺ and X⁻ stay constant.Marking: 1 mark for equal rates, 1 for constant concentrations.
Question 8 Comparing salts (2 marks)
s(AgCl)/s(AgI) = √(1.8 × 10⁻¹⁰ / 8.5 × 10⁻¹⁷) = √(2.118 × 10⁶) = about 1455.Marking: 1 mark for using the square root, 1 for the ratio.
