AP Chemistry: Solubility Equilibrium and Ksp

AP Chemistry – Solubility Equilibrium and Ksp

AP Chemistry Study Guide: Solubility Equilibrium and Ksp

What This Is

Solubility equilibrium describes how much of a slightly soluble ionic compound dissolves in water before the solution becomes saturated. The solubility product constant (Ksp) quantifies this equilibrium, helping predict whether a precipitate will form in a reaction. This topic is crucial for the AP exam because it combines equilibrium concepts with real-world applications like water treatment, medicine (kidney stones), and environmental chemistry (ocean acidification). For example, fluoride in toothpaste relies on solubility principles—too much fluoride can form insoluble calcium fluoride, which is why toothpaste concentrations are carefully controlled.

Key Terms & Concepts

• Solubility (s): The maximum amount of a substance that can dissolve in a given volume of solvent at a specific temperature (usually in mol/L or g/L).
• Solubility Product Constant (Ksp): The equilibrium constant for the dissolution of a slightly soluble ionic compound. For AₓBᵧ(s) ⇌ xA⁺(aq) + yB⁻(aq), Ksp = [A⁺]ˣ[B⁻]ʸ.
• Example: For AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq), Ksp = [Ag⁺][Cl⁻].
• Saturated Solution: A solution where the maximum amount of solute has dissolved, and undissolved solid remains in equilibrium with the dissolved ions.
• Ion Product (Q): The product of ion concentrations in a solution at any point (not necessarily at equilibrium). Compare Q vs. Ksp to predict precipitation:
• Q < Ksp: Unsaturated, no precipitate.
• Q = Ksp: Saturated, at equilibrium.
• Q > Ksp: Supersaturated, precipitate forms.
• Common Ion Effect: The solubility of a salt decreases when a common ion is already present in the solution (e.g., adding NaCl to a saturated AgCl solution reduces AgCl solubility).
• Molar Solubility (s): The number of moles of a compound that dissolve per liter of solution (directly related to Ksp).
• Selective Precipitation: Using differences in Ksp values to separate ions in a mixture (e.g., separating Ag⁺ from Pb²⁺ by adding Cl⁻).
• pH and Solubility: Some salts (e.g., hydroxides, carbonates) are more soluble in acidic solutions because H⁺ reacts with the anion (e.g., CaCO₃(s) + 2H⁺ → Ca²⁺ + H₂O + CO₂).
• Ksp vs. Solubility: Ksp is a constant at a given temperature, while solubility (s) depends on other ions in solution (e.g., common ion effect).
• Temperature Dependence: Most solids become more soluble with increasing temperature, but Ksp values are temperature-specific (always check the given temperature on the exam!).

Step-by-Step / Process Flow

1. Calculating Ksp from Solubility (s)

Problem: The solubility of PbI₂ is 1.2 × 10⁻³ M at 25°C. Calculate its Ksp.
Steps:
1. Write the dissociation equation:
PbI₂(s) ⇌ Pb²⁺(aq) + 2I⁻(aq)
2. Express ion concentrations in terms of s:
- [Pb²⁺] = s = 1.2 × 10⁻³ M
- [I⁻] = 2s = 2.4 × 10⁻³ M (because 2 I⁻ ions form per PbI₂) 3. Write the Ksp expression:
Ksp = [Pb²⁺][I⁻]²
4. Plug in values and solve:
Ksp = (1.2 × 10⁻³)(2.4 × 10⁻³)² = 6.9 × 10⁻⁹

2. Calculating Solubility (s) from Ksp

Problem: The Ksp of Ag₂CrO₄ is 1.1 × 10⁻¹² at 25°C. Calculate its molar solubility (s).
Steps:
1. Write the dissociation equation:
Ag₂CrO₄(s) ⇌ 2Ag⁺(aq) + CrO₄²⁻(aq)
2. Express ion concentrations in terms of s:
- [Ag⁺] = 2s
- [CrO₄²⁻] = s
3. Write the Ksp expression:
Ksp = [Ag⁺]²[CrO₄²⁻] = (2s)²(s) = 4s³
4. Plug in Ksp and solve for s:
1.1 × 10⁻¹² = 4s³ → s³ = 2.75 × 10⁻¹³ → s = 6.5 × 10⁻⁵ M

3. Predicting Precipitation (Q vs. Ksp)

Problem: Will a precipitate form when 50.0 mL of 0.0020 M AgNO₃ is mixed with 50.0 mL of 0.0010 M NaCl? (Ksp of AgCl = 1.8 × 10⁻¹⁰) Steps:
1. Calculate initial ion concentrations after mixing:
- Total volume = 100.0 mL = 0.100 L
- [Ag⁺] = (0.050 L × 0.0020 M) / 0.100 L = 0.0010 M
- [Cl⁻] = (0.050 L × 0.0010 M) / 0.100 L = 0.00050 M
2. Calculate Q (ion product):
Q = [Ag⁺][Cl⁻] = (0.0010)(0.00050) = 5.0 × 10⁻⁷
3. Compare Q to Ksp:
- Q (5.0 × 10⁻⁷) > Ksp (1.8 × 10⁻¹⁰) → Precipitate forms!

4. Common Ion Effect

Problem: What is the solubility of CaF₂ in 0.10 M NaF? (Ksp of CaF₂ = 3.9 × 10⁻¹¹) Steps:
1. Write the dissociation equation:
CaF₂(s) ⇌ Ca²⁺(aq) + 2F⁻(aq)
2. Express ion concentrations in terms of s:
- [Ca²⁺] = s
- [F⁻] = 0.10 + 2s ≈ 0.10 M (since s is very small, 2s is negligible) 3. Write the Ksp expression:
Ksp = [Ca²⁺][F⁻]² = s(0.10)²
4. Plug in Ksp and solve for s:
3.9 × 10⁻¹¹ = s(0.01) → s = 3.9 × 10⁻⁹ M
(Compare to solubility in pure water: s = 2.1 × 10⁻⁴ M—much lower due to common ion effect!)

Common Mistakes

Mistake 1: Forgetting the Stoichiometry in Ksp Expressions

• Mistake: Writing Ksp = [Ag⁺][Cl⁻] for AgCl but Ksp = [Ag⁺][CrO₄²⁻] for Ag₂CrO₄ (missing the exponent for Ag⁺).
• Correction: Always balance the dissociation equation first! For Ag₂CrO₄ ⇌ 2Ag⁺ + CrO₄²⁻, Ksp = [Ag⁺]²[CrO₄²⁻].

Mistake 2: Ignoring Units in Solubility Calculations

• Mistake: Using grams instead of moles when calculating Ksp (e.g., plugging in 0.1 g/L instead of converting to mol/L).
• Correction: Ksp is always in terms of molarity (mol/L). Convert grams to moles using molar mass first.

Mistake 3: Assuming Solubility = Ksp

• Mistake: Thinking a higher Ksp always means higher solubility (e.g., AgCl (Ksp = 1.8 × 10⁻¹⁰) vs. Ag₂CrO₄ (Ksp = 1.1 × 10⁻¹²)—AgCl is actually more soluble because of different stoichiometry).
• Correction: Compare molar solubilities (s), not Ksp values, when determining which compound is more soluble.

Mistake 4: Misapplying the Common Ion Effect

• Mistake: Assuming adding a common ion increases solubility (e.g., adding NaCl to AgCl increases AgCl solubility).
• Correction: The common ion effect decreases solubility (Le Chatelier’s Principle: adding Cl⁻ shifts equilibrium left, forming more AgCl(s)).

Mistake 5: Forgetting to Account for Dilution When Mixing Solutions

• Mistake: Calculating Q using the original concentrations of two solutions without accounting for dilution when they’re mixed.
• Correction: Always calculate new concentrations after mixing (use M₁V₁ = M₂V₂).

AP Exam Insights

1. Ksp Calculations Are a FRQ Favorite

• What’s tested: Calculating Ksp from solubility, solubility from Ksp, or predicting precipitation (Q vs. Ksp).
• Tricky part: Stoichiometry (exponents in Ksp expressions) and units (must be mol/L).
• Example FRQ: "A student mixes 100. mL of 0.010 M Pb(NO₃)₂ with 100. mL of 0.020 M NaI. Will PbI₂ precipitate? (Ksp of PbI₂ = 7.9 × 10⁻⁹)"

2. Common Ion Effect in Multiple-Choice

• What’s tested: How solubility changes when a common ion is added (e.g., "Which of the following will decrease the solubility of CaCO₃?").
• Trick: Adding a non-common ion (e.g., NaNO₃) has no effect on solubility (only common ions matter).

3. pH and Solubility

• What’s tested: Salts with basic anions (OH⁻, CO₃²⁻, S²⁻) are more soluble in acidic solutions.
• Example: "Which of the following salts will have increased solubility in a solution with pH = 2?"
• Answer: CaCO₃ (because CO₃²⁻ + 2H⁺ → H₂O + CO₂).

4. Selective Precipitation

• What’s tested: Using Ksp differences to separate ions (e.g., "Which ion will precipitate first when NaCl is added to a solution containing Ag⁺ and Pb²⁺?").
• Trick: The ion with the smaller Ksp for its chloride salt precipitates first (AgCl before PbCl₂).

Quick Check Questions

1. Multiple Choice

The Ksp of Mg(OH)₂ is 1.8 × 10⁻¹¹ at 25°C. What is its molar solubility in pure water? (A) 1.7 × 10⁻⁴ M (B) 3.6 × 10⁻⁶ M (C) 1.8 × 10⁻¹¹ M (D) 3.2 × 10⁻⁴ M

✅ Answer: (A) 1.7 × 10⁻⁴ M Explanation: For Mg(OH)₂ ⇌ Mg²⁺ + 2OH⁻, Ksp = [Mg²⁺][OH⁻]² = s(2s)² = 4s³. Solving 4s³ = 1.8 × 10⁻¹¹ gives s = 1.7 × 10⁻⁴ M.

2. Short FRQ

A student mixes 50.0 mL of 0.010 M Ca(NO₃)₂ with 50.0 mL of 0.020 M NaF. The Ksp of CaF₂ is 3.9 × 10⁻¹¹.
(a) Calculate the ion product (Q) immediately after mixing.
(b) Will a precipitate form? Justify your answer.

✅ Answer:
(a) Q = 5.0 × 10⁻⁶
- After mixing, [Ca²⁺] = (0.050 L × 0.010 M) / 0.100 L = 0.0050 M
- [F⁻] = (0.050 L × 0.020 M) / 0.100 L = 0.010 M
- Q = [Ca²⁺][F⁻]² = (0.0050)(0.010)² = 5.0 × 10⁻⁶

(b) Yes, a precipitate will form.
- Q (5.0 × 10⁻⁶) > Ksp (3.9 × 10⁻¹¹), so the solution is supersaturated, and CaF₂ will precipitate.

Last-Minute Cram Sheet

1. Ksp expression: For AₓBᵧ ⇌ xA⁺ + yB⁻, Ksp = [A⁺]ˣ[B⁻]ʸ.
2. Molar solubility (s): For AB ⇌ A⁺ + B⁻, Ksp = s²; for AB₂ ⇌ A²⁺ + 2B⁻, Ksp = 4s³.
3. Q vs. Ksp: Q > Ksp → precipitate forms; Q < Ksp → no precipitate.
4. Common ion effect: Adding a common ion decreases solubility (e.g., NaCl lowers AgCl solubility).
5. pH and solubility: Salts with basic anions (OH⁻, CO₃²⁻, S²⁻) are more soluble in acidic solutions.
6. Temperature matters: Ksp values are temperature-dependent (always check the given temp!).
7. Selective precipitation: The ion with the smaller Ksp for its salt precipitates first.
8. Dilution: Always recalculate concentrations after mixing solutions (use M₁V₁ = M₂V₂).
9. ⚠️ Units: Ksp and solubility must be in mol/L (convert grams to moles first!).
10. ⚠️ Stoichiometry: Don’t forget exponents in Ksp expressions (e.g., [Ag⁺]² for Ag₂CrO₄).