AP Chemistry: Thermodynamics of Dissolving and Born‑Haber Cycle

AP Chemistry – Thermodynamics of Dissolving and Born‑Haber Cycle

AP Chemistry Study Guide: Thermodynamics of Dissolving & Born-Haber Cycle

What This Is

This topic explains why some ionic compounds dissolve in water (or don’t) and how energy changes during the process. The Born-Haber Cycle is a step-by-step energy accounting tool that predicts whether a compound will form (e.g., why NaCl is stable but NaCl₂ isn’t). On the AP exam, you’ll use these concepts to calculate lattice energy, predict solubility, and explain real-world phenomena like why road salt (CaCl₂) lowers freezing points more than table salt (NaCl) or why fertilizers (like KNO₃) dissolve in soil water to nourish plants.

Key Terms & Concepts

• Dissolution: The process of a solute (e.g., NaCl) breaking apart into ions in a solvent (e.g., water). Example: Salt dissolving in water to form Na⁺ and Cl⁻ ions.
• Enthalpy of Solution (ΔHₛₒₗₙ): The overall heat change when 1 mole of a solute dissolves. Can be exothermic (–ΔH, feels warm) or endothermic (+ΔH, feels cold).
• Example: Dissolving NH₄NO₃ in water absorbs heat (endothermic), used in instant cold packs.
• Lattice Energy (ΔHₗₐₜₜᵢcₑ): The energy released when gaseous ions form a solid ionic lattice (always exothermic). Higher charge or smaller ion size → stronger lattice energy.
• Hydration Energy (ΔHₕᵧd): The energy released when water molecules surround and stabilize ions (always exothermic). Smaller ions (e.g., Li⁺) have higher hydration energy than larger ones (e.g., K⁺).
• Born-Haber Cycle: A Hess’s Law application that breaks ionic compound formation into steps to calculate lattice energy.
• Key steps: Sublimation, ionization energy, bond dissociation, electron affinity, lattice energy.
• Solubility Rules: Empirical rules predicting which ionic compounds dissolve in water (e.g., nitrates (NO₃⁻) are always soluble).
• Entropy (ΔS): A measure of disorder. Dissolution usually increases entropy (ΔS > 0) because ions spread out in solution.
• Gibbs Free Energy (ΔG = ΔH – TΔS): Determines if dissolution is spontaneous.
• ΔG < 0: Spontaneous (dissolves).
• ΔG > 0: Non-spontaneous (doesn’t dissolve).
• Henry’s Law: Solubility of a gas in a liquid is proportional to its partial pressure (S = kH × P).
• Example: CO₂ dissolves better in soda under high pressure.
• Colligative Properties: Properties that depend on number of solute particles, not identity (e.g., freezing point depression, boiling point elevation).
• Formula: ΔT = i × K × m (i = van’t Hoff factor, K = constant, m = molality).

Step-by-Step: Solving a Born-Haber Cycle Problem

Goal: Calculate the lattice energy of MgO (given data).

1. Write the formation reaction:
   Mg(s) + ½O₂(g) → MgO(s) (ΔH_f = –602 kJ/mol)

2. Break it into steps (Hess’s Law):

3. Sublimation of Mg: Mg(s) → Mg(g) (ΔH_sub = +148 kJ/mol)
4. Ionization of Mg: Mg(g) → Mg²⁺(g) + 2e⁻ (ΔH_IE = +2188 kJ/mol)
5. Bond dissociation of O₂: ½O₂(g) → O(g) (ΔH_bond = +249 kJ/mol)
6. Electron affinity of O: O(g) + 2e⁻ → O²⁻(g) (ΔH_EA = +737 kJ/mol)

7. Lattice energy: Mg²⁺(g) + O²⁻(g) → MgO(s) (ΔH_lattice = ?)

8. Apply Hess’s Law:
   ΔH_f = ΔH_sub + ΔH_IE + ΔH_bond + ΔH_EA + ΔH_lattice
   –602 = 148 + 2188 + 249 + 737 + ΔH_lattice

9. Solve for ΔH_lattice:
   ΔH_lattice = –602 – (148 + 2188 + 249 + 737) = –3924 kJ/mol

10. Interpret: The high lattice energy (–3924 kJ/mol) explains why MgO is insoluble in water (hydration energy can’t overcome it).

Common Mistakes

• Mistake: Forgetting that lattice energy is exothermic (–) but ionization energy is endothermic (+).
  Correction: Lattice energy is released when ions form a solid, so it’s negative. Ionization energy is absorbed to remove electrons, so it’s positive.

• Mistake: Mixing up ΔH_solution with ΔH_lattice.
  Correction: ΔH_solution = ΔH_lattice (endothermic) + ΔH_hydration (exothermic). Example: NaCl dissolves because ΔH_hydration > ΔH_lattice.

• Mistake: Ignoring charge magnitude in lattice energy.
  Correction: MgO (2+ and 2–) has a much higher lattice energy than NaCl (1+ and 1–) because of stronger Coulombic attractions.

• Mistake: Assuming all dissolutions are exothermic.
  Correction: Many are endothermic (e.g., NH₄NO₃ in cold packs) because ΔH_lattice > ΔH_hydration.

• Mistake: Forgetting the van’t Hoff factor (i) in colligative properties.
  Correction: For CaCl₂, i = 3 (dissociates into 3 ions), so it lowers freezing point 3× more than glucose (i = 1).

AP Exam Insights

• FRQ Hotspot: You’ll often be asked to calculate lattice energy using a Born-Haber cycle or predict solubility based on ΔH and ΔS.
• Example: “Explain why MgO is insoluble in water but NaCl is soluble, using thermodynamic data.”
• Multiple-Choice Trap: Questions may give ΔH_solution and ask for ΔH_hydration (you’ll need to recall ΔH_solution = ΔH_lattice + ΔH_hydration).
• Tricky Distinction: Enthalpy (ΔH) vs. Entropy (ΔS) in dissolution.
• Example: CaCO₃ doesn’t dissolve in water because ΔH is too endothermic, even though ΔS increases.
• Lab Connection: Freezing point depression labs (e.g., measuring i for NaCl vs. CaCl₂) are common.

Quick Check Questions

1. Multiple Choice: Which of the following has the highest lattice energy?
   a) NaCl
   b) MgO
   c) KCl
   d) CaS
   Answer: b) MgO (Higher charges (2+/2–) and smaller ions → stronger lattice energy.)

2. Short FRQ: The dissolution of NH₄NO₃ in water is endothermic. Explain why this process can still be spontaneous.
   Answer: The increase in entropy (ΔS > 0) from ions spreading in solution makes ΔG = ΔH – TΔS negative at high temperatures, driving spontaneity.

3. Multiple Choice: What is the van’t Hoff factor (i) for Al₂(SO₄)₃ in water?
   a) 2
   b) 3
   c) 5
   d) 6
   Answer: c) 5 (Dissociates into 2 Al³⁺ + 3 SO₄²⁻ = 5 ions.)

Last-Minute Cram Sheet

1. Born-Haber Cycle Steps: Sublimation → Ionization → Bond Dissociation → Electron Affinity → Lattice Energy.
2. ΔH_solution = ΔH_lattice (endothermic) + ΔH_hydration (exothermic).
3. Lattice energy ↑ with charge ↑ and ion size ↓. (MgO > NaCl)
4. Hydration energy ↑ with ion charge ↑ and size ↓. (Li⁺ > Na⁺ > K⁺)
5. ΔG = ΔH – TΔS: Spontaneous if ΔG < 0.
6. Colligative properties depend on # of particles (i). (CaCl₂ i = 3, glucose i = 1)
7. Solubility rules: Nitrates (NO₃⁻) and Group 1 metals (Na⁺, K⁺) are always soluble.
8. Henry’s Law: Gas solubility ∝ pressure (S = kH × P).
9. ⚠️ Lattice energy is exothermic (–), but ionization energy is endothermic (+).
10. ⚠️ Don’t forget the van’t Hoff factor (i) in colligative property calculations!