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 NaCl? 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 (CaCl?) lowers freezing points more than table salt (NaCl) or why fertilizers (like KNO?) 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 (?H): The overall heat change when 1 mole of a solute dissolves. Can be exothermic (–?H, feels warm) or endothermic (+?H, feels cold).
• Example: Dissolving NH?NO? in water absorbs heat (endothermic), used in instant cold packs.
• Lattice Energy (?H?c?): The energy released when gaseous ions form a solid ionic lattice (always exothermic). Higher charge or smaller ion size-stronger lattice energy.
• Hydration Energy (?Hd): 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 (NO) are always soluble).
• Entropy (?S): A measure of disorder. Dissolution usually increases entropy (?S > 0) because ions spread out in solution.
• Gibbs Free Energy (?G = ?H – T?S): Determines if dissolution is spontaneous.
• ?G < 0: Spontaneous (dissolves).
• ?G > 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: CO? 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: ?T = 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) + ½O?(g)-MgO(s) (?H_f = –602 kJ/mol)

2. Break it into steps (Hess’s Law):

3. Sublimation of Mg: Mg(s)-Mg(g) (?H_sub = +148 kJ/mol)
4. Ionization of Mg: Mg(g)-Mg²?(g) + 2e? (?H_IE = +2188 kJ/mol)
5. Bond dissociation of O?: ½O?(g)-O(g) (?H_bond = +249 kJ/mol)
6. Electron affinity of O: O(g) + 2e?-O²?(g) (?H_EA = +737 kJ/mol)

7. Lattice energy: Mg²?(g) + O²?(g)-MgO(s) (?H_lattice = ?)

8. Apply Hess’s Law: ?H_f = ?H_sub + ?H_IE + ?H_bond + ?H_EA + ?H_lattice –602 = 148 + 2188 + 249 + 737 + ?H_lattice

9. Solve for ?H_lattice: ?H_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 ?H_solution with ?H_lattice. Correction: ?H_solution = ?H_lattice (endothermic) + ?H_hydration (exothermic). Example: NaCl dissolves because ?H_hydration > ?H_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., NH?NO? in cold packs) because ?H_lattice > ?H_hydration.

• Mistake: Forgetting the van’t Hoff factor (i) in colligative properties. Correction: For CaCl?, 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 ?H and ?S.
• Example: “Explain why MgO is insoluble in water but NaCl is soluble, using thermodynamic data.”
• Multiple-Choice Trap: Questions may give ?H_solution and ask for ?H_hydration (you’ll need to recall ?H_solution = ?H_lattice + ?H_hydration).
• Tricky Distinction: Enthalpy (?H) vs. Entropy (?S) in dissolution.
• Example: CaCO? doesn’t dissolve in water because ?H is too endothermic, even though ?S increases.
• Lab Connection: Freezing point depression labs (e.g., measuring i for NaCl vs. CaCl?) 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 NH?NO? in water is endothermic. Explain why this process can still be spontaneous. Answer: The increase in entropy (?S > 0) from ions spreading in solution makes ?G = ?H – T?S negative at high temperatures, driving spontaneity.

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

Last-Minute Cram Sheet

1. Born-Haber Cycle Steps: Sublimation-Ionization-Bond Dissociation-Electron Affinity-Lattice Energy.
2. ?H_solution = ?H_lattice (endothermic) + ?H_hydration (exothermic).
3. Lattice energy-with charge-and ion size ?. (MgO > NaCl)
4. Hydration energy-with ion charge-and size ?. (Li? > Na? > K?)
5. ?G = ?H – T?S: Spontaneous if ?G < 0.
6. Colligative properties depend on # of particles (i). (CaCl? i = 3, glucose i = 1)
7. Solubility rules: Nitrates (NO) 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!