AP Chemistry Lattice Energy

Q: What is lattice energy?

Lattice energy is the energy released when gaseous cations and anions come together to form one mole of an ionic solid. A larger value means stronger attractions in the crystal and a more stable lattice. Some textbooks define it for the reverse process, so the sign convention varies, but the larger magnitude always means stronger attraction.

Q: How do ion charge and ion size affect lattice energy?

Lattice energy increases as the product of the ion charges increases and as the distance between the ion centers decreases. Higher charges and smaller ions give larger lattice energies. When the two effects point in different directions, the charge difference usually wins because it changes the charge product by a factor of 2 or 4.

Q: Does a higher lattice energy mean a higher melting point?

For ionic compounds of similar structure, yes. A larger lattice energy means stronger attractions that take more energy to overcome, so the solid melts at a higher temperature. For example, MgO melts near 2850°C and NaCl near 801°C.

Q: Do I need to calculate lattice energy on the AP Chemistry exam?

The skill the course emphasizes is comparing ionic compounds with Coulomb's law, using charges and ion sizes, rather than computing a numerical lattice energy. Check the current course and exam description for the exact scope.

Q: Why is Coulomb's law written with r squared for force but r for energy?

The attractive force between two ions is proportional to q₁q₂/r², while the potential energy of the pair is proportional to q₁q₂/r. Use the force form when a question asks about force and the energy form when it asks about energy; both predict the same ranking for ionic compounds.

How ion charge and size set the strength of an ionic solid, with ranking, force-scaling, and melting-point reasoning in four worked examples.

Lattice energy questions ask you to compare ionic compounds, then justify the order with Coulomb's law. The justification is more important than the answer: a ranking with no reference to charge and distance earns little credit. The ionic vs covalent bonds guide covers how to identify bond types; this page goes deeper on the strength of the ionic attraction, with numbers that show how much each factor matters.

What Lattice Energy Is and How Charge and Size Control It

Lattice energy is the energy released when gaseous ions come together to form one mole of an ionic solid. The larger it is, the stronger the attractions in the crystal and the more energy needed to pull it apart. Coulomb's law gives the two controls:

Charge: the attraction grows with the product of the ion charges, |q₊ × q₋|. A 2+/2− pair has a product of 4; a 1+/1− pair has 1.
Distance: the attraction weakens as the distance between ion centers grows, and that distance is the sum of the two ionic radii, r₊ + r₋.

A handy comparison number is |q₊q₋| / (r₊ + r₋). Textbook lattice energies, plotted in the chart below, fall close to a straight line against that estimate, so the simple model ranks compounds reliably. The estimate here uses the energy form, 1/d; the force form uses 1/d², and both give the same ranking in every example on this page.

Worked Example 1: Ranking Ionic Compounds With the Same Charges

Rank NaF, NaCl, and KCl from highest to lowest lattice energy. Use ionic radii of Na⁺ 102 pm, K⁺ 138 pm, F⁻ 133 pm, and Cl⁻ 181 pm.

All three have a charge product of 1, so only the distance matters.
NaF: 102 + 133 = 235 pm.
NaCl: 102 + 181 = 283 pm.
KCl: 138 + 181 = 319 pm.
The shortest distance gives the strongest attraction, so the order is NaF > NaCl > KCl.

Textbook values of about 923, 787, and 715 kJ/mol agree. In an exam answer, say it with the law: “the charges are equal, but the ions in NaF are closest together, so by Coulomb's law NaF has the strongest attraction.” Ionic radii follow the trends in periodic trends: a cation is smaller than its atom, an anion is larger, and size grows down a group.

Worked Example 2: Deciding Whether Charge or Size Wins

Rank CaO, LiF, and NaCl from highest to lowest lattice energy, using Ca²⁺ 100 pm, O²⁻ 140 pm, Li⁺ 76 pm, and the radii from Example 1.

CaO: charge product 4, distance 100 + 140 = 240 pm, estimate 4/240 × 1000 = 16.7.
LiF: charge product 1, distance 76 + 133 = 209 pm, estimate 1/209 × 1000 = 4.8.
NaCl: charge product 1, distance 283 pm, estimate 3.5.
Order: CaO > LiF > NaCl.

The ions in LiF are 26% closer than in NaCl, a modest gain, while the charge product is four times larger in CaO. That is why charge usually outweighs size: doubling both charges multiplies the numerator by four, while even a large difference in radius changes the distance by a smaller factor. The textbook values, about 3401, 1030, and 787 kJ/mol, confirm the order. A magnesium oxide crystal does even better: its estimate of 18.9 is 5.3 times the estimate for NaCl, close to the measured ratio of about 4.8.

Worked Example 3: Explaining a Melting Point Difference in Free-Response Form

MgO melts at about 2850°C and NaCl at 801°C. Explain the difference in terms of Coulomb's law.

1. Name the interaction: both are ionic solids held together by electrostatic attractions between cations and anions.
2. Compare charges: Mg²⁺ and O²⁻ have a charge product of 4, versus 1 for Na⁺ and Cl⁻.
3. Compare distances: Mg²⁺ (72 pm) and O²⁻ (140 pm) sit closer together than Na⁺ and Cl⁻.
4. Conclude: the attraction in MgO is much stronger, so more energy is needed to separate the ions and melt the solid.

A complete answer links a stated property, the melting point, to a structural cause through a named law. Related reasoning explains why ionic solids do not conduct electricity but molten ones do: the ions are fixed in the lattice until melting frees them. The molecular counterpart, where melting depends on forces between molecules instead, is in intermolecular forces.

Worked Example 4: Scaling the Coulomb Force When Charge or Distance Changes

Two oppositely charged ions attract with force F. What happens to F if (a) both charges are doubled with the distance unchanged, (b) the distance doubles with the charges unchanged, and (c) the pair is Mg²⁺–O²⁻ instead of Na⁺–Cl⁻ at the contact distances 212 pm and 283 pm?

Use F ∝ q₁q₂/r².
(a) The charge product is 2 × 2 = 4 times larger, so F becomes 4F.
(b) The distance factor is 1/2², so F becomes F/4.
(c) F(MgO)/F(NaCl) = (4/212²) ÷ (1/283²) = 4 × 283²/212² ≈ 7.1.

The 7.1 here is a ratio of forces between two ion pairs, while the 5.3 in Example 2 is a ratio of energy estimates for the whole crystal. They measure different quantities, but both say MgO is held together far more strongly. Matching the quantity to the question, force with r² and energy with r, avoids losing points.

Five Lattice Energy Practice Questions With Answers

Which has the higher lattice energy, KBr or NaBr? (K⁺ 138 pm, Na⁺ 102 pm)
Show answer
NaBr. The charges and the anion are the same, but Na⁺ is smaller, so the ions are closer and the attraction is stronger.
Rank LiF, NaCl, and MgO from lowest to highest lattice energy.
Show answer
NaCl < LiF < MgO. MgO has the largest charge product by a wide margin, and LiF has smaller ions than NaCl.
Why does CaO have a higher melting point than KF?
Show answer
Ca²⁺/O²⁻ has a charge product of 4 against 1 for K⁺/F⁻, and the ions are also closer (about 240 pm against 271 pm). Both factors strengthen the attraction.
One ion's charge doubles and the other's triples at the same separation. By what factor does the attractive force change?
Show answer
The charge product changes by 2 × 3 = 6, so the force is 6 times larger.
Why do ionic solids conduct electricity only when molten or dissolved?
Show answer
In the solid the ions are fixed in the lattice and cannot move. Melting or dissolving frees them to carry charge.

Common Lattice Energy Mistakes

Ranking by size alone. A 2+/2− compound beats a 1+/1− compound even when its ions are not smaller.
Using atomic radii. The distance that matters is between ions, and cations are smaller and anions larger than their atoms.
Mixing force and energy forms. Force goes with 1/r², energy with 1/r; use the one the question asks about.
Calling it “bond energy.” Lattice energy describes the whole crystal, not a single ion pair.
Answering without Coulomb's law. Give the ranking and the reason, naming the charges and distances.
Forgetting sign conventions. Some books define lattice energy for the reverse process; the larger magnitude still means stronger attraction.

Comparing ionic strength is a steady source of free-response points in Unit 2. To see how a stronger Unit 2 would shift your overall estimate, the AP Chem Score Calculator turns section scores into a 1–5 range.

Frequently Asked Questions

What is lattice energy?