Structure of Ionic Solids: Lattices, Coulomb's Law, and Why Salt Shatters
60 min · 2.3
Objective
Students will predict and justify relative lattice energies and physical properties (melting point, brittleness, conductivity) of ionic compounds using ionic charge, ionic radius, and the Coulombic model of the 3-D lattice — at AP rigor targeting SP 1, 4, 5, and 6.
Hook
5 minBring out a chunk of rock salt (halite) and a hammer on a paper towel. Ask: 'Copper wire bends when I hit it. Why does this salt shatter into perfect little cubes instead?' Give one firm tap so students see the clean cleavage into cube-shaped fragments. Tell them by the end of class they will explain, at the particle level, exactly why the salt shatters that way — and why table salt melts near 800 °C but ice melts near 0 °C. Do NOT tell them the answer yet; harvest 2–3 guesses on the board. Targets SP 6 (claim from observation).
Direct instruction
- 6m
Ionic solids are extended lattices, not molecules
Content
An ionic compound like NaCl is NOT a molecule. In the solid, each Na⁺ is surrounded by 6 Cl⁻ nearest neighbors and each Cl⁻ is surrounded by 6 Na⁺ — this is the rock-salt structure with a 6:6 coordination number. The chemical formula 'NaCl' is a formula unit: it reports the smallest whole-number ratio (1:1) of ions in the lattice, not a discrete two-atom particle. The lattice extends in three dimensions for as many ions as the crystal contains — a grain of salt is on the order of 10¹⁹ ion pairs. CsCl adopts a different geometry: each Cs⁺ sits at the center of a cube of 8 Cl⁻ (8:8 coordination) because Cs⁺ is large enough to touch 8 anions at once. Coordination number is set by the relative sizes of cation and anion (radius ratio), not by the charges alone.
Delivery
Anchor this on the NaCl lattice image the slide shows — walk students around one Na⁺ and count its 6 Cl⁻ neighbors out loud, then do the reverse for a Cl⁻. Directly attack the biggest misconception here: 'There is no such thing as one NaCl molecule.' Ask 'If I circle two ions in this picture and call them a molecule, what's wrong with that?' Expected: any Na⁺ is equally bonded to 6 Cl⁻, so picking one is arbitrary. Contrast with the CsCl image showing 8-coordinate geometry to reinforce that geometry depends on ion size. Targets SP 1 (interpret particulate model).
- 7m
Lattice energy and Coulomb's law
Content
The strength of the ionic lattice is measured by lattice energy — the energy released when gaseous ions collapse into 1 mol of solid: Na⁺(g) + Cl⁻(g) → NaCl(s), ΔH = −787 kJ/mol. Its magnitude comes from Coulomb's law for electrostatic potential energy: E ∝ (q₁·q₂)/r, where q₁ and q₂ are the ion charges and r is the center-to-center distance between them (approximately r_cation + r_anion). Two levers control lattice energy: (1) product of charges — doubling one charge doubles E, and doubling both quadruples it; (2) interionic distance — smaller ions give larger |E|. Compare NaCl (−787 kJ/mol, charges ±1, r ≈ 283 pm) to MgO (−3795 kJ/mol, charges ±2, r ≈ 210 pm). MgO's lattice energy is roughly 4.8× larger because both charges doubled (×4) AND the ions are smaller (×~1.2). Melting points track this: NaCl melts at 801 °C, MgO at 2852 °C.
Delivery
Write the proportionality E ∝ q₁q₂/r on the board once and leave it up all class. Have students verbally predict what happens to |E| if you double q₁ (doubles), double both charges (×4), halve r (×2). Confront the third misconception head-on: students obsess over charges and forget r. Ask 'LiF vs. CsI — same ±1 charges. Which has higher lattice energy and why?' Expected: LiF, because Li⁺ and F⁻ are tiny so r is small. Emphasize charge density combines both effects. Targets SP 5 (proportional reasoning) and SP 4 (using a model to predict).
- 7m
Properties explained: brittleness, melting point, and conductivity
Content
Three macroscopic properties of ionic solids all trace to the same lattice + Coulomb model. (1) High melting points: melting requires overcoming Coulombic attractions across the whole 3-D lattice, so mp scales with lattice energy — NaCl 801 °C, MgO 2852 °C, Al₂O₃ 2072 °C. (2) Brittleness and cleavage: ionic crystals are not brittle because their bonds are weak — they are brittle because a small mechanical shift of one layer by one ion-diameter suddenly aligns Na⁺ over Na⁺ and Cl⁻ over Cl⁻. The attractions instantly become repulsions and the layers fly apart along a flat cleavage plane. That is why the halite in the hook split into cubes, not why it 'crumbled.' (3) Conductivity: solid NaCl does NOT conduct even though it is full of charged particles, because the ions are locked in fixed lattice sites and cannot migrate. Melt it (NaCl(l), ~801 °C) or dissolve it (NaCl(aq)), and the freed ions carry current.
Delivery
Use the slide's before/after 'layer shift' diagram. Physically model it with two hands offset by a fist-width — say 'Same lattice, one shove, now every ion is next to its twin — instant repulsion.' This is the anchor for misconception #2 (weak bonds). Then flip to conductivity: 'Why does molten NaCl light the bulb but solid NaCl doesn't, even though both contain Na⁺ and Cl⁻?' Expected: mobility, not presence, of charges. Targets SP 6 (explain macroscopic property from particulate model).
Activities
- 25m
Lattice-Energy Ranking Lab with Melting-Point CheckLab
Students work in pairs to rank six ionic compounds by predicted lattice energy from Coulomb's law, then check their predictions against actual melting points, then observe a teacher-run heat demo comparing NaCl and CaCl₂ in a crucible. Targets SP 5 (Mathematical Routines) and SP 6 (Argumentation from evidence). Run of show: 1) Distribute the handout below and the six labeled samples per pair (do NOT allow tasting or ingestion — MgO and CaO are irritants). 2) Students complete Parts 1–3 individually first (8 min), then compare in pairs (4 min). 3) Teacher demo (8 min): heat ~2 g NaCl in a crucible with the Bunsen burner for 3–4 min — students observe it does NOT melt over a normal flame (mp 801 °C is above a Bunsen's ~1500 °C tip but crucible bottoms reach maybe 700–900 °C; note ionic solids often just glow, not melt visibly). Repeat with CaCl₂ (mp 772 °C) — students often see softening / fusing. Discuss what this tells them about relative lattice energies. If your burner reliably melts NaCl, even better. 4) Whole-class debrief (5 min): review the ranking, highlight the LiF vs. NaCl comparison as evidence that r matters. Student handout: Part 1 — Reference data (fill in from cards) Ionic radii (pm): - Li⁺ = 76 Na⁺ = 102 K⁺ = 138 Mg²⁺ = 72 Ca²⁺ = 100 - F⁻ = 133 Cl⁻ = 181 O²⁻ = 140 Melting points (°C, look up after ranking): - NaCl = 801 KCl = 770 LiF = 845 MgO = 2852 CaO = 2572 CaCl₂ = 772 Part 2 — Predict For each compound, compute the Coulombic proxy value C = |q₁ · q₂| / r, where r = r_cation + r_anion (in pm). Show units. Then rank the six compounds from LARGEST predicted lattice energy (1) to SMALLEST (6). - NaCl: q₁q₂ = ______ r = ______ pm C = ______ - KCl: q₁q₂ = ______ r = ______ pm C = ______ - LiF: q₁q₂ = ______ r = ______ pm C = ______ - MgO: q₁q₂ = ______ r = ______ pm C = ______ - CaO: q₁q₂ = ______ r = ______ pm C = ______ - CaCl₂: q₁q₂ = ______ r = ______ pm C = ______ Predicted ranking (strongest → weakest lattice): 1. ______ 2. ______ 3. ______ 4. ______ 5. ______ 6. ______ Part 3 — Check against melting points Write the six compounds in order of ACTUAL melting point (highest → lowest): 1. ______ 2. ______ 3. ______ 4. ______ 5. ______ 6. ______ - Which two compounds' order did your Coulombic prediction get RIGHT that a 'charges only' argument would get wrong? Explain in one sentence. ______ - Do NOT skip the ionic-radius term. A student who ranks only by charge product would predict MgO ≈ CaO. What data proves that wrong? ______ Part 4 — Demo observation After watching NaCl and CaCl₂ in the crucible, answer: - Which sample showed visible change first? ______ - Both compounds contain Cl⁻. Explain the difference in behavior using charge, radius, and lattice energy. ______ Part 5 — Argue from evidence (SP 6) A classmate claims: 'MgO has a higher melting point than NaCl because it has stronger ionic bonds.' In 2–3 sentences, refine this claim using specific charge and radius values from Part 1. Use the word 'Coulombic' at least once.
Materials
- Small labeled watch glasses or weigh boats of: NaCl, KCl, LiF, MgO, CaO, CaCl₂ (~1 g each)
- Ionic radius reference card (given below on the handout)
- Melting-point reference card (given below on the handout)
- Bunsen burner, ring stand, clay triangle, crucible, crucible tongs
- Nichrome wire loop for optional flame test
- Safety goggles and heat-resistant gloves for the demo station
Example outputs
- MgO: q₁q₂ = 4, r = 212 pm, C = 0.0189 pm⁻¹ → ranked #1; matches actual mp 2852 °C.
- LiF: q₁q₂ = 1, r = 209 pm, C = 0.00478 pm⁻¹ → ranked #3, higher than NaCl (C = 0.00353) even though both have ±1 charges — proves ionic radius matters. Actual mp: LiF 845 °C > NaCl 801 °C. ✓
- Part 5 sample: 'MgO's lattice energy is greater because both charges are ±2 (quadrupling the Coulombic product) AND the ions are smaller than Na⁺/Cl⁻, decreasing r. Both effects together — not the vague word 'stronger' — explain the ~2000 °C difference in melting point.'
Formative assessment
10 minWhich of the following correctly ranks the lattice energies (most negative → least negative) of NaF, KCl, and MgO? A) NaF > MgO > KCl B) MgO > NaF > KCl C) KCl > NaF > MgO D) MgO > KCl > NaF (Targets SP 4 — model analysis)
multiple choiceB) MgO > NaF > KCl. Reasoning: - MgO: charges ±2 × ±2 = 4; small ions → largest |E|. - NaF: charges ±1; small ions (Na⁺ 102, F⁻ 133). - KCl: charges ±1; large ions (K⁺ 138, Cl⁻ 181) → largest r → smallest |E|. Charge product dominates (MgO wins big), then ionic radius decides between the two ±1 salts.Solid NaCl does not conduct electricity, but molten NaCl does. Solid Cu conducts in both states. In 2–3 sentences, explain the difference between solid NaCl and molten NaCl at the particle level, and state WHY the presence of ions alone is not sufficient for conductivity. (Targets SP 6 — argumentation)
short answerIn solid NaCl, Na⁺ and Cl⁻ ions occupy fixed positions in the 3-D lattice and cannot migrate, so even though charge carriers exist, they cannot flow — no current. When NaCl is melted, the lattice breaks down and the ions become mobile, so an applied field moves Na⁺ one way and Cl⁻ the other, carrying current. Conductivity requires both charged particles AND their mobility; ions alone are not sufficient.A student strikes a crystal of NaCl with a hammer and it cleaves into small cubes rather than deforming like copper. Explain the cleavage using a labeled particle-level description of what happens when one layer of the lattice is displaced by one ion-diameter. Your answer must reference Coulombic interactions. (Targets SP 1 and SP 6)
short answerBefore the strike, each Na⁺ is surrounded by 6 Cl⁻ (and vice versa), so every nearest-neighbor interaction is attractive. When the hammer shifts one layer by roughly one ionic diameter, every Na⁺ in the shifted layer now sits directly above another Na⁺, and every Cl⁻ above another Cl⁻. Coulombic attractions between opposite charges are suddenly replaced by strong repulsions between like charges, driving the layers apart along a flat cleavage plane. The bonds are not weak — the geometry of like-charge alignment is what shatters the crystal into cubes.Calculate the ratio of Coulombic potential energies E(CaO) / E(NaF), using r ≈ r_cation + r_anion with Ca²⁺ = 100 pm, O²⁻ = 140 pm, Na⁺ = 102 pm, F⁻ = 133 pm. Report to 2 significant figures and state what this predicts about their relative melting points. (Targets SP 5 — mathematical routines)
calculationE ∝ (q₁q₂)/r. - CaO: q₁q₂ = (2)(2) = 4; r = 100 + 140 = 240 pm; E ∝ 4/240 = 0.01667 pm⁻¹ - NaF: q₁q₂ = (1)(1) = 1; r = 102 + 133 = 235 pm; E ∝ 1/235 = 0.004255 pm⁻¹ Ratio = 0.01667 / 0.004255 ≈ 3.9 CaO's Coulombic energy is ~3.9× that of NaF, driven almost entirely by the ±2 charges (r is nearly identical). Prediction: CaO has a much higher melting point. Actual values (2572 °C vs. 993 °C) confirm this.
Vocabulary
- crystal lattice
- The repeating 3-D array of alternating cations and anions that makes up an ionic solid; there is no discrete molecule.
- formula unit
- The simplest whole-number ratio of ions in an ionic lattice (e.g., NaCl represents one Na⁺ per one Cl⁻, not a molecule).
- coordination number
- The number of oppositely charged nearest-neighbor ions surrounding a given ion in the lattice (6 in NaCl, 8 in CsCl).
- lattice energy
- The energy released when gaseous ions come together to form one mole of an ionic solid; a measure of the strength of ionic bonding.
- Coulombic attraction
- Electrostatic force between opposite charges; the potential energy scales as E ∝ (q₁q₂)/r.
- ionic radius
- The effective size of an ion in a lattice; cations shrink and anions expand relative to their neutral atoms.
- charge density
- Ratio of ionic charge to ionic radius (or volume); high charge density means strong Coulombic interactions.
- brittleness
- Tendency of ionic solids to fracture along cleavage planes when a layer shifts and like charges align.
- cleavage plane
- A flat plane along which an ionic crystal cleanly splits when stress aligns like-charged ions.
Common misconceptions
- 'NaCl is a molecule.' It is not — the solid is an extended 3-D lattice where each Na⁺ has 6 Cl⁻ neighbors; the formula NaCl reports the 1:1 ratio (formula unit), not a two-atom particle.
- 'Ionic crystals shatter because the bonds are weak.' Wrong — the bonds are very strong. Shifting one layer by one ion-diameter aligns like charges, and the huge Coulombic repulsion that suddenly appears is what fractures the crystal.
- 'Lattice energy depends only on charges.' Charge product usually dominates, but ionic radius sets r in E ∝ q₁q₂/r. LiF has a larger lattice energy than NaCl despite identical charges because Li⁺ and F⁻ are smaller.
- 'Ionic solids conduct because they contain ions.' Presence of charge carriers is not enough — mobility is required. In the solid, ions are locked in place; only molten or dissolved ionic compounds conduct.
Materials checklist
- Chunk of rock salt (halite) + small hammer + paper towel for the hook
- Safety goggles for every student
- ~1 g each of NaCl, KCl, LiF, MgO, CaO, CaCl₂ in labeled weigh boats (one set per pair)
- Bunsen burner, striker, ring stand, clay triangle, 2 crucibles, crucible tongs
- Ionic-radius and melting-point reference cards (values listed on student handout)
- Printed student handout (Parts 1–5)
- Whiteboard/marker for the persistent 'E ∝ q₁q₂/r' anchor