Lattice Energy
Energy to separate ionic solid into gaseous ions
Understanding Lattice Energy
Lattice energy is the energy required to completely separate one mole of an ionic solid into gaseous ions, or conversely, the energy released when gaseous ions combine to form one mole of ionic solid. It's a measure of the strength of ionic bonds and the stability of ionic crystals. Higher lattice energies indicate stronger ionic bonding and more stable compounds.
The concept was developed through theoretical work by Max Born and Fritz Haber in the early 20th century. The Born-Haber cycle, named after them, uses Hess's law to calculate lattice energy indirectly from measurable thermochemical quantities. Direct measurement is impossible because we cannot physically separate ionic solids into gaseous ions in a single step.
Lattice energy depends primarily on ionic charges and ionic radii following Coulomb's law. Compounds with highly charged ions (like Mg²⁺O²⁻) and small ionic radii have much higher lattice energies than those with singly charged larger ions (like Cs⁺I⁻). This explains periodic trends in melting points, solubility, and hardness of ionic compounds.
Born-Haber Cycle
ΔHf = ΔHsub + ΔHion + ΔHdiss + ΔHEA + U
Rearranged to solve for lattice energy U
- U = lattice energy (target quantity)
- ΔHf = standard enthalpy of formation (measured)
- ΔHsub = sublimation enthalpy of metal
- ΔHion = ionization energy(ies) of metal
- ΔHdiss = bond dissociation energy of nonmetal
- ΔHEA = electron affinity of nonmetal
Thermochemical Cycle Steps:
1. Sublimate solid metal to gas | 2. Ionize metal atoms | 3. Dissociate nonmetal molecules | 4. Add electrons to nonmetal | 5. Form ionic lattice (releases U)
Coulombic Estimation (Born-Landé Equation)
U = (NA M z⁺ z⁻ e²) / (4π ε₀ r₀) × (1 - 1/n)
Simplified: U ∝ (Q₊ × Q₋) / r
Key Relationships:
- Lattice energy increases with higher ionic charges (z⁺, z⁻)
- Lattice energy increases with smaller ionic radii (r₀)
- Madelung constant (M) accounts for crystal structure geometry
- Born exponent (n) relates to electron compressibility
Detailed Example: NaCl
Calculate lattice energy using Born-Haber cycle with experimental thermodynamic data:
Step 1: Gather data (all per mole)
ΔHf(NaCl, s) = -411 kJ/mol
ΔHsub(Na, s → g) = +108 kJ/mol
IE₁(Na, g → Na⁺) = +496 kJ/mol
½ ΔHdiss(Cl₂, g → 2Cl) = +122 kJ/mol
EA(Cl, g → Cl⁻) = -349 kJ/mol
Step 2: Apply Hess's Law
ΔHf = ΔHsub + IE + ½ΔHdiss + EA + U
Step 3: Solve for U
U = ΔHf - (ΔHsub + IE + ½ΔHdiss + EA)
U = -411 - (108 + 496 + 122 - 349)
U = -411 - 377 = -788 kJ/mol
Answer: U ≈ -788 kJ/mol
Negative sign indicates energy released when lattice forms (exothermic). Some texts report as +788 kJ/mol for lattice dissociation.
Factors Affecting Lattice Energy
Ionic Charge
Higher charges produce much larger lattice energies. MgO (Mg²⁺, O²⁻) has U ≈ -3850 kJ/mol vs NaCl (Na⁺, Cl⁻) at -788 kJ/mol — nearly 5× greater!
Ionic Size
Smaller ions pack closer together, increasing electrostatic attraction. LiF (small ions) has -1037 kJ/mol while CsI (large ions) has only -600 kJ/mol.
Crystal Structure
Different arrangements (NaCl-type, CsCl-type, fluorite) have different Madelung constants affecting lattice energy by 5-10%.
Polarization Effects
Covalent character (ion polarization) in compounds like AgI reduces lattice energy compared to purely ionic model predictions.
Comparative Lattice Energies
| Compound | Ion Charges | Lattice Energy (kJ/mol) | Melting Point (°C) |
|---|---|---|---|
| LiF | +1, -1 | -1037 | 842 |
| NaCl | +1, -1 | -788 | 801 |
| MgO | +2, -2 | -3850 | 2852 |
| CaO | +2, -2 | -3520 | 2613 |
| CsI | +1, -1 | -600 | 621 |
Notice: Higher lattice energy correlates with higher melting point.
Applications and Implications
Melting and Boiling Points
Higher lattice energies require more thermal energy to overcome ionic attractions, resulting in higher melting and boiling points.
Solubility in Water
Solubility depends on competition between lattice energy and hydration energy. High lattice energy reduces solubility unless hydration energy is also very high.
Hardness of Solids
Ionic compounds with high lattice energies (like corundum Al₂O₃) are extremely hard materials.
Predicting Compound Formation
Lattice energy calculations help predict whether ionic compound formation is thermodynamically favorable.
Important Notes
- Sign Convention: Some sources define U as energy required to break lattice (+), others as energy released forming it (-). Check context.
- Magnitude Matters: Regardless of sign convention, larger |U| means more stable ionic compound.
- MgO vs NaCl: MgO has much higher lattice energy due to +2/-2 charges producing 4× stronger Coulombic attraction.
- Periodic Trends: Within a group, lattice energy decreases down (larger ions). Across period, generally increases (smaller ions, higher charge).
- Cannot Measure Directly: Born-Haber cycle is essential because lattice energy cannot be measured experimentally in a single step.
- Theoretical Models: Born-Landé and Kapustinskii equations provide theoretical estimates agreeing well with Born-Haber cycle results.