Lattice Energy
U = -(N_A×M×z⁺×z⁻×e²)/(4πε₀r₀)×(1-1/n). Born-Landé and Born-Haber cycle. Ionic crystal stability, Madelung constant.
Why This Chemistry Calculation Matters
Why: Lattice energy governs ionic crystal stability, solubility, melting points. Born-Haber links thermochemical data.
How: Born-Landé: U from charges, distance, Madelung constant. Born-Haber: U = ΔH_f - ΔH_sub - IE - ½ΔH_diss - EA.
- ●Higher |U| for smaller ions, higher charges. MgO ~ -3795 kJ/mol.
- ●Madelung: NaCl 1.7476, CsCl 1.7627, fluorite 2.5194.
- ●Born exponent n typically 5-12 from compressibility.
Lattice Energy Examples
🧂 NaCl
Sodium chloride - common salt
⚗️ KCl
Potassium chloride
💎 LiF
Lithium fluoride - high lattice energy
🔥 MgO
Magnesium oxide - very high lattice energy
🏗️ CaO
Calcium oxide
🧪 NaBr
Sodium bromide
⚗️ KBr
Potassium bromide
🔬 CsCl
Cesium chloride - different structure
💎 ZnS
Zinc sulfide - zinc blende
🦷 CaF₂
Calcium fluoride - fluorite structure
📊 NaCl Born-Haber
NaCl using Born-Haber cycle
🔥 MgO Born-Haber
MgO using Born-Haber cycle
💎 LiF Born-Haber
LiF using Born-Haber cycle
🏗️ CaCl₂
Calcium chloride
💎 Al₂O₃
Aluminum oxide
Calculate Lattice Energy
⚠️For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
U = -(N_A×M×z⁺×z⁻×e²)/(4πε₀r₀)×(1-1/n). Born-Landé.
— IUPAC
Madelung constant M depends on crystal geometry.
— Crystallography
Born-Haber: U from formation, sublimation, IE, EA.
— Thermochemistry
NaCl U ≈ -787 kJ/mol; MgO ≈ -3795 kJ/mol.
— NIST
Lattice Energy
Lattice energy is the energy released when gaseous ions combine to form one mole of an ionic solid. It's a measure of the strength of ionic bonding and determines many properties of ionic compounds.
Born-Landé equation for lattice energy
Common Ionic Compounds
| Compound | Formula | Distance (pm) | M | n | U (kJ/mol) | Structure |
|---|---|---|---|---|---|---|
| Sodium Chloride | ext{NaCl} | 283 | 1.7476 | 9.1 | -787 | Rock salt |
| Potassium Chloride | ext{KCl} | 314 | 1.7476 | 9.0 | -715 | Rock salt |
| Lithium Fluoride | ext{LiF} | 201 | 1.7476 | 5.9 | -1030 | Rock salt |
| Magnesium Oxide | ext{MgO} | 210 | 1.7476 | 7.0 | -3795 | Rock salt |
| Calcium Oxide | ext{CaO} | 240 | 1.7476 | 7.0 | -3464 | Rock salt |
| Sodium Bromide | ext{NaBr} | 298 | 1.7476 | 9.5 | -732 | Rock salt |
| Potassium Bromide | ext{KBr} | 329 | 1.7476 | 9.5 | -682 | Rock salt |
| Cesium Chloride | ext{CsCl} | 356 | 1.7627 | 10.7 | -657 | Cesium chloride |
| Zinc Sulfide | ext{ZnS} | 234 | 1.6381 | 5.0 | -2855 | Zinc blende |
| Calcium Fluoride | CaF_{2} | 254 | 2.5194 | 7.0 | -2630 | Fluorite |
Key Concepts
Madelung Constant
Geometry-dependent constant that accounts for the arrangement of ions. Rock salt (NaCl): 1.7476, Cesium chloride: 1.7627, Fluorite: 2.5194.
Born Exponent
Accounts for repulsive forces between ions. Typically 5-12, determined from compressibility measurements. Higher n = stronger repulsion.
Factors Affecting U
Higher charges and smaller distances increase lattice energy. Lattice energy increases with charge product (z⁺ × z⁻) and decreases with distance.
How Does Lattice Energy Work?
Lattice energy results from the balance between attractive electrostatic forces and repulsive forces between ions. The Born-Landé equation treats ions as point charges and accounts for both effects.
⚡ Example: NaCl
Given Values
z⁺ = +1 (Na⁺)
z⁻ = -1 (Cl⁻)
r₀ = 283 pm
M = 1.7476
n = 9.1
Calculation
Electrostatic term:
≈ -860 kJ/mol
Repulsion correction:
1 - 1/9.1 = 0.890
U ≈ -787 kJ/mol
When to Use This Calculator
Lattice energy calculations are essential for understanding ionic bonding, predicting solubility, and analyzing crystal stability in materials science and chemistry.
Solubility Prediction
Higher lattice energy generally means lower solubility. Compare lattice energy with hydration energy to predict solubility trends.
- Solubility trends
- Hydration energy balance
- Ion size effects
Melting Point
Compounds with higher lattice energy have higher melting points due to stronger ionic bonds requiring more energy to break.
- Melting point trends
- Bond strength analysis
- Thermal stability
Born-Haber Cycle
Use thermochemical data to calculate lattice energy indirectly when direct calculation is difficult.
- Formation enthalpy
- Ionization energy
- Electron affinity
Practical Examples
Example: NaCl Lattice Energy
Given:
- z⁺ = +1, z⁻ = -1
- r₀ = 283 pm
- M = 1.7476
- n = 9.1
Solution:
Electrostatic ≈ -860 kJ/mol
Repulsion = 1 - 1/9.1 = 0.890
U ≈ -787 kJ/mol
Example: MgO Lattice Energy
Given:
- z⁺ = +2, z⁻ = -2
- r₀ = 210 pm
- M = 1.7476
- n = 7.0
Solution:
Higher charges & smaller distance
Electrostatic ≈ -4200 kJ/mol
U ≈ -3795 kJ/mol
Limitations and Considerations
⚠️ Born-Landé Limitations
- • Assumes point charges (no size)
- • Ignores covalent character
- • Born exponent is approximate
- • Temperature effects not included
- • May deviate for complex ions
✓ Improvements
- • Kapustinskii equation (empirical)
- • Extended Born-Mayer equation
- • Quantum mechanical calculations
- • Crystal field theory
- • Density functional theory