Lattice Energy
Lattice energy is the energy required to completely separate one mole of a solid ionic compound into its constituent gaseous ions at infinite separation, or equivalently the energy released when gaseous ions combine to form the ionic lattice. It is always endothermic when defined as the energy of separation (positive value), and is a key measure of the stability and strength of an ionic compound. Lattice energy increases with increasing ionic charge and decreasing ionic radius, following the trend predicted by Coulomb's law.
Key Formula
E_lattice ∝ |z+| × |z-| / (r+ + r-)
LaTeX: E_{\text{lattice}} \propto \frac{|z^+||z^-|}{r_+ + r_-}
| Symbol | Meaning | Unit |
|---|---|---|
| z+ | Charge of the cation | dimensionless (integer) |
| z– | Charge of the anion | dimensionless (integer) |
| r+ | Radius of the cation | pm |
| r– | Radius of the anion | pm |
Worked Example
Problem
Using the Born-Haber cycle, the lattice energy of NaCl is –787 kJ/mol. Predict whether MgO or NaCl has a higher lattice energy, given: ionic radii — Na⁺: 102 pm, Cl⁻: 181 pm, Mg²⁺: 72 pm, O²⁻: 140 pm; charges — Na⁺/Cl⁻: ±1, Mg²⁺/O²⁻: ±2.
Solution
Step 1: Apply the proportionality E_lattice ∝ |z+|×|z–| / (r+ + r–). Step 2: For NaCl: |1|×|1| / (102 + 181) = 1 / 283 = 0.00353. Step 3: For MgO: |2|×|2| / (72 + 140) = 4 / 212 = 0.01887. Step 4: Ratio MgO/NaCl = 0.01887 / 0.00353 ≈ 5.35. Step 5: MgO should have roughly 5× greater lattice energy than NaCl.
Answer
MgO has a lattice energy of approximately –3795 kJ/mol, about 4.8× larger than NaCl (–787 kJ/mol), due to higher ionic charges (2+ and 2–) and smaller ionic radii, consistent with Coulomb's law prediction.
Lattice Energies of Common Ionic Compounds
| Compound | Cation | Anion | Lattice Energy (kJ/mol) |
|---|---|---|---|
| NaF | Na⁺ | F⁻ | –923 |
| NaCl | Na⁺ | Cl⁻ | –787 |
| NaBr | Na⁺ | Br⁻ | –747 |
| MgO | Mg²⁺ | O²⁻ | –3795 |
| CaO | Ca²⁺ | O²⁻ | –3414 |
| Al₂O₃ | Al³⁺ | O²⁻ | –15916 |
Interactive Tools
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Related Terms
Bond Dissociation Energy
Bond dissociation energy (BDE), also called bond energy, is the enthalpy change (ΔH) required to homolytically cleave a specific covalent bond in a gaseous molecule, breaking it into two neutral radical fragments. It is always a positive value (endothermic process) and serves as a direct measure of bond strength — higher BDE means a stronger, more stable bond. BDE values are used to estimate the enthalpy of reactions using Hess's law: bonds broken (endothermic) minus bonds formed (exothermic) gives the overall reaction enthalpy.
Electronegativity
Electronegativity is a measure of the tendency of an atom to attract a shared pair of electrons toward itself within a covalent bond, expressed on a dimensionless scale. The most widely used scale is the Pauling scale, where fluorine is assigned the highest value of 3.98, making it the most electronegative element, and caesium the lowest at 0.79. Electronegativity determines bond polarity, the character of chemical bonds (ionic vs. covalent), and influences molecular properties such as reactivity, acid strength, and solubility.
Ionic Bond
An ionic bond is a type of chemical bond formed through the complete transfer of one or more electrons from a metal atom to a non-metal atom, creating oppositely charged ions that attract each other electrostatically. This electrostatic attraction between cations (positively charged) and anions (negatively charged) holds the compound together in a crystal lattice structure. Ionic bonds are responsible for the properties of salts such as high melting points, brittleness, and electrical conductivity when dissolved in water.
From Latin "latticium" (framework, lattice), referring to the ordered three-dimensional framework of ions in a crystal. "Energy" derives from Greek "energeia" (activity, operation). The term has been used in physical chemistry since the development of crystal field theory in the early 20th century.