Lattice Energy (Born-Lande)

Core idea

Overview

Lattice energy measures the strength of the electrostatic forces within an ionic crystal, representing the energy released when gaseous ions form a solid lattice. It is a fundamental thermodynamic quantity that scales directly with the product of ionic charges and inversely with the distance between the ion centers.

When to use: Use this relationship to compare the relative stabilities of different ionic salts or to predict trends in melting points and solubility. It is most applicable to compounds with predominantly ionic character where the ions can be treated as point charges in a structured arrangement.

Why it matters: Understanding lattice energy allows scientists to explain why certain substances, like magnesium oxide, have extremely high melting points compared to others like sodium chloride. It is essential for constructing Born-Haber cycles to calculate enthalpies that cannot be measured directly in a laboratory.

Symbols

Variables

E = Lattice Energy Est, k = Constant, Q^+ = Cation Charge, Q^- = Anion Charge, d = Ionic Distance

E

Lattice Energy Est

kJ/mol

k

Constant

Variable

Q^{+}

Cation Charge

Variable

Q^{-}

Anion Charge

Variable

d

Ionic Distance

nm

Walkthrough

Derivation

Formula: Born-Landé Equation (Reference)

A physical model for lattice energy based on electrostatic attraction and short-range repulsion; typically used as extension beyond A-Level.

Ions treated as point charges (electrostatics).
Repulsion modelled by an empirical Born exponent n.
Crystal structure captured by a Madelung constant M.

1

State the Equation:

Shows lattice energy increases with charge magnitude and decreases with larger ion separation $r_{0}$ .

E = - \frac{N _{A} M z ^{+} z ^{-} e ^{2}}{4 π ε _{0} r _{0}} (1 - \frac{1}{n})

Note: At A-Level you normally use Born–Haber cycles qualitatively/quantitatively rather than this formula.

Result

E = - \frac{N _{A} M z ^{+} z ^{-} e ^{2}}{4 π ε _{0} r _{0}} (1 - \frac{1}{n})

Source: Standard curriculum — A-Level Chemistry (Lattice enthalpy extension)

Visual intuition

Graph

Graph unavailable for this formula.

The graph displays an inverse curve where the lattice energy decreases rapidly as the ionic distance increases, eventually approaching zero. For a chemistry student, this shape demonstrates that ions positioned very close together result in significantly higher energy values, while increasing the distance between them quickly weakens the lattice strength. The most important feature of this curve is that the energy never truly reaches zero, meaning that some level of attractive force persists even as the ionic distance becomes very large.

Graph type: inverse

Why it behaves this way

Intuition

A regular, repeating arrangement of positively and negatively charged spheres, attracting each other with forces that depend on their charges and the distances between their centers.

Δ H_{l a tt}

Enthalpy change when gaseous ions form one mole of a solid ionic lattice.

A more negative value signifies a stronger, more stable ionic lattice, as more energy is released during its formation.

Q^{+}

Magnitude of the charge on the cation.

Higher charge increases the electrostatic attraction between ions, strengthening the lattice.

Q^{-}

Magnitude of the charge on the anion.

Higher charge increases the electrostatic attraction between ions, strengthening the lattice.

r^{+}

Ionic radius of the cation.

Smaller cation allows for closer approach to anions, increasing electrostatic attraction and strengthening the lattice.

r^{-}

Ionic radius of the anion.

Smaller anion allows for closer approach to cations, increasing electrostatic attraction and strengthening the lattice.

Q^{+} Q^{-}

Product of the magnitudes of the ionic charges.

Electrostatic force is directly proportional to the product of charges; a larger product means stronger attraction and a more stable lattice.

r^{+} + r^{-}

Sum of the ionic radii, approximating the internuclear distance between cation and anion centers.

Larger internuclear distance weakens electrostatic attraction due to Coulomb's law, leading to a less stable lattice.

Signs and relationships

\frac{Q^+ Q^-}{r^+ + r^-}: This entire term is always positive. A larger positive value indicates stronger electrostatic attraction, leading to a more stable ionic lattice. Since lattice energy ( $Δ$ $H_{l a tt}$ )

Free study cues

Insight

Canonical usage

Lattice energy is typically reported as a molar enthalpy change in kilojoules per mole (kJ/mol).

Common confusion

Using different units for the radii of the cation and anion (e.g., mixing nm and pm) which invalidates the sum in the denominator.

Dimension note

The charge values Q are typically used as dimensionless integers in the simplified proportionality, though they represent multiples of the elementary charge e.

Unit systems

$D e l t a H_{l} a tt$ kJ mol^-1 - Reported as negative for lattice formation (exothermic) or positive for lattice dissociation (endothermic) depending on the specific convention used.

$Q^{+}, Q^{-}$ dimensionless - In the proportionality model, these are treated as integer multiples of the elementary charge (e.g., +1, +2, -1).

$r^{+}, r^{-}$ pm - Ionic radii are most commonly cited in picometers (pm) or Angstroms (A). Consistency is required for comparison.

Ballpark figures

Quantity:

One free problem

Practice Problem

An ionic compound consists of a monovalent cation (Q1=1) and a monovalent anion (Q2=1). If the proportionality constant k is 1200 and the interionic distance d is 2.5 units, calculate the lattice energy (E).

Constant1200

Cation Charge1

Anion Charge1

Ionic Distance2.5 nm

Solve for: $E$

Hint: Multiply the constant by the product of the charges, then divide by the distance.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

In explaining why MgO has a higher melting point than NaCl, Lattice Energy (Born-Lande) is used to calculate Lattice Energy Est from Constant, Cation Charge, and Anion Charge. The result matters because it helps connect measured amounts to reaction yield, concentration, energy change, rate, or equilibrium.

Study smarter

Tips

Prioritize ion charge over size when comparing compounds; charges have a more significant impact.
Sum the individual ionic radii of the cation and anion to determine the total inter-ionic distance d.
The proportionality constant k accounts for the crystal's geometry and electronic repulsion characteristics.
High lattice energy values typically correlate with low water solubility and high thermal stability.

Avoid these traps

Common Mistakes

Forgetting both charge and size affect lattice energy.
Confusing lattice energy sign convention.

Keep going

Related Formulas

Common questions

Frequently Asked Questions

A physical model for lattice energy based on electrostatic attraction and short-range repulsion; typically used as extension beyond A-Level.

Use this relationship to compare the relative stabilities of different ionic salts or to predict trends in melting points and solubility. It is most applicable to compounds with predominantly ionic character where the ions can be treated as point charges in a structured arrangement.

Understanding lattice energy allows scientists to explain why certain substances, like magnesium oxide, have extremely high melting points compared to others like sodium chloride. It is essential for constructing Born-Haber cycles to calculate enthalpies that cannot be measured directly in a laboratory.

Forgetting both charge and size affect lattice energy. Confusing lattice energy sign convention.

In explaining why MgO has a higher melting point than NaCl, Lattice Energy (Born-Lande) is used to calculate Lattice Energy Est from Constant, Cation Charge, and Anion Charge. The result matters because it helps connect measured amounts to reaction yield, concentration, energy change, rate, or equilibrium.

Prioritize ion charge over size when comparing compounds; charges have a more significant impact. Sum the individual ionic radii of the cation and anion to determine the total inter-ionic distance d. The proportionality constant k accounts for the crystal's geometry and electronic repulsion characteristics. High lattice energy values typically correlate with low water solubility and high thermal stability.

References

Sources

Atkins' Physical Chemistry
IUPAC Gold Book: Lattice energy (enthalpy)
Wikipedia: Lattice energy
IUPAC Gold Book
NIST CODATA
Atkins' Physical Chemistry, 11th Edition, Oxford University Press
Shriver & Atkins' Inorganic Chemistry, 6th Edition, W. H. Freeman and Company
IUPAC Gold Book (Compendium of Chemical Terminology), 'lattice energy' entry

Overview

Variables

Derivation

State the Equation:

Graph

Intuition

Insight

Practice Problem

Real-World Context

Tips

Common Mistakes

Related Formulas

Enthalpy of Reaction

Frequently Asked Questions

Sources