Lattice Enthalpy

What Lattice Enthalpy Means

When you hold a crystal of sodium chloride in your hand, you are holding a vast three‑dimensional network of Na⁺ and Cl⁻ ions locked together by electrostatic forces. To break that network apart into isolated, gaseous ions — to go from NaCl(s) to Na⁺(g) + Cl⁻(g) — you must supply energy. That energy, measured per mole of the compound, is called the lattice enthalpy.

The textbook defines it precisely: Lattice enthalpy of an ionic solid is the energy required to completely separate one mole of the solid into its constituent gaseous ions, at infinite separation.

For NaCl, the lattice enthalpy is 788 kJ mol⁻¹. That number tells you: to pull apart one mole of solid NaCl into one mole of Na⁺(g) and one mole of Cl⁻(g), with the ions so far apart they no longer feel each other, you must put in 788 kJ of energy.

Why It Cannot Be Calculated from Simple Force Laws Alone

You might think: the force between two point charges is given by Coulomb’s law, so why not just add up all the attractions and repulsions in the crystal? The problem is that a crystal is not a pair of ions. It is a repeating three‑dimensional array. Every Na⁺ is surrounded by six Cl⁻ neighbours, but also by twelve Na⁺ next‑nearest neighbours, eight Cl⁻ further away, and so on, out to infinity. The total energy is the sum of an infinite series of Coulomb interactions, and the geometry of the crystal — the way the ions are arranged in space — determines how that series converges.

So lattice enthalpy depends on two things:

1. The strength of the ionic bonds (charge and distance), and
2. The crystal structure (the arrangement of ions in the lattice).

Because the crystal is a three-dimensional array, the lattice enthalpy cannot be computed from one pair's attraction and repulsion alone — the geometry of the entire crystal has to enter the calculation.

The Born–Landé Equation (Conceptual Outline)

The section stops at this qualitative picture; the natural quantitative next step looks like this. The key idea is that the total lattice energy $U$ (the magnitude of the lattice enthalpy, usually taken as positive for the endothermic separation) can be written as a sum of two contributions:

• Attractive term: Coulomb attraction between oppositely charged ions, which is negative (energy is lowered when ions come together).
• Repulsive term: A short‑range repulsion that prevents the ions from collapsing into each other, which is positive and falls off very rapidly as the distance increases.

The attractive part alone would be:

where:

• $N_A$ is Avogadro’s number,
• $M$ is the Madelung constant — a pure number that depends only on the crystal geometry (e.g., 1.7476 for the rock‑salt structure),
• $z^+$ and $z^-$ are the charges on the cation and anion,
• $e$ is the elementary charge,
• $\varepsilon_0$ is the permittivity of free space,
• $r_0$ is the equilibrium interionic distance.

The repulsive term is usually taken as $B/r^n$, where $B$ and $n$ (the Born exponent) are constants. Minimising the total energy with respect to $r$ gives the Born–Landé equation:

This equation is enrichment beyond the syllabus — nothing here requires memorising it. The important point for now is that lattice enthalpy cannot be calculated from Coulomb’s law alone — the crystal geometry (through the Madelung constant) and the repulsive forces (through the Born exponent) must be included.

Key Points to Remember

• Lattice enthalpy is always endothermic (positive) for the separation process. The reverse process — formation of the solid from gaseous ions — is exothermic by the same amount.
• The larger the charges on the ions, the greater the lattice enthalpy. For example, MgO (Mg²⁺ and O²⁻) has a much higher lattice enthalpy than NaCl.
• The smaller the interionic distance, the greater the lattice enthalpy. So LiF has a higher lattice enthalpy than CsI, even though the charges are the same.
• The crystal structure matters: two compounds with the same charges and similar ionic radii but different structures will have different lattice enthalpies because the Madelung constant differs.

Summary of the Section’s Core Ideas

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