What Is Lattice Energy in Ionic Compounds?

Lattice energy describes the energetic strength of an ionic crystal. It is useful for comparing ionic compounds and for building Born–Haber cycles, which use measured thermochemical quantities to determine an otherwise difficult-to-measure energy.

The term has two common sign conventions. Always check which process a source or problem defines before comparing values.

Two conventions for lattice energy

In the formation convention, lattice energy is the enthalpy change for gaseous ions forming one mole of an ionic solid:

$$\mathrm{Na^+(g) + Cl^-(g) \rightarrow NaCl(s)}$$

This process releases energy, so its enthalpy change is negative. For sodium chloride it is about $-787\ \mathrm{kJ\,mol^{-1}}$.

In the separation convention, lattice energy is the enthalpy required to break one mole of an ionic solid into its gaseous ions:

$$\mathrm{NaCl(s) \rightarrow Na^+(g) + Cl^-(g)}$$

This is the reverse process, so its enthalpy change is positive: about $+787\ \mathrm{kJ\,mol^{-1}}$ for NaCl. The two values have equal magnitude and opposite signs.

Some books use “lattice energy” for the energy change at 0 K, while others mean lattice enthalpy at a stated temperature, often 298 K. In introductory thermochemistry, the terms are often used interchangeably. Follow the definitions and temperature specified in your course or problem.

What determines its magnitude?

Ionic attraction is electrostatic. A simplified model suggests that the strength of the attraction increases with the product of the ionic charges and decreases as the distance between ions increases. Consequently:

• Higher ionic charges usually mean a larger lattice-energy magnitude. The attractions in MgO, with doubly charged ions, are generally stronger than those in NaCl, with singly charged ions.
• Smaller ions can approach more closely, usually increasing attraction. This is why ion sizes matter even when the charges are the same.
• Crystal structure matters because each ion interacts with many surrounding ions, not just one oppositely charged neighbor. The arrangement is represented in simple models by a structure-dependent Madelung constant.

These are trends, not a substitute for calculation. Crystal structure, short-range repulsion, and other effects influence measured or modelled values.

Calculating lattice energy with a Born–Haber cycle

A Born–Haber cycle applies Hess’s law: the sum of enthalpy changes around a cycle must equal the enthalpy change for the overall reaction. For NaCl, the formation reaction is

$$\mathrm{Na(s) + \tfrac12 Cl_2(g) \rightarrow NaCl(s)}$$

The same change can be described in stages: convert solid sodium to gaseous atoms, split chlorine molecules into gaseous atoms, ionize sodium, add an electron to chlorine, and combine the gaseous ions into the crystal.

Using approximate standard enthalpy data in $\mathrm{kJ\,mol^{-1}}$:

Step	Enthalpy change
$\mathrm{Na(s) \rightarrow Na(g)}$	$+108.7$
$\mathrm{\tfrac12 Cl_2(g) \rightarrow Cl(g)}$	$+121.7$
$\mathrm{Na(g) \rightarrow Na^+(g) + e^-}$	$+495.8$
$\mathrm{Cl(g) + e^- \rightarrow Cl^-(g)}$	$-349.0$
$\mathrm{Na(s) + \tfrac12 Cl_2(g) \rightarrow NaCl(s)}$	$-411.0$

Let $\Delta H_{\mathrm{latt,form}}$ be the enthalpy for forming the crystal from gaseous ions. Hess’s law gives:

$$\begin{aligned} -411.0 &= 108.7 + 121.7 + 495.8 - 349.0 + \Delta H_{\mathrm{latt,form}} \\ \Delta H_{\mathrm{latt,form}} &= -411.0 - (108.7 + 121.7 + 495.8 - 349.0) \\ &= -788.2\ \mathrm{kJ\,mol^{-1}} \end{aligned}$$

So the formation-convention lattice enthalpy is approximately $-788\ \mathrm{kJ\,mol^{-1}}$. With the separation convention, it is approximately $+788\ \mathrm{kJ\,mol^{-1}}$. Differences of a few kilojoules per mole from reference values can result from rounding or the chosen data set.

Common mistakes

• Dropping the sign convention: A negative formation value and a positive separation value can describe the same compound. State the process as well as the number.
• Using the full chlorine bond energy: The formation reaction consumes half a mole of $\mathrm{Cl_2}$ per mole of NaCl, so the atomization step uses half the bond dissociation enthalpy.
• Treating lattice energy as a bond between one ion pair: A crystal is a three-dimensional array. Lattice energy accounts for the overall ionic arrangement, not just one isolated pair.
• Confusing lattice energy with enthalpy of formation: The formation enthalpy describes making the solid from elements in their standard states; lattice enthalpy describes forming it from gaseous ions. A Born–Haber cycle links the two but they are not the same quantity.