Born-Haber Cycles & Lattice Enthalpy (AQA A Level Chemistry): Video

Hi, I'm Eleanor with 3 years of experience teaching Chemistry, and this video is about Born-Haber cycles and lattice enthalpy.

Born-Haber cycles combine several thermodynamic terms into a single diagram that lets you calculate lattice enthalpy, and comparing that calculated value against a theoretical one is what reveals covalent character in "ionic" compounds.

A Born-Haber cycle brings together the enthalpy of formation, atomisation, ionisation energy and electron affinity to calculate lattice enthalpy, which can't be measured directly. Comparing that calculated lattice enthalpy against a theoretical value based on a perfect ionic model shows how ionic — or covalent — a compound really is.

This video starts with the thermodynamic terms that go into the cycle, then covers how the cycle is constructed and used to calculate lattice enthalpy, and finishes with what happens when the calculated and theoretical values are compared.

The enthalpy of formation is the enthalpy change when one mole of a compound is formed from its elements in their standard states. The enthalpy of atomisation is the enthalpy change when one mole of gaseous atoms is formed from an element in its standard state, and it's always endothermic. Ionisation energy is the energy needed to remove an electron from a gaseous atom to form a gaseous ion, and is always endothermic; electron affinity is the enthalpy change when one mole of electrons is added to one mole of gaseous atoms, and the first electron affinity is usually exothermic. Lattice enthalpy can be defined as either lattice formation, which is exothermic, or lattice dissociation, which is endothermic. Lattice enthalpy of formation is the enthalpy change when one mole of an ionic compound forms from its gaseous ions under standard conditions.

A Born-Haber cycle is drawn with energy increasing upward: endothermic steps are drawn as arrows pointing up, and exothermic steps as arrows pointing down. The elements in their standard states sit near the start of the cycle, and from there the cycle shows the steps needed to convert them into gaseous ions — atomisation, then ionisation or electron affinity — before those ions come together to form the ionic lattice. This indirect route can then be compared with the direct route, the enthalpy of formation of the compound straight from its elements, which is what makes it possible to calculate the lattice enthalpy.

Applying Hess's Law to a completed Born-Haber cycle gives the lattice enthalpy as the enthalpy of formation minus the sum of all the other enthalpy changes in the indirect route. The same cycle can be rearranged to calculate any stage in it, not just the lattice enthalpy. Some values need to be doubled depending on the compound: for magnesium chloride, for example, the electron affinity of chlorine is needed twice, since two moles of chlorine atoms are converted to two moles of chloride ions.

A theoretical lattice enthalpy can be calculated from the geometry, charge and distance between ions in a purely ionic model, and compared against the experimental value obtained from a Born-Haber cycle. For a compound like sodium chloride, the two values agree closely, supporting the ionic model. But for compounds like zinc sulfide, the gap between the theoretical and experimental values is much larger, showing that the bonding has covalent character. This happens because smaller, more highly charged ions distort the electron cloud of the oppositely charged ion, and the larger and more highly charged that neighbouring ion is, the more easily its electron cloud is distorted.

Lattice enthalpy can be defined as either dissociation, which is positive, or formation, which is negative — expect either in exam questions. Don't forget to show the electron in the ionisation step of a Born-Haber cycle — omitting them can lose marks.

The thermodynamic terms — enthalpy of formation, atomisation, ionisation energy and electron affinity — build the Born-Haber cycle. Applying Hess's Law to that cycle gives the lattice enthalpy, which can't be measured directly any other way. Comparing that calculated value against a theoretical value based on a purely ionic model is what reveals covalent character in compounds that otherwise look ionic.