Enthalpy: Lattice energy, atomisation and electron affinity

In this lesson, we will learn:

• To define the lattice energy for ionic compounds.
• To understand the factors that affect lattice enthalpy.
• To define the enthalpy of atomisation for a substance.
• To define the electron affinity for a substance.
• To understand these enthalpy terms in the context of a Born-Haber cycle.

• This lesson looks at a few new enthalpy definitions that are important in finding the overall enthalpy changes of reactions. They can be used together when they are needed for a specific reaction to construct Born-Haber cycles, which are just an application of Hess’s law which we saw in Calculating enthalpy: Hess’s law.


• Lattice energy is the change in energy that occurs when one mole of an ionic substance is formed from its oppositely charged gaseous ions.
  In other words, lattice energy is the strength of the ionic interactions in the ionic lattice. Definitions can vary because some define it by the energy released when the ionic lattice forms from the gaseous ions, and others by the energy required to break the lattice up (turning the ionic solid back into gaseous ions). The sign might be positive or negative, but the energy value is the same!
  The best way to clear this up is to refer to:
• Dissociation or breaking the lattice up, (positive enthalpy change) or;
• Formation of the lattice (negative enthalpy change).


• Because lattice energy measures the strength of the ionic forces in an ionic compound, the factors that affect it are what makes ions attracted to each other. There are two factors that dominate lattice energy:
• The charge of the positive and negative ions. The larger the charge difference, the stronger the interaction.
• The ionic radii of the positive and negative ions. The smaller the ionic radii, the closer together the oppositely charged ions can get to each other. Ions closer together interact more strongly.
Charge is particularly important. You can see this when looking at the lattice energies of ionic compounds. For elements in the same period, compounds made of singly charged ions (such as NaF) have substantially lower lattice energy than compounds with doubly-charged ions (such as CaO).¹


• Lattice energy cannot be measured directly, but it is very important as it explains the stability we observe in ionic compounds when trying to break them up.
• When metals and non-metals react, an ionic lattice product is highly favourable, where for example in NaCl, Each Na⁺ ion is surrounded in 3d space by several oppositely charged Cl^- ions and vice versa.
• The problem is that there are several small steps to get from the elements in their standard state (e.g. Na _(s) and ½ Cl_{2 (g)}) to ionic products, many of them costing energy before the lattice can form from the gaseous ions. This makes the enthalpy of formation misleadingly small for ionic substances.
• When we apply Hess’s law and take in the enthalpies of the smaller steps between (such as ionization and atomization, see below) with the enthalpy of formation, we find the lattice energies. We will see calculations on this later.


• The standard enthalpy of atomisation, $\triangle$_atH, is the enthalpy change that occurs when one mole of gaseous atoms, completely separated from one another, is produced from a chemical substance in its standard state.
  Because this definition is about breaking up the attractive forces in a substance, (usually an elemental sample), is it always positive. The atoms have gained the energy you put in to break their bonds.
• This term is to PRODUCE ONE MOLE of atoms not to atomise one mole! Your $\triangle$_atH equation should be for one mole in the products, not reactants. Don’t make this common mistake in calculations!
• This is used for diatomic molecules like the halogens or oxygen. When these form ions, they don’t go straight from Cl₂ or O₂ to 2Cl^- or O^2-. There are steps, the first of these is atomisation, such as O₂ $\,$→$\,$ 2O. The energy cost to produce one mole of gaseous O atoms from O₂ gas, its standard state, would be its standard enthalpy of atomisation.
• Don’t overthink this: how would you get one mole of O gas from O₂ gas? Break the double bond in one mole of O₂ (that’s one mole of O=O bonds, or bond enthalpy!) and you’ll get 2 moles of O, which is twice what you need, so just take half of this.
  You’ll see in data sheets that the enthalpy of atomisation ($\triangle$_atH) for elemental diatomic gases is half of the bond enthalpy, because the standard state is already a gas, so only the breaking of one mole of the bond (e.g. N₂, Cl-Cl, O=O) is needed, with that energy value halved.


• Electron affinities are energy changes that occur when one mole of electrons are attracted into the outer shell of one mole of atoms in the gas state. This will reduce the charge of the atoms by one, usually from 0 to -1. Because an atom could technically attract any number of moles of electrons, the electron affinity definitions are numbered:
• The first electron affinity is the energy change when one mole of electrons is gained by one mole of gaseous atoms to form one mole of ions with a -1 charge.
Electron affinity is the opposite of ionisation energy (we saw this in Periodicity: Ionisation energies); instead of losing electrons to get a positive charge, electron affinity is gaining electrons to get a negative charge!
• Just like there are ionisation energy trends in the metals, there are electron affinity trends in non-metals which become negative ions.
  These trends of how readily the halogens become ions have been looked at in other lessons. In short, the first electron affinity decreases going down the groups, except for fluorine¹ because of its very small atomic radius. If you need to know how easily an atom becomes a negative ion, electron affinity gives you the answer.


• These enthalpy terms can be used together in Born-Haber cycles to calculate lattice enthalpy. Even though lattice energies cannot be measured directly, If you know the other enthalpy measurements, you can find the lattice enthalpy by using all the enthalpy values around by applying Hess’s law.


¹ Source for electron affinity data and other enthalpy terms: ATKINS, P. W., & DE PAULA, J. (2006).?Atkins' Physical chemistry. Oxford, Oxford University Press.