If you're studying chemistry, you might have heard of the Born-Haber cycle. It's a way for us to figure out how much energy is needed to make an ionic lattice. To do this, we look at how energy changes when we make the lattice from its gaseous ions.

In this article, we'll explain the difference between two important terms: lattice enthalpy of formation and enthalpy of dissociation. Then, we'll dive into enthalpy of atomisation and enthalpy of formation. Finally, we'll show you how to draw a Born-Haber cycle. If you want to learn how to calculate lattice enthalpy, keep reading! We'll even walk you through some examples.

What is lattice enthalpy?

Lattice enthalpy () is the enthalpy change involved in forming one mole of an ionic lattice from gaseous ions under standard state conditions. It is also the enthalpy change involved when one mole of an ionic lattice breaks up to form its scattered gaseous ions under standard state conditions. The thermodynamic standard state of a substance is its most pure and stable form under standard pressure (1 atm) and at 25℃ (298 K)[^3]. We represent standard states with the symbol 0 or 𝛉.

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In chemistry, we use two definitions for lattice enthalpy. Lattice formation enthalpy is the energy needed to form one mole of an ionic lattice from gaseous ions under standard state conditions. Lattice dissociation enthalpy, on the other hand, is the energy needed to break one mole of an ionic lattice into its scattered gaseous ions under standard state conditions.

Lattice enthalpy helps scientists predict how easily an ionic compound will dissolve in water. However, we can't directly measure the change in lattice enthalpy. Instead, we calculate it using enthalpy changes that we can measure experimentally. These values are used in a Born-Haber cycle, which helps us understand the process of forming an ionic lattice. In the next section, we'll explain how a Born-Haber cycle works and how we use it to calculate lattice enthalpy.

Enthalpy changes

Have a look at the Born-Haber cycle below. How many different enthalpy changes can you spot?

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To calculate lattice enthalpy using a Born-Haber cycle, we need to fill in as many enthalpy changes as possible, including enthalpy of formation, ionisation energy, bond enthalpy, electron affinity, and enthalpy of atomisation. These values can then be used with Hess' Law to calculate the lattice enthalpy.

Starting at the same point in the cycle, we can calculate the lattice enthalpy using the direct or indirect route. The direct route involves adding the enthalpy of formation and enthalpy of atomisation, then subtracting the ionisation energy, bond enthalpy, and electron affinity. The indirect route involves calculating the enthalpy changes for each step of the cycle and adding or subtracting them accordingly. By using a Born-Haber cycle, we can better understand the process of forming an ionic lattice and calculate its lattice enthalpy, even though this value cannot be directly measured.

What is enthalpy change of formation?

The standard molar enthalpy of formation is the enthalpy change when one mole of a compound is formed from its elements in their standard states. It is also known as the standard enthalpy change of formation. The equation for the enthalpy of formation of water would be:

2H2 + O2 → 2H2O

ΔHf = -285.8 kJ/mol

This equation shows that the enthalpy change of formation for water is -285.8 kJ/mol. This means that when one mole of water is formed from its elements, hydrogen and oxygen, it releases -285.8 kJ/mol of energy.

What is standard enthalpy of atomisation?

The standard enthalpy of atomisation () is the enthalpy change when one mole of gaseous atoms is formed from its element in its standard state.

Before you can form gaseous ions in a Born-Haber cycle, you will need to atomise the elements that make up the compound. That means you take the elements in their standard states and turn them into monatomic gases as shown below:

½Cl2(g) → Cl(g) 𝚫Hat𝛉 = +122 kj mol-1

Enthalpy of atomisation values are always positive because you need energy to break the bonds between the atoms and turn them into gaseous atoms. In other words: 𝚫Hat𝛉 is always endothermic.

Ionisation energy and electron affinity

Atoms become ions by losing or gaining electrons in order to achieve a complete valence shell. The energy required to remove one electron from the outer shell of an atom is called the first ionisation energy, while the energy released when an atom gains an electron is called electron affinity.

When constructing a Born-Haber cycle, it is important to include individual steps for ionisation energy and electron affinity. An example of this is shown below:

Na(s) → Na(g) + 1e- (ionisation energy)

1/2Cl2(g) + 1e- → Cl-(g) (electron affinity)

Na(s) + 1/2Cl2(g) → NaCl(s) (enthalpy of formation)

NaCl(s) → Na(g) + Cl(g) (enthalpy of atomisation)

By including ionisation energy and electron affinity as individual steps, we can better understand the energy changes involved in the formation of an ionic lattice. This information, along with the standard enthalpies of formation and enthalpies of atomisation found on a table, can be used to calculate the lattice enthalpy using Hess' Law.

Bond enthalpy

Bond enthalpy is the amount of energy required to break a specific covalent bond in one mole of a molecule into separate atoms in the gas phase. While you may need to know this definition for your exams, it is not typically included in Born-Haber diagrams.

When drawing a Born-Haber cycle, it is important to show the enthalpy changes involved in splitting an ionic lattice into its gaseous ions in the following order:

1. The enthalpy of formation of the compound.
2. Enthalpy of atomisation of each element.
3. The first ionisation energy of the metal.
4. Subsequent ionisation enthalpies if applicable.
5. The first electron affinity of the non-metal.
6. Subsequent electron affinities if applicable.

These enthalpy changes must be drawn in this order because the first ionisation energy cannot come before the atomisation enthalpy, and the electron affinity must come after the ionisation energy. This is because the non-metal can only gain an electron after the metal has lost one.

To illustrate this, let's draw a Born-Haber cycle for the formation of sodium chloride (NaCl):

Na(s) + 1/2Cl2(g) → NaCl(s) (enthalpy of formation)

Na(s) → Na(g) (enthalpy of atomisation for sodium)

1/2Cl2(g) → Cl(g) (enthalpy of atomisation for chlorine)

Na(g) → Na+(g) + e- (first ionisation energy of sodium)

Na+(g) → Na2+(g) + e- (second ionisation energy of sodium)

Cl(g) + e- → Cl-(g) (first electron affinity of chlorine)

Cl-(g) + e- → Cl2-(g) (second electron affinity of chlorine)

By drawing a Born-Haber cycle in this way, we can better understand the energy changes involved in the formation of an ionic lattice and use this information to calculate the lattice enthalpy.

We will construct a Born-Haber cycle for the lattice formation enthalpy of potassium chloride (KCl). We start with KCl, and go round the cycle filling in all the different enthalpies until we arrive at the beginning again. We use downward arrows for exothermic enthalpies and upwards arrows for endothermic enthalpy changes.

Step 1

Separate potassium chloride (KCl) into the atoms of the elements using enthalpy of formation.

Step 1: Separate the ionic solid into the atoms of the elements.

Step 2

Atomise potassium (K) using enthalpy of atomisation

Step 2: Atomise the metal element.

Step 3

Atomise chlorine (Cl) using enthalpy of atomisation.

Step 3: Atomise the non-metal element.

Step 4

Ionise potassium using first ionisation energy.

Step 4: Ionise the metal element using the ionisation energy.

Step 5

Ionise chlorine using first electron affinity.

Step 5: Ionise the non-metal using the electron affinity.

Step 6

Complete the cycle with the lattice enthalpy.

Step 6: Complete the cycle!

Well done! You’ve completed the Born-Haber cycle for potassium chloride. Notice how we followed the steps from enthalpy of formation to the last electron affinity. The steps to draw a Born-Haber cycle are always the same. As a recap here is the order of enthalpy changes:

The enthalpy of formation of the compound. Enthalpy of atomisation of each element. The first ionisation energy of the metal. Subsequent ionisation enthalpies if appropriate. First electron affinity of the non-metal. Subsequent electron affinities if appropriate.

Great job summarizing the key takeaways of Born-Haber cycles! To add to this, it's important to note that Born-Haber cycles are used to calculate the lattice enthalpy of an ionic compound, which is a measure of the strength of the bonds within the compound. By understanding the various enthalpy changes involved in forming or breaking up an ionic lattice, we can calculate the lattice enthalpy and gain insight into the stability and properties of the compound.

Born Haber Cycles

What are the steps of the Born-Haber cycle?

Enthalpy of atomisation of each element.First ionisation energy of the metal.Subsequent ionisation enthalpies, if applicable.First electron affinity of the non-metal.Subsequent electron affinities if applicable.

What is meant by Born-Haber cycles?

A Born-Haber cycle is a theoretical model we use to calculate lattice enthalpy. We do this by comparing enthalpy changes involved in forming an ionic lattice from its gaseous ions to the standard enthalpy of formation of the ionic compound.

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