# Lattice Energy: Definition, Trends & Equation

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• 0:00 What Is Lattice Energy?
• 2:41 Factors Influencing…
• 3:52 Calculating Lattice Energy
• 5:43 The Born-Haber Cycle
• 6:29 Lesson Summary

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Lesson Transcript
Instructor: Kelsey Skodje

Kelsey has taught college chemistry and biochemistry and has a Ph.D. in bioinorganic chemistry.

This lesson discusses the concept of lattice energy in ionic solids. We'll look at what factors affect the strength of bonds in ionic solids. We'll also go over how to use the Born-Haber Cycle to calculate lattice energy.

## What Is Lattice Energy?

Lattice energy is a type of potential energy that relates to the stability of ionic solids. Ionic solids are very stable, which means that it takes a lot of energy to break their bonds. One place we can see these effects is in their melting point. You may have once used a recipe that calls for melting sugar, which is not an ionic solid. However, table salt, which looks very similar, would never melt at a temperature suitable for cooking. This is because table salt, or sodium chloride, is an ionic solid with incredibly stable bonds. You need an enormous amount of energy to break those bonds so salt is difficult to melt. When melting sugar, however, you only have break weak interactions between the sugar molecules.

The type of energy we're discussing is called lattice energy because it refers to ionic solids where the ions are arranged in what is known as a crystal lattice.

Lattice energy is also known as lattice enthalpy and can be stated in two ways. One way is the energy released when gaseous ions combine to form an ionic solid. The other is the energy required to transform an ionic solid into its component gaseous ions. Either way, we can see that lattice energy is a measure of the forces between the ions in an ionic solid.

To avoid confusion, we can say that the lattice energy required to break the bonds in an ionic solid and form gaseous ions is the lattice dissociation enthalpy, and the energy released when gaseous ions bind to make an ionic solid is the lattice formation enthalpy.

Ionic solids are always more stable than gaseous ions, meaning that ionic solids are in a lower energy state than gaseous ions. This means that the lattice dissociation enthalpy will always be a positive number, and the lattice formation enthalpy will always be a negative number.

Let's consider the lattice energy of sodium chloride. Sodium chloride is very stable and requires 788 kJ to entirely convert one mole of it into gaseous ions. Thus, we can say that the lattice dissociation enthalpy is +788 kJ/mol and the lattice formation enthalpy is -788 kJ/mol. Overall, sodium chloride's lattice energy is 788 kJ/mol.

The more stable the ionic solid, the larger the lattice energy will be. This is because the more stable bonds are, the harder they are to break. This is like how you'd need more energy to break apart a sturdy chair than a flimsy one.

## Factors Influencing Lattice Energy

There are several factors that affect the strength of ionic bonds, and we'll look at how these relate to lattice energy. The two qualities that most affect the lattice energy of a substance are the charge on its ions and the distance between them.

Ions with greater charge also have greater lattice energy. For example, sodium fluoride has a lattice energy of 923 kJ/mol while the lattice energy of another ionic solid, magnesium fluoride, is 2957 kJ/mol. Here, magnesium has a charge of +2, while sodium's charge is +1. The greater charge present in magnesium fluoride holds the ions together more tightly, raising the lattice energy.

Ionic radius is a measure of the size of an ion. Compounds that have smaller ions will have higher lattice energies because the ions can get closer together. This factor contributes to the difference in lattice energy between sodium fluoride (923 kJ/mol) and magnesium fluoride (2957 kJ/mol) as well. In addition to having a greater charge, magnesium is smaller than sodium.

## Calculating Lattice Energy

It's impossible to actually measure either the formation of an ionic solid from gaseous ions or the reverse process. However, we can calculate lattice energy from a series of other experimental values. We'll discuss what these values are and then look at how to use them to calculate lattice energy.

In order to calculate lattice energy, we look at the energy of each measurable step in the formation of an ionic solid and put it all together using Hess' Law. In order to understand Hess' Law, we need to know a few other terms first.

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