# Born-Haber Cycles: Calculating Lattice Enthalpy

Instructor: Saranya Chatterjee

Saranya has a masters degree in Chemistry and in Secondary Education. She has taught high school, AP chemistry for 2 years and is teaching undergraduate college chemistry for 3 years.

In this lesson, you'll learn about lattice energy, lattice enthalpy, and the Born-Haber cycle. Learn how to calculate lattice enthalpy using the Born-Haber cycle and predict covalent character in an ionic compound.

## Lattice Enthalpy

Before going into the discussion of this term, we need to know what a lattice is. In science, when we say lattice, we usually refer to a crystal lattice. Now automatically, a question comes to our mind: what is a crystal lattice? A crystal is a highly transparent substance with a regular geometric shape. The 3-dimensional arrangement of atoms or ions (charged atoms) in a systematic pattern within a crystal gives rise to a crystal lattice. For example, if we say 'sodium chloride crystal lattice', we mean a regular geometrical pattern of sodium and chloride ions alternately arranged in a systematic manner.

Any crystal lattice can be formed from its constituent ions or can be broken down into its constituent ions; the energy involved in the process is called lattice energy or lattice enthalpy.

## Discussion on Lattice Enthalpy

Lattice enthalpy is usually applicable to ionic compounds, which are compounds of metals and non-metals. Lattice enthalpy (H) values are usually represented in kilojoules (KJ).

If we want to prepare sodium chloride crystal lattice, the lattice enthalpy of sodium chloride will be the energy necessary to form solid sodium chloride crystal from gaseous sodium and chloride ions. The formation of a solid crystal usually releases a huge amount of energy into the environment; hence, the process is exothermic. Exothermic processes have negative enthalpy (H) values.

The process of making a crystal lattice involves a number of steps, starting from the gaseous ions to the solid crystal, which is clearly explained in the famous Born-Haber cycle.

## Born-Haber Cycle

The Born-Haber cycle represents a series of steps leading to the formation of an ionic compound from its constituent gaseous ions. It helps us to calculate the lattice enthalpy of an ionic compound. The Born-Haber cycle deals with ionic compounds only where metals tend to form cations, which are positively charged ions, and non-metals form anions, which are negatively charged.

Let's discuss the formation of the simplest and the most familiar ionic compound sodium chloride, or table salt, from its constituent elements in their standard states. By standard states, we mean the states in which they occur in nature. So, we will start with solid sodium metal and gaseous chlorine molecule.

As you can see in the accompanying diagram, the first step involves formation of gaseous sodium metal from solid sodium metal. This is called the sublimation energy of sodium, and represented by Hsub. This step is endothermic, with sublimation energy of sodium being +108 KJ. The second step is the formation of a chlorine atom from a diatomic (composed of two atoms) chlorine molecule by the method of dissociation represented by Hdiss. This step is also endothermic with the bond dissociation energy of diatomic chlorine molecule being +122 KJ.

The third step is the ionization of gaseous sodium atom to form a sodium ion, which is basically the process of removing an electron from metallic sodium. The energy change in the process is referred to as the ionization energy (IE) of sodium and is represented as IE. This step is endothermic, with the ionization energy of sodium being +496 KJ.

The fourth step is the addition of an electron to a gaseous chlorine atom, which is defined as the electron affinity (EA) of chlorine and is represented by EA. This step is exothermic, with EA of chlorine being -349 KJ. So, from the third and the fourth steps we get sodium and chloride ions.

Now, the final step is to form sodium chloride crystal from sodium and chloride ions.

If you look at the diagram carefully, you will see that the only component missing in the diagram is the lattice energy (U), the value of which will be provided to you to calculate lattice enthalpy or H. Here, U of NaCl is -788 KJ. Now let's do the math to find out the lattice enthalpy.

Hf = Hsub(Na) + IE(Na) + Hdiss(Cl2) + EA(Cl) + U

= (+108 + 496 + 122 -349 - 788) KJ

= - 411 KJ

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