# Lattice Energy

Did you know that the structure of table salt (NaCl) is a crystal lattice? When chemists need to dissociate sodium chloride into the ions Na+ and Cl-, they require a lot of energy because Ionic Solids have high melting and boiling points. This energy is called lattice energy

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• First, we will look at the definition of lattice energy.
• Then, we will talk about the trends in lattice energy.
• After, we will talk about how to calculate lattice energy.

## Lattice Energy Definition

Before diving into lattice energy and its definition, let's review ionic bonding. Ionic bonds usually happen between a metal and a non-metal when there is a transfer of electrons between elements with significant differences in electronegativity. In other words, if the difference in electronegativity surpasses 1.7, an ionic bond will form.

Electronegativity refers to the ability of a particular atom to attract electrons to itself.

In the periodic table, electronegativity increases across a period and increases up a group (figure 1).

Figure 1. Periodic table trends: Electronegativity, Isadora Santos - StudySmarter Originals.

Let's look at an example!

Is the bond in potassium chloride (KCl) ionic or covalent?

The first thing we need to do is look at the electronegativity values of potassium (K) and chlorine (Cl). Potassium has an EN value of 0.8, whereas chlorine has an EN value of 3.0.

Now, we can calculate the difference in electronegativity between them.

$$\text{Difference in EN = 3.0 - 0.8 = 2.2}$$

Since the difference exceeds 1.7, thus the bond in KCl is an ionic bond!

Ionic compounds are those that contain ionic bonds. These compounds are brittle, and they have high melting and boiling points. They are solids are room temperature, and they form a crystal lattice structure.

Ionic Solids are those that are made up of ions joined together by ionic bonding.

The crystal lattice structure of potassium chloride (KCl) is shown below (figure 2). Notice that the cation (K+) surrounds the anion (Cl-) on all sides.

Figure 2. Lattice structure of KCl, Isadora Santos - StudySmarter Originals.

To break ionic solids, a lot of kinetic energy is needed to break the bonds that exist between the ions. This is where lattice energy comes into the picture.

Lattice energy ($$\Delta H_{latt}^{\Theta}$$) is the energy required to separate 1 mol of an ionic compound into gaseous ions.

For example, the lattice energy for the reaction between magnesium and chlorine is 2536 kJ mol-1.

$$\text{MgCl}_{2}(s)\longrightarrow \text{Mg}^{2+} (g)\text{ + 2Cl}^{-}(g)\text{ }$$

If we had the formation of MgCl2 instead, the lattice energy would still be the same, but it would be negative due to the release of energy!

## Lattice Energy Trends

Now, let's take a look at the trends for lattice energy. The first factor affecting lattice energy is the charge on the ions, and the higher the ionic charge, the higher the lattice energy. This is because ions of higher charge tend to have a stronger attraction toward each other. Therefore, more energy is released when bonds are formed between them.

When it comes to the ionic radius, the general trend is that smaller ions (small ionic radii) will have higher lattice energy. And, why is that? It is because the attraction between ions gets stronger as the distance between them decreases!

## Lattice Energy Equation

We can use these trends to predict which ionic solid would have the highest lattice energy by using the equation below:

$$\text{Lattice Energy} \propto \frac{q_{1}\times q_{2} }{r}$$

Predict which of the following would have the highest lattice energy and rank them from smallest to highest lattice energy.

1. LiI
2. CsBr
3. MgCl2
4. ZnO

First, we need to write down the charges for each of these ions.

• Li+1 and I-1
• Cs+1 and Br-1
• Mg2+ and Cl-1
• Zn2+ and O2-

Now, since lattice energy is proportional to $$\frac{q_{1}\times q_{2} }{r}$$ (and r does not vary), we can first try to estimate based on the charges. Since ZnO is the one with the greatest charge numbers, it will have the highest lattice energy.

Now, if two compounds have the same charges (as is happening in the case of LiI and CsBr), the one with the smaller ions will have higher energy. Therefore, the order from smallest to highest lattice energy is:

$$\text{CsBr < LiI < MgCl}_{2}\text{ < ZnO}$$

## Lattice Energy Calculation

It turns out that lattice energy cannot be determined experimentally. But, to calculate the thermodynamic lattice energy of ionic solids, we can use the Born-Haber Cycle.

The Born-Haber cycle is a method used to calculate the lattice energy or Enthalpy of Formation of ionic compounds formed from gaseous ions.

The Born-Haber cycle assumes that the final product is the solid ionic compound. So, the cycle always starts with the elements in their standard state. Then, the elements are converted into gaseous ions, and lastly, they are converted into a solid lattice.

Figure 4 shows the basic diagram of the Born-Haber cycle for the reaction of a metal (X) with a diatomic halogen (X2).

$$\text{M (s) + }\frac{1}{2}\text{X}_{2} \longrightarrow \text{MX (s)}$$

Figure 4. Born-Haber cycle, Isadora Santos - StudySmarter Originals.

At the start, we have a chemical reaction for the formation of HX (s) under normal conditions. The first part involves changing the solid metal into a gaseous state and converting X2 into X.

• The energy absorbed /released when the metal solid turns into metal gas is called the enthalpy of sublimation.
• The energy absorbed/released to change X2 into X is known as enthalpy of dissociation.

Then, the gaseous elements are converted into gaseous ions. The energy absorbed/released by the metal gas in this process is called ionization energy, whereas the energy absorbed/released by the halogen (g) is called Electron Affinity. Finally, the energy released in the formation of HX from the gaseous ions M+ and X- is the lattice energy!

The Enthalpy of Formation is the sum of all the energies (1,2,3,4, and 5) in the Bohr Haber cycle!

## Lattice Energy of NaCl

Now that we know how the Born-Haber cycle works, let's us take a look at the Bohr-Haber cycle diagram for the formation of sodium chloride (NaCl). Notice that, the lattice energy of NaCl is - 788 kJ.

• The negative sign means that the energy is released when the NaCl (s) is formed.

Figure 5. Born-haber cycle of NaCl, Isadora Santos - StudySmarter Originals.

To calculate lattice energy from the Born-Haber cycle, we use the equation below:

$$\text{Lattice Energy (U) = }\Delta H_{f} \text{ - ( }\Delta H_{sub} \text{ + }\Delta H_{diss} \text{ + } IE \text{ + }EA )$$

So, if we were to use the different energy values to calculate the energy, we would get -788 kJ.

$$\text{Lattice Energy (U) }= \text{- 411 kJ- (122 kJ+ 108 kJ+ 496 kJ - 349 kJ)} =\text{- 788 kJ}$$

## Importance of Lattice Energy

So, what is the importance of lattice energy in the formation of a salt? Lattice energy helps chemists determine the strength of ionic solids and how much energy is needed to form an ionic solid from gaseous ions, or break the ionic bond to convert the ionic solid into its gaseous ions!

Now, I hope that you were able to understand the concept of lattice energy a bit better!

## Lattice Energy - Key takeaways

• Ionic bonds usually happen between a metal and a non-metal when there is a transfer of electrons between elements with significant differences in electronegativity.
• The higher the charge of the ions, the higher the lattice energy.
• Smaller ions (small ionic radii) will have higher lattice energy.
• The Born-Haber cycle is a method used to calculate the lattice energy of ionic compounds formed from gaseous ions.

## References

1. Theodore Lawrence Brown, Eugene, H., Bursten, B. E., Murphy, C. J., Woodward, P. M., Stoltzfus, M. W., & Lufaso, M. W. (2018). Chemistry : the central science (14th ed.). Pearson.
2. House, J. E., & Kathleen Ann House. (2016). Descriptive inorganic chemistry. Amsterdam ; Boston ; Heidelberg ; London ; New York ; Oxford ; Paris ; San Diego ; Singapore ; Sydney ; Tokyo Elsevier.

#### Flashcards in Lattice Energy 13

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What is lattice energy?

Lattice energy is the energy required to separate 1 mol of an ionic compound into gaseous ions.

How do you calculate lattice energy?

To experimentally calculate lattice energy, we can use the Born-Haber cycle.

How do you find the lattice energy trend?

The first factor affecting lattice energy is the charge on the ions, and the higher the ionic charge, the higher the lattice energy.

When it comes to ionic radius, the general trend is that smaller ions (small ionic radii) will have higher lattice energy

Why does NaCI have low lattice energy?

This is because lattice energy is proportional to the ionic charges (+1/-1). So, compared to MgO (+2/-2), NaCl has a low lattice energy.

Why is lattice energy important?

Lattice energy helps chemists determine the strength of ionic solids and how much energy is needed to form an ionic solid from gaseous ions, or break the ionic bond to convert the ionic solid into its gaseous ions

What factors affect lattice energy?

The two factors affecting lattice energy are ionic size and ionic charge.

## Test your knowledge with multiple choice flashcards

_______ usually happen between a metal and a non-metal when there is a transfer of electrons between elements with significant differences in electronegativity.

Electronegativity refers to the ability of a particular atom to attract _____ to itself.

Electronegativity ______ across a period and increases up a group

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