#### Need Help?

Get in touch with us

# Lattice Energy – Explanation, Factors & Formulas

Apr 14, 2023

## Lattice Energy

Lattice energy evaluates the intensity of the ionic bonds present in an ionic compound. It sheds light on several ionic solids’ characteristics, such as their volatility, solubility, and hardness. Ionic solid lattice energy cannot be determined directly. However, it can be easily calculated using the Born-Haber cycle. The SI unit of lattice energy in kilojoules per mole (kJ/mol).

### What is Lattice Energy?

Ionic compounds are more persistent because of the electrostatic force present between the two opposing ions. After creating ions, they come together to form an ionic compound. The energy released during this procedure is called lattice energy. In other words, it is the energy generated when an anion and a cation unite to produce one mole of an ionic compound. Therefore, we may write.

A+ + B → A+B + Lattice energy

Alternatively, it can be viewed as the energy needed to endothermically break one mole of an ion crystal to gaseous ions in space (vacuum). As a result, this amount has a positive value at all times.

While some sources describe lattice energy differently, i.e., the amount of energy released during the exothermic formation of an ionic solid from its gaseous ionic components, this definition requires that lattice energy always has a negative value.

As a result, it can be defined as the energy released when gaseous ions react to form one mole of a solid ionic compound. It can also refer to the energy that enables one mole of a solid ionic compound to dissociate into its component gaseous ions. The lattice energy of a particular ionic molecule might either be a positive or negative value, based on the definition we use.

### Exothermic or Endothermic?

Endothermic – We can see lattice energies as either exothermic or endothermic processes depending on the terminology we use. As per the initial definition, the structure of the lattice energy value changes with the breakdown of an ionic compound. Because this process uses energy, it is considered endothermic, which holds a positive value.

Exothermic – When a process produces heat, it is exothermic. According to the second definition, creating an ionic compound requires exothermic lattice energy, holding a negative value.

### Factors Affecting Lattice Energy

The ionic bond tenacity increases with an increase in the lattice energy. Additionally, the size or radius of the ions, as well as the charge of the ions, affect the lattice energy.

#### a) Ionization Radius

Lattice energy diminishes as the distance variable is increased. The increased distance between large ions generally results in ionic compounds with decreased lattice energies. Larger lattice energies are produced in the ionic compounds of smaller ions. As a result, the lattice energy decreases as the ion radius grows.

The graph of lithium halide’s lattice energy is shown below. It reduces as halide size grows down the group. It is because when ions become larger, their nuclei become further apart. As a result, they are less attracted, resulting in less lattice energy being produced.

#### b) Ionization Charge

The lattice energy increases as the ion charge variable is increased. Accordingly, ions with higher charge intensities will result in ionic compounds with higher lattice energies. Consequently, ions with weaker charges cause their compounds’ lattice energies to fall.

As a result of their stronger attraction to one another, lattice energy rises as ion charge increases. Compared to +1 or -1 ions, +2 or -2 ions will release more lattice energy. Here, we can observe that MgO’s lattice energy is significantly higher than NaCl.

#### Lattice Energy Formula

The energy generated when two gaseous ions with opposite charges come together to create an ionic solid is known as lattice energy. The two ions attract one another, and this exothermic reaction releases energy. Although lattice energy can be fairly complex, Coulomb’s law is frequently used to simplify it.

The lattice energy formula can be stated as follows:

LE = kQ1Q2 / r

Where,

LE = lattice energy

k = 2.31 x 10-19 J-nm

Q1 and Q2 = the relative charges of the component ions in an ionic compound

r = distance or radius between the ion centers

### Lattice Energy Formula Practice Question:

Q. State the lattice energy of chlorine and sodium ions with a 1.0 nm distance between them?

Answer: In this case, nm stands for a nanometer (10-9 m), and sodium and chlorine both create positive ions.

LE = kQ1Q2 / r

LE = 2.31 X 10-19 J-nm (+1) (-1) / 1.0nm

LE = -2.31 X 10-19 J

#### How to Calculate Lattice Energy?

So, how to find lattice energy? Hess’s law (known as the Born Haber cycle) calculates lattice energy. This law states that no matter how many stages a reaction takes, the energy change is always the same for that reaction. Therefore, the total energy required will be the same whether an ionic compound is formed in a few stages or all at once. For instance, the pure sodium and chlorine gas reactions produce sodium chloride crystals. Whether it reacts in a few stages or all at once, the change in the energy level will be the same.

### The Born-Haber Cycle for the Crystallization of Sodium Chloride is Shown Below.

Here are the steps involved in sodium chloride formation:

#### Stage 1:

The first stage entailed converting sodium from its typical solid state into a gaseous state.

Na(s) → Na(g) ΔHatom = +107 kJ/mol

This process is called atomization, and the energy change that occurs during it is referred to as atomization energy. Atomization energy is the energy needed to change one mole of a gaseous atom from its initial state. The atomization energy in this stage is +107 kJ/mol.

#### Stage 2:

The second stage entailed splitting the chlorine molecule into gaseous chlorine atoms. The dissociation bond’s energy is +122 kJ/mol.

1/2Cl2(g) → Cl(g) ΔHBE = +122 kJ/mol

#### Stage 3:

In the third stage, sodium is ionized while still in a gaseous state to produce positively charged sodium ions by giving up an electron. The ionization energy in this stage is +494 kJ/mol.

Na(g) → Na+(g) + e ΔHIE1 = +494 kJ/mol

#### Stage 4:

In this stage, an electron is added to the chlorine atom to create a negatively charged chloride ion in a gaseous form. For this reaction, the electron released has an electron affinity of -349 kJ/mol.

Cl(g) + e → Cl(g) ΔHEA1 = -349 kJ/mol

#### Stage 5:

The creation of sodium chloride from its gaseous ions is the final and fifth stage. It is necessary to determine the lattice energy produced during this operation, which should be negative.

Na+(g) + Cl(g) → NaCl(s) ΔHLE = -? kJ/mol

If the entire reaction takes a single step, the heat formation is -411 kJ/mol.

Na(s) + 1/2Cl2(g) → NaCl(s) ΔHf = -411 kJ/mol

In accordance with Hess’s law,

ΔHf = ΔHatom + ΔHBE + ΔHIE1 + ΔHEA1 + ΔHLE

⇒ -411 = 107 + 122 + 494 -349 + ΔHLE

⇒ ΔHLE = -785 kJ/mol

Therefore, sodium chloride has a lattice energy of -785 kJ/mol.

### Have You Heard?

The Born-Haber cycle is a method used for analyzing reaction energies. The names Max Born and Fritz Haber were given in honor of the two German scientists who discovered it in 1919. The cycle concerns how a metal—typically a Group I or Group II element—reacts with a halogen or another non-metallic element, like oxygen, to generate an ionic combination. The main application of Born-Haber cycles is to compute lattice energy, which cannot be observed directly.

### Lattice Energy Trend

In summation, the lattice energy trend rises as the ion charge rises and the distance or radius falls. More specifically, it rises through the bottom to top groups and from left to right throughout periods.

The following graphic depicts trends in lattice energy from the periodic table:

### Conclusion

The lattice energy can be classified as the energy change when one mole of a crystalline ionic compound is formed from its component ions, which are believed to be in the gaseous state. It gauges the compressive forces that hold ionic solids together. Numerous additional physical characteristics, including absorption, toughness, and volatility, are related to the magnitude of the lattice energy. The Born-Haber cycle estimates lattice energy, which is typically impossible indirectly.

### Frequently Asked Questions

#### 1. What is Lattice Energy?

Lattice energy can be expressed as the specific amount of energy produced when the gaseous ions react during the generation of one mole of a solid ionic compound. It also refers to the energy that makes it possible for one mole of a solid ionic compound to split into its component gaseous ions.

#### 2. Which Compound has the Highest Lattice Energy?

Among these compounds, sodium fluoride (NaF) has the highest lattice energy because it contains ions with the same charge as sodium and because the lattice energy rises with the size of the ions.

#### 3. Which Compound has the Lowest Lattice Energy?

As ion size grows, the lattice energy drops. Cesium iodide has the largest cation and anion sizes compared to other compounds. Therefore, cesium iodide has the lowest lattice energy.

#### 4. What Uses Do You See for Lattice Energy?

The following are the common applications of lattice energy:

• Lattice energy aids in determining the energy produced from a chemical when a certain number of ions come together to form that complex.
• It is mostly employed to gauge the potency of ionic solid substances.
• Ionic solids typically have high lattice energies, which increase their stability and make it difficult to break the bonds between them in the complex.

Comments:

#### Butanoic Acid – Structure, Properties, Uses

Butanoic Acid The carboxylic acid, butanoic acid, has the structural …

Read More >>

#### What is Iodoform? Characteristics and Uses

Iodoform The formula for Iodoform is CHI3. It is biotic …

Read More >>

#### Lead Acetate – Definition, Properties, Uses

Lead Acetate Have you ever licked lipstick when you sketch …

Read More >>