Lattice Energy - Meaning, Definition, Factors, Differences, Calculation, FAQs

Lattice Energy Understanding

Lattice energy is the energy change that accompanies the formation of one mole of an ionic crystalline solid from its free gaseous ions. The sign of this lattice energy may vary from negative to positive, positive or negative, depending on the manner a corresponding process is run.

Calculations of lattice energy are most of the time heterogeneous, and demands are very high since they are experimentally indirect, being acquired from the Born-Haber cycle.

The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔH_lattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid MX, the lattice energy is the enthalpy change of the process:

MX(s) $\longrightarrow$ Mⁿ⁺(g)+X^n-(g) $\Delta \mathrm{H}_{\text {lattice }}$

The lattice energy ΔHlattice of an ionic crystal can be expressed by the following equation:

$\Delta \mathrm{H}_{\text {lattice }}=\frac{\mathrm{C}\left(\mathrm{Z}^{+}\right)\left(\mathrm{Z}^{-}\right)}{\mathrm{R}_0}$

in which C is a constant that depends on the type of crystal structure; Z⁺ and Z^– are the charges on the ions, and Ro is the interionic distance. Thus, the lattice energy of an ionic crystal increases rapidly as the charges of the ions increase and the sizes of the ions decrease.

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The Born-Haber Cycle

It is not possible to measure lattice energies directly. However, the lattice energy can be calculated using the equation given in the previous section or by using a thermochemical cycle. The Born-Haber cycle is an application of Hess’s law that breaks down the formation of an ionic solid into a series of individual steps:

• ΔH_f°, the standard enthalpy of formation of the compound

• IE, the ionization energy of the metal

• EA, the electron affinity of the nonmetal

• ΔH_s°, the enthalpy of sublimation of the metal

• D, the bond dissociation energy of the nonmetal

• ΔH_lattice, the lattice energy of the compound

The figure given below shows the Born-Haber cycle for the formation of solid cesium fluoride.

The Born-Haber cycle shows the relative energies of each step involved in the formation of an ionic solid from the necessary elements in their reference states.

For Caesium fluoride, the lattice energy can be calculated using the given values as follows:

$\Delta H_{\text {lattice }}=(553.5+76.5+79.4+375.7+328.2) \mathrm{kJ} / \mathrm{mol}=1413.3 \mathrm{~kJ} / \mathrm{mol}$

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Types and Factors Influencing Lattice Energy Lattice energy

1. Formation Lattice Energy: The energy belonging to the reaction when gaseous ions come together to form one mole of an ionic solid. Since this process is exothermic, the lattice energy change is negative.

2. Dissociation Lattice Energy: The energy changes when one mole of an ionic solid breaks up into its constituent gaseous ions. It is an endothermic process, so lattice energy is always positive.

The lattice energy depends on:

Ionic charge: In case the charge of the ions increases then electro-static attraction and hence lattice energy of the ionic solid increases. For instance, the lattice enthalpy of magnesium oxide is higher compared to sodium chloride due to the reason that Mg²⁺ and O²⁻ have higher charges compared to Na⁺ and Cl‾.

Ionic Radius: The smaller the ions, the closer the ions get to one another, increasing the attraction forces between them and hence lattice energy. For example, lithium fluoride, due to its size, has lower lattice energy than potassium bromide. This is because lithium ions are smaller in comparison to potassium ions and offer better interaction.

Thus the knowledge of these factors assumes prime importance in understanding the different properties of ionic compounds like solubility, melting points, and stabilities.

Related Topics Link

• Crystallization
• Bcc Fcc Primitive Cubic Unit Cell
• Amorphous solid
• Frenkel Defect

Real-Life Applications of Lattice Energy

The importance of information on lattice energy gets underlined for two things: the synthesis of new ionic compounds having some desired properties.

Most of the fabrication processes for ceramics and glasses strongly rely on lattice energy because these materials are mainly composed of ionic, and hence strong compounds. In turn, such compounds are held together by strong ionic bonds and are thus very stable and robust. Lattice energy, lying at the very heart of chemical education, is one of the myriad central concepts bared to the student in chemistry to introduce him to some fundamentals with ionic bonding and crystal structures. Far too often, though, this is done using the Born-Haber cycle—where lattice energy is a part of the process—in efforts to explain to advanced students just how it is possible to calculate and interpret energy changes associated with the formation of an ionic compound.

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Recommended topic video on (Lattice Energy)

Some Solved Examples

Example 1: Lattice energy is inversely proportional to the sum of radii of

1) Radius of anion

2) Radius of cation

3) Sum of radii of ions

4) Sum of radii of atoms

Solution:

As we have learned,

Lattice Energy(Ionic Bond Energy) $\propto \frac{\text { Cation Charge } \cdot \text { Anion Charge }}{\text { Cation Radius }+ \text { Anion Radius }}$

Hence, the answer is the option (3).

Example 2: Lattice energy is always

1) Exothermic

2) Endothermic

3) Ectothermic

4) Hypothermic

Solution

As we have learned, Lattice energy is the energy required to completely separate one mole of solid ionic compound into its constituent gaseous ions.

As the definition implies, this process will always be endothermic; thus, the value for lattice energy will be positive.

Hence, the answer is the option (2).

Example 3: A type of enthalpy cycle that is used to calculate lattice energy is

1) Hess's Law

2) Born-Haber cycle

3) Haber process

4) Contact process

Solution

Born Haber's cycle is used to determine the value of lattice energy.

Hence, the answer is the option (2).

Example 4: Which one of the following has the largest lattice energy?

1) MgF₂
2) NaF
3) CaF₂
4) AlF₃

Solution

Lattice energy is directly proportional to charge and inversely proportional to size of ions.In MgF₂ we have Mg²⁺ ion, In NaF we have Na⁺ ion, In CaF₂ we have Ca²⁺ ion, InAlF₃ we have Al³⁺ ion. So, if we look on charges then AlF₃ has largest lattice energy. Hence, the answer is the option (4).

Example 5:

Order the lattice energies (highest → lowest) among LiF, NaF, and KF.

Solution:
Lattice energy increases with higher ionic charges (here same) and decreases with larger ion radii. F⁻ is constant; cation size increases Li⁺ < Na⁺ < K⁺, so LiF > NaF > KF.

Example 6:

The lattice energy of NaCl is U. If MgCl₂ had same ionic distances and geometry, what would be its lattice energy approximately (in terms of U)?
(1) 2U
(2) 3U
(3) 4U
(4) 6U

Solution:

Lattice energy $\propto z^{+} z^{-}$.
- For $\mathrm{NaCl}, \mathrm{z}^{+}=+1, \mathrm{z}^{-}=-1 \rightarrow$ product $=1$
- For $\mathrm{MgCl}_2$, effectively $\mathrm{Mg}^{2+}$ with $2 \times \mathrm{Cl}^{-} \rightarrow$ product $(2 \times 1)=2$ (or you can think lattice energy sum over interactions is about twice)
Hence approx $2 U$.

Hence, the answer is option (1)

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Summary

Lattice Energy describes the energy that occurs, in either the formation or dissociation process of the ionic compounds. It is a direct measure of the strength of ionic bonding within the crystal lattice: the larger (more negative) the lattice energy, the more stable and stronger the ionic solid. Lattice energy cannot be measured directly, but is usually deduced via thermochemical cycles (e.g. Born–Haber) or estimated by theoretical formulae. Understanding lattice energy is fundamental for explaining melting points, solubility, hardness, and stability of ionic compounds—crucial in chemical analysis and competitive exam problems.

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