How to Find Lattice Energy?

The lattice energy is the energy released when one mole of ionic crystal is formed from the gaseous ions. It can also be defined as the energy required to break one mole of ionic crystal into its gaseous components. It is represented by the kJmol^-1.

However, it cannot be determined directly. It can be calculated by the energy cycle, which is known as the Born-Haber cycle. Note that, this cycle is the application of Hess’s law.

Determination of lattice energy of sodium chloride

The energy triangle of the sodium chloride is given below:

The enthalpy of the formation of sodium chloride can be determined by the calorimeter, which is -411kJmol^-1.

The lattice energy of the sodium chloride can be determined by this formula:

ΔH_l = ΔH_f – ΔH_x → (i)

where,

• ΔH_f = Enthalpy of formation
• ΔH_l = Lattice energy
• ΔH_x =  ΔH_s + ΔHi + ΔH_at + ΔH_e 

The following steps involved in the determination of ΔH_x of sodium chloride.

• Sublimation of Na

The first step of the Born-Haber cycle is the sublimation of sodium.

Na_(s)→ Na_(g)                                         ΔH_s = 108 kJmol^-1

• Ionization of the Na 

The ionization involves the removal of electrons from sodium to form Na⁺.

Na(g)→ Na⁺_(g) + 1e^–                                ΔH_i = 496kJmol^-1

• Atomization of chlorine 
• The atomization involves the formation of the chlorine atom.

1/2 Cl_2(g) → Cl_(g)                                            ΔH_at = 121 kJmol^-1

• Electron affinity of chlorine 

Cl_(g) + e^– → Cl^–_(g)                 ΔH_e = -349kJmol^-1

Thus,

  ΔH_x =        ΔH_s + ΔHi + ΔH_at + ΔH_e 

So putting the values,

ΔH_x = 108 + 496 + 121- 349 = 376 kJmol^-1

The lattice energy of sodium chloride can be determined by the following:

ΔH_l = ΔH_f – ΔH_x

Putting the values,

ΔH_l = -411 – 376 = -787kJmol^-1

Hence,

ΔH_l = -787kJmol^-1

It is to be noted that this energy value helps us to determine the stability of sodium chloride.

Key Takeaways

Terms related to the Born-Haber cycle and lattice energy to know:

• Ionization energy: The ionization energy is the minimum amount of energy that is required to remove the electron from the atom to form an ion. However, as the stability of the atom increases the ionization energy also increases.
• Enthalpy of atomization: When one mole of an atom is formed from the element. The amount of heat absorbed is known as the enthalpy of atomization. However, the enthalpy of atomization is always positive.
• Enthalpy of formation: The amount of heat released or absorbed when one mole of a compound is formed from the element is known as enthalpy of formation. However, it can positive and negative.
• Enthalpy of sublimation: The amount of heat required to convert one mole of solid into a gas is known as the enthalpy of sublimation. It is always positive.
• Electron affinity: The amount of energy released or absorbed when one electron is added to the gaseous atom is known as electron affinity.

Related Resources

• Ionization Energy Trends: Major Factors and Exceptions
• Lattice Energy: Born Haber Cycle and Enthalpy

Concepts Berg

Which compound has the highest lattice energy?

Lithium fluoride has the highest value of lattice energy. This is because of the smallest size of the cation and anion.

What uses do you see for lattice energy?

The lattice energy is used to measure the stability of the ionic solids. The greater the value of lattice energy, the ionic solids will be more stable.

How do hydration and lattice energies differ?

Hydration energy is the energy that is released when one mole of ions undergoes hydration. Whereas the lattice energy is the energy that is released when one mole of ionic crystal is formed from the gaseous ions.

How is this energy related to solubility?

If lattice energy is equal to or less than hydration energy, the solubility is greater. Whereas when hydration energy is less than lattice energy the solubility will be decreased.

References

• A textbook of physical chemistry thermodynamic and chemical equilibrium by K.L Kapoor