Born - Haber Cycle

Why is the Born - Haber Cycle Used?

Ionic solids are stable compounds. The enthalpies required for the formation of the ionic molecules do not account for stability alone. These compounds also have additional stability because of the lattice energy present in its solid structure. The lattice energy present cannot be measured. This is where the Born-Haber cycle allows us to determine and understand the lattice energies of the ionic solids. In order to understand the idea of lattice energy and calculate it, a Born-Haber cycle is used. 

What is the Born - Haber Cycle?

The Born-Haber cycle is a classic approach to measure the reaction energies. The cycle is mostly concerned with the formation of an ionic solid from the metals (Group I or Group II) when reacted with a halogen or a non-metallic element like oxygen.

Application of Born – Haber Cycle?

Born-Haber cycles are primarily used in calculating the lattice energy which cannot be measured otherwise. The lattice energy is the enthalpy change involved in the formation of ionic solids from gaseous ions or the energy involved in breaking the ionic solids into gaseous ions. A Born-Haber cycle applies Hess’ law to calculate the lattice energy by comparing the standard enthalpy change in the formation of the ionic solid from the elements to the enthalpy that is required to form the gaseous ions from the elements. 

Explain Born - Haber Cycle - Born – Haber Cycle Definition

There are several other concepts that one has to understand before getting to the Born – Haber cycle and applying it to determine the lattice energy of an ionic solid. Some of them are:

  • Ionization Energy: The energy required to take off an electron from the neutral ion/atom. In order to do this, there should be an input of energy, which is why it is always positive. Ionization energy is noted to be increasing across the periodic table from left to right, and decreasing from top to bottom. However, there are some exceptions due to the unpredictable stability of completely filled/half-filled orbitals.

  • Electron Affinity: The energy released when an electron is added to a neutral ion/atom. The energy released is known to have a negative value, but due to the definition of affinity, it is denoted as a positive value. When used to calculate the lattice energy, one has to subtract the electron affinity and not add it because of the positive value. The electron affinity is known for increasing from left to right and decreasing from top to bottom in a periodic table.

  • Dissociation Energy: The energy needed to break a compound apart. Dissociation is an endothermic process that requires an input of energy. Therefore, its value is always positive. The magnitude of it is dependent on the electronegativity of the atoms involved in the compound.

  • Sublimation Energy: Known as the energy of atomization, it is required to turn the compound from solid to gas while passing through the liquid phase. It is again an input of energy and is always positive.

  • The heat of Formation: It is the change in energy when a particular compound is formed from elements. It can be either positive or negative based on the atoms involved and their interaction.

  • Hess's Law: The overall change in energy determined by breaking the process into steps and adding changes in each step. The Born – Haber cycle is based on the Hess' law and its application of ionic solid.

Describe the Born – Haber cycle

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  • Step 1: Determine the energy of all the metals and non-metals in the elemental forms. Subtract the heat of formation of the ionic solid by combining these elements. This will be used as the energy of ionic solids in the equation.

  • Step 2: According to the Born–Haber cycle, the elements shall be in the gaseous forms. Add the enthalpy change by turning the elements into the gaseous states. 

  • Step 3: Metals usually exist as single atoms, which is why there won't be any dissociation energy for them. But nonmetals are polyatomic species. Calculate the dissociation energy for the non-metals and add them to the value obtained in step 2.

  • Step 4: Both metals and nonmetals are now to be changed to ionic solids. To do this, add the ionization energy of the metal to the value of step 3. Following that, subtract the electron affinity of non-metal from the value of step 3. 

  • Step 5: Now, the metal and nonmetal will be combined to release an energy called lattice energy. The value of this energy is the difference of values from Step 1 and Step 4.

Born – Haber Cycle Equation

Heat of formation= Dissociation Energy + Sublimation Energy + Ionization Energies – Electronic Affinities + Lattice Energy.

Born – Haber Cycle Example

Find the lattice energy of MgCl2(s).

𝚫Hf0 (MgCl2) = 𝚫Hsub0 + I.E. + Dissociating energy + E.A - Lattice Energy

Lattice Energy = 𝚫Hsub0 + I.E. + Dissociating energy + E.A - 𝚫Hf0 (MgCl2)

Lattice Energy = 147kJ/mol + 2188.4 kJ/mol + 248 kJ/mol - (2 x 349kJ/mol) + 642kJ/mol

Lattice Energy = 2527.4 kJ/mol

Where, I.E = Ionization energy

E.A = Electron Affinity

FAQ (Frequently Asked Questions)

1. What is Lattice Energy?

Lattice Energy, a type of potential energy can be defined in two different ways. One, it is the energy required to break an ionic solid while converting its atoms into ions (gaseous). This definition gives a value to the lattice energy, which is always positive because the reaction is endothermic. Second, it is the energy used in the reverse process where the gaseous ions bind to form the atoms of an ionic solid.

2. Is Lattice Energy, Negative or Positive?

Lattice Energy is used to display the stability of ionic solids. While we expect an ordered structure to be less stable as the entropy for it would be low, the case is not the same. In most cases, the value of the lattice energy will always be negative, given the reaction is exothermic. In cases where gaseous ions bind to form atoms, it is the energy required for the conversion, and the values are expressed in kJ/mol units.

3. What Happens During the Enthalpy Change in an Ionic Solid Compound?

A crystalline structure lets its ion interact with multiple ions (of opposite charge), causing a favourable enthalpy change in the system. During the interaction of the oppositely charged ions, a lot of energy is released, and this energy prompts the ionic solids to have high boiling and melting points. Some ionic solids, when treated with high temperatures, even decompose before reaching the boiling/melting point.