The Born-Haber cycle is a method for calculating reaction energies. It was named after Max Born and Fritz Haber, two German scientists who invented it in 1919Additionally, it was independently developed by Kasimir Fajans and simultaneously published in the same journal's issue. The cycle is concerned with how a metal—typically a Group I or Group II element—reacts with a halogen or another non-metallic element, like oxygen, to form an ionic compound.
In order to calculate lattice energy (or, more precisely, enthalpy), which cannot be measured directly, Born-Haber cycles are primarily used.
What is Lattice Enthalpy?
Lattice enthalpy measures the strength of the forces between the ions in an ionic solid. The stronger the forces, the greater the lattice enthalpy. Those forces are only completely broken when the ions are present as gaseous ions, spread so far apart that the attraction between them is negligible.
What is Hess's Law?
Hess' Law states that the overall change in energy of a process can be calculated by breaking it down into phases and then summing the energy changes of each phase. In the Born Haber Cycle, Hess' Law is effectively applied to an ionic solid.
Before the Born-Haber Cycle can be used to calculate the lattice energy of an ionic solid, the following concepts must be understood:
Ionisation Energy
The minimum energy required to remove the most loosely bound electron from an isolated gaseous atom, positive ion, or molecule is referred to as ionisation energy.
Electron Affinity
The amount of energy released when an electron attaches to a neutral atom or molecule in the gaseous state to form an anion is defined as an atom's or molecule's electron affinity.
Dissociation Energy
One measure of the strength of a chemical bond AB is the bond-dissociation energy. It is the standard enthalpy change that occurs when AB is cleaved by homolysis into fragments A and B, which are usually radical species.
Sublimation Energy
The enthalpy of sublimation, also known as the heat of sublimation, is the amount of heat required to sublimate one mole of a substance at a given combination of temperature and pressure, which is usually standard temperature and pressure. It is equal to the solid's cohesive energy.
Heat of Formation
Heat of formation, also known as enthalpy of formation or standard enthalpy of formation, is the amount of heat absorbed or evolved when one mole of a compound is formed from its constituent elements, with each substance in its normal physical state (gas, liquid, or solid).
How do you use the Born-Haber Cycle?
Step 1: Establish the energy of the metal and non-metal in each of their constituent elements. Subtract the heat of formation from this. The result is the ionic solid's energy, which is used to calculate the lattice energy.
Step 2: The reacting substances should be in their gaseous states. Add the enthalpy changes needed to convert one element to gas, then do the same for the other elements.
Step 3: No dissociation energy is added to this element because metals are found in nature as a single atom. However, a lot of non-metals are polyatomic species, like Cl, which is Cl2 in its elemental form. Therefore, the value from Step 2 must be multiplied by the energy needed to convert Cl2 into 2Cl atoms.
Step 4: From their ionic solids, convert the metal and non-metal into their ionic forms. For the value obtained from Step 3, multiply it by the metal's ionization energy. Subtract the non-metal's electron affinity from the initial value.
Step 5: A release of energy occurs as the metal and non-metal come together to form the ionic solid. This energy is called the lattice energy. The difference between the values of Steps 1 and 4 represents the final lattice energy value.
Born Haber Cycle Equation
One equation can represent the Born Haber cycle equation or Born Haber cycle formula.
Heat of formation = Heat of atomization of Dissociation energy + (sum of Ionization energies) + (sum of Electron affinities) + Lattice energy
This basic equation includes electron affinity. When entering a number, consider whether the energy is released (exothermic reaction) or absorbed (endothermic reaction) for each electron affinity.
- When energy is released, the value should be negative.
- The number should be positive if energy is received.
When the equation is rearranged to solve for lattice energy, the following results:
Lattice energy = Heat of formation- Heat of atomization- Dissociation energy- (Sum of Ionization energies)- (Sum of Electron Affinities)
Things to Remember
- Ionic solids are stable substances, and the enthalpies required for ionic molecule synthesis do not account for stability.
- Due to the lattice energy present in their solid form, ionic compounds are also more stable.
- The Born-Haber cycle is triggered because it is impossible to calculate how much lattice energy is present.
- We can calculate and understand ionic solid lattice energies using the Born Haber cycle.
- A Born Haber cycle is used to understand and calculate the concept of lattice energy.
- A significant negative value of lattice enthalpy indicates that electrostatic forces between oppositely charged ions are stronger in the lattice.
- Since covalent compounds do not contain ions, they cannot have lattice enthalpies.