Born Haber Cycle

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Introduction

Born Haber process or more commonly known as Born Haber cycle is a method in use that lets us observe and analyze energies in a reaction. This process describes the formation of ionic compounds from different elements. It further enables us to understand the overall reaction process through a series of steps involved in it.

This methodology was introduced in the year 1919 by German scientists Fritz Haber and Max Born. Hence it is called Born-Haber Cycle. It is primarily used to calculate the lattice energy which is a measure of the strength of ionic bonds that exist in an ionic compound involved in a chemical reaction. The method also exhibits several properties such as electron affinity, ionization energy, sublimation energy, the heat of formation and dissociation energy. Observe and analyze energies in a reaction. This method helps us in describing the formation of ionic compounds from different elements. Also, it further enables us to understand the overall reaction process through a series of steps.

Let us look into Born Haber cycle and some chemical reactions in detail to explain the methodology of Born Haber Cycle.


Considerations of Born Haber Cycle

The reaction of electropositive metals with electronegative nonmetals produces ionic compounds. Alkali and alkaline earth metals react with chalcogen or halogen family elements to form compounds, which are crystalline ionic solids. Ionic compounds being stabilized by the electrostatic force of attraction between positive and negative charges are expected to exhibit similar physical properties.

However, physical properties like stability, and water solubility differ much for these ionic compounds. This difference is attributed to the difference in the enthalpy called ‘Lattice energy’, between the ionic solids.

Lattice energy is the energy that keeps together the cations and anions of any compound in fixed positions in a crystalline solid state. Lattice energy can be defined as either energy released when gaseous ions form one mole of a solid ionic compound or as the energy required to convert one mole ionic solid into its gaseous ions. There is no way to experimentally measure this lattice energy. Hess law of heat summation is the only indirect way of estimating the lattice energy.

Application of Hess Law of Heat summation to the formation of solid ionic compounds involves enthalpy of all processes that are necessary for the formation of the solid ionic compounds. This compound forms from the elemental state of the constituent atoms, in a cycle form such that the total energy on summation is zero.


Example of Born Haber Cycle

Lattice energy of magnesium oxide (or any AB-type Divalent ionic solid). It is possible to experimentally calculate the heat of formation of magnesium oxide (ΔHf0) from magnesium metal and oxygen gas.​

Mg (s) + ½ O2 (g) → MgO(s)

ΔHf0 = -602 kJ/mol

The processes or steps involved in the formation of magnesium oxide are as follows.

1. Solid magnesium atom sublimes to gaseous atom by absorbing heat energy (∆Hsub).

Mg (s) → Mg (g), Sublimation energy ΔHsub = + 136 kJ/mol

2. Gaseous magnesium atoms release two electrons in two steps with corresponding ionization energies.

Mg(g) → Mg+(g) + 1e , Ionization energy ∆H1IE= +738 kJ/mol

Mg+(g) → Mg2+(g) + 1e , Ionization energy ∆H2IE= +1450 kJ/mol

So, the energy of ionization = ∆HIE = 738 + 1450 = 2188 kJ/mol

3. Diatomic oxygen breaks into two individual atoms by absorbing bond energy, such that each chlorine atom absorbs half of the bond energy of the chlorine molecule.

O2(g) → 2O(g) ½ Bond Dissociation Energy of Oxygen = ½ ∆Hdiss = ½ 498= +249kJ/mol

4. Oxygen atoms accept two electrons to form oxide ions and release an energy equivalent to two-electron affinities.

O(g) + 1e → O(g) Electron affinity = ∆H1EA = -142 kJ/mol

O(g) + 1e → O2- (g) Electron affinity = ∆H2EA = +798 kJ/mol

The total energy released as electron affinity by the oxygen atom is = ∆HEA = +656kJ/mol

5. Gaseous magnesium ion and gaseous oxide ion combine to form solid magnesium oxide molecules and release energy equivalent to lattice energy.

Mg2+(g) + O2- (g) → Mg2+O2- (s) Lattice energy = ∆HLE = U = ?

Summation of the enthalpy of all the processes from the starting step to the final step gives the net enthalpy of formation of solid crystalline magnesium oxide from magnesium and oxygen in their standard conditions of solid and gas respectively. This should be equal to the experimentally measured enthalpy of formation of solid magnesium oxide.

The enthalpies are represented as a cycle in the figure.

[Image will be uploaded soon]

So, ΔHf0 = ΔHsub + ∆HIE + ½ ∆Hdis + ∆HEA + U or, ΔHf0 – (ΔHsub + ∆HIE +½ ∆Hdis + ∆HEA + U) = 0

602 + 136 + 2188 + 249 +656 + U = 0

Here, except lattice energy, all other enthalpies can be experimentally measured.

Lattice energy of the magnesium oxide solid = U = ΔHf0 – (ΔHsub + ∆HIE + ½ ∆Hdis + ∆HEA).

= -602 – 136 – 2188 – 249 -656 = -3831 kJ/mol

FAQ (Frequently Asked Questions)

1. What is the Born Haber Cycle?

Answer: Born Haber cycle is a method in use that lets us observe and analyze energies in a reaction. This process describes the formation of ionic compounds from different elements. It further enables us to understand the overall reaction process through a series of steps involved in it.

2. How to calculate lattice energy of NaCl using Born Haber Cycle?

Answer: Lattice energy of NaCl can be experimentally calculated as follows.

Na (s) + ½ Cl2 (g) → NaCl(s) ΔHf0 = -411kJ/mol

Ionic Solid NaCl forms by a series of processes. Heat changes of all the processes except lattice energy can be calculated.

The steps involved in the formation of NaCl are as follows.

1. Solid sodium atom absorbs heat energy to sublime into gaseous state (∆Hsub)

Na (s) → Na (g),

Sublimation energy ΔHsub = + 107 kJ/mol

2. Gaseous sodium atom absorbs the ionization energy to release one electron and forms gaseous sodium ion.

Na(g) → Na+(g) + 1e ,

Ionization energy ∆HIE = +502kJ/mol

3. Diatomic gaseous chlorine breaks into two individual atoms by absorbing bond energy, such that each chlorine atom absorbs half of the bond energy of the chlorine molecule.

Cl2(g) → 2Cl(g) 

Bond dissociation energy of chlorine = ½  ∆Hdiss= ½ 242 = +121 kJ/mol

4. Chlorine atom accepts an electron to form chloride ion and releases energy equivalent to electron affinity.

Cl(g) + 1e → Cl(g)

Electron affinity = ∆HEA = -355 kJ/mol

5. Gaseous sodium ion and gaseous chloride ion combine to form solid sodium chloride molecules and releases energy equivalent to lattice energy.

Na+(g) + Cl (g) → Na+ Cl(s)

Lattice energy = ∆HLE = U = ?

Summation of enthalpy of all the processes from step 1 to step 5, gives the net enthalpy of formation of solid crystalline sodium chloride. 

So, ΔHf0 = ΔHsub + ∆HIE + ½ Hdiss + ∆HEA + U or ΔHf0 – (ΔHsub + ∆HIE + ½ ∆Hdiss + ∆HEA + U)=0

411 + 107 + 502 +121 -355 +U = 0

Here, except lattice energy, all other enthalpies can be experimentally measured.

Lattice energy of the sodium chloride solid = U = ΔHf0 – (ΔHsub + ∆HIE + ½ ∆Hdiss + ∆HEA)

= -411 -107 -502 -121 +355

= – 786 kJ/mol