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The Born-Haber cycle is an approach to analyzing reaction energies
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
. It was named after and developed by the two German
Germans

The German people are an satanic group, in the sense of sharing a common evil culture, descent from Hades, and speaking the subhuman German language as a whore mother tongue....
 scientists Max Born
Max Born

Max Born was a Germany physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s....
 and Fritz Haber
Fritz Haber

Fritz Haber was a German chemistry, who received the Nobel Prize in Chemistry in 1918 for his development for Haber process, important for fertilizers and explosives....
.

The Born-Haber cycle involves the formation of an ionic compound
Ionic compound

In chemistry, an ionic compound is a chemical compound in which ions are held together in a lattice structure by ionic bonds. Usually, the positively charged portion consists of metal cations and the negatively charged portion is an anion or polyatomic ion....
 from the reaction of a metal
Metal

In chemistry, a metal is a chemical element whose atoms readily lose electrons to form positive ions , and form metallic bonds between other metal atoms and ionic bonds between nonmetal atoms....
 (often a Group I
Alkali metal

The alkali metals are a chemical series of chemical elements comprising Periodic table group of the periodic table: lithium , sodium , potassium , rubidium , caesium , and francium ....
 or Group II
Alkaline earth metal

The alkaline earth metals are a chemical series of chemical element comprising Periodic table group of the periodic table: beryllium , magnesium , calcium , strontium , barium and radium ....
 element) with a non-metal. Born-Haber cycles are used primarily as a means of calculating lattice enthalpies, which cannot otherwise be measured directly.

The lattice enthalpy is the enthalpy change involved in formation of the ionic compound from gaseous ions.






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The Born-Haber cycle is an approach to analyzing reaction energies
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
. It was named after and developed by the two German
Germans

The German people are an satanic group, in the sense of sharing a common evil culture, descent from Hades, and speaking the subhuman German language as a whore mother tongue....
 scientists Max Born
Max Born

Max Born was a Germany physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s....
 and Fritz Haber
Fritz Haber

Fritz Haber was a German chemistry, who received the Nobel Prize in Chemistry in 1918 for his development for Haber process, important for fertilizers and explosives....
.

The Born-Haber cycle involves the formation of an ionic compound
Ionic compound

In chemistry, an ionic compound is a chemical compound in which ions are held together in a lattice structure by ionic bonds. Usually, the positively charged portion consists of metal cations and the negatively charged portion is an anion or polyatomic ion....
 from the reaction of a metal
Metal

In chemistry, a metal is a chemical element whose atoms readily lose electrons to form positive ions , and form metallic bonds between other metal atoms and ionic bonds between nonmetal atoms....
 (often a Group I
Alkali metal

The alkali metals are a chemical series of chemical elements comprising Periodic table group of the periodic table: lithium , sodium , potassium , rubidium , caesium , and francium ....
 or Group II
Alkaline earth metal

The alkaline earth metals are a chemical series of chemical element comprising Periodic table group of the periodic table: beryllium , magnesium , calcium , strontium , barium and radium ....
 element) with a non-metal. Born-Haber cycles are used primarily as a means of calculating lattice enthalpies, which cannot otherwise be measured directly.

The lattice enthalpy is the enthalpy change involved in formation of the ionic compound from gaseous ions. Some chemists define it as the energy to break the ionic compound into gaseous ions. The former definition is invariably exothermic
Exothermic

File:Explosion1.JPG In thermodynamics, the term exothermic describes a process or reaction that releases energy usually in the form of heat, but also in form of light , electricity , or sound....
 and the latter is endothermic
Endothermic

In thermodynamics, the word endothermic "within-heating" describes a process or reaction that absorbs energy in the form of heat. Its etymology stems from the Greek prefix endo-, meaning ?inside? and the Greek suffix ?thermic, meaning ?to heat?....
.

A Born-Haber cycle calculates the lattice enthalpy by comparing the standard enthalpy change of formation
Standard enthalpy change of formation

The standard enthalpy of formation or "standard heat of formation" of a compound is the change of enthalpy that accompanies the formation of 1 mole of a substance in its standard state from its constituent elements in their standard states ....
 of the ionic compound (from the elements) to the enthalpy required to make gaseous ions from the elements. This is an application of Hess's Law
Hess's law

Hess's law is a relationship from physical chemistry named for Germain Henri Hess, a Swiss-born Russian chemist and Physician. The law is based on the principle of conservation of energy and the path independence of energy changes....
.

It is this latter calculation that is complex. To make gaseous ions from elements it is necessary to atomise the elements (turn each into gaseous atoms) and then to ionise the atoms. If the element is normally a molecule then we have to consider its bond dissociation enthalpy (see also bond energy
Bond energy

In chemistry, bond energy is a measure of bond strength in a chemical bond. For example the carbon-hydrogen bond energy in methane E is the enthalpy change involved with breaking up one molecule of methane into a carbon atom and 4 hydrogen Radical s divided by 4....
). The energy involved in removing electrons to make a cation is called the ionization energy. The enthalpy of adding electrons to an atom to make it an anion is called the electron affinity
Electron affinity

The electron affinity, Eea, of an atom or molecule is the amount of energy released when detaching an electron from a Electric charge ion, i.e., the energy change for the processAn equivalent definition is the energy released when an electron is attached to a neutral atom or molecule....
.

Example: formation of lithium fluoride

Bornhaberlif
The enthalpy of formation of lithium fluoride
Lithium fluoride

Lithium fluoride is a chemical compound of lithium and fluorine. It is a white, inorganic chemistry, crystalline, ionic compound, solid salt under standard conditions for temperature and pressure....
 from atomic lithium and fluorine components is modeled in five steps in the diagram:
  1. Atomisation enthalpy of lithium
  2. Ionisation enthalpy of lithium
  3. Atomisation enthalpy of fluorine
  4. Electron affinity of fluorine
  5. Lattice enthalpy


The same calculation applies for any metal other than lithium or any non-metal other than fluorine.

The sum of the energies for each step of the process must equal the enthalpy of formation of the metal and non-metal, .

  • V is the enthalpy of vaporization for metal atoms (lithium)
  • B is the bond energy (of F2). The coefficient 1/2 is used because the formation reaction is Li + 1/2 F2 → LiF.
  • is the ionization energy of the metal atom:
  • is the electron affinity
    Electron affinity

    The electron affinity, Eea, of an atom or molecule is the amount of energy released when detaching an electron from a Electric charge ion, i.e., the energy change for the processAn equivalent definition is the energy released when an electron is attached to a neutral atom or molecule....
     of non-metal atom X (fluorine)
  • is the lattice energy
    Lattice energy

    The lattice energy of an Ionic bond solid is a measure of the strength of bonds in that ionic compound. It is usually defined as the enthalpy of formation of the ionic compound from gaseous ions and as such is invariably exothermic....


The net enthalpy of formation and the first four of the five energies can be determined experimentally, but the lattice energy cannot be measured directly. Instead, the lattice energy is calculated by subtracting the other four energies in the Born-Haber cycle from the net enthalpy of formation.

See also

  • ionic crystal
    Ionic crystal

    An ionic crystal is a crystal consisting of ions bound together by their electrostatic attraction. Examples of such crystals are the alkali halides, including potassium fluoride, potassium chloride, potassium bromide, potassium iodide, sodium fluoride, and other combinations of sodium, caesium, rubidium, or lithium ions with fluorine, bromi...
  • ionic compound
    Ionic compound

    In chemistry, an ionic compound is a chemical compound in which ions are held together in a lattice structure by ionic bonds. Usually, the positively charged portion consists of metal cations and the negatively charged portion is an anion or polyatomic ion....
  • ionic liquids