Born–Haber cycle
The Born–Haber cycle is an approach to analyzing reaction energies. It was named after and developed by the two German scientists Max Born and Fritz Haber.
The Born–Haber cycle involves the formation of an ionic compound from the reaction of a metal (often a Group I or Group II element) with a non-metal. Born–Haber cycles are used primarily as a means of calculating lattice energies (or more precisely enthalpies[1]) 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 and the latter is endothermic.
A Born–Haber cycle calculates the lattice enthalpy by comparing the standard enthalpy change of formation 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.
This latter calculation 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). The energy required to remove one or more electrons to make a cation is a sum of successive ionization energies; for example the energy needed to form Mg2+ is the first plus the second ionization energies of Mg. The energy released when one electron is added to an atom to make it an anion is called the electron affinity.
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[edit] Example: formation of lithium fluoride
The enthalpy of formation of lithium fluoride from its elements lithium and fluorine in their stable forms is modeled in five steps in the diagram:
- Atomisation enthalpy of lithium
- Ionisation enthalpy of lithium
- Atomisation enthalpy of fluorine
- Electron affinity of fluorine
- 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, ΔHf.
- V is the enthalpy of sublimation 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.
- IEM is the ionization energy of the metal atom:
- EAX is the electron affinity of non-metal atom X (fluorine)
- UL is the lattice energy (defined as exothermic here)
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.[2]
The word cycle refers to the fact that one can also equate to zero the total enthalpy change for a cyclic process, starting and ending with LiF(s) in the example. This leads to 
which is equivalent to the previous equation.
[edit] See also
[edit] References
- ^ The difference between energy and enthalpy is very small and the two terms are interchanged freely in this article.
- ^ Moore, Stanitski, and Jurs. Chemistry: The Molecular Science. 3rd edition. 2008. ISBN 0-495-10521-X. pages 320-321.
