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The '''Born–Haber cycle''' is an approach to analyze reaction [[energy|energies]]. It was named after and developed by the two [[Germans|German]] scientists [[Max Born]] and [[Fritz Haber]]. The cycle is concerned with the formation of an [[ionic compound]] from the reaction of a [[metal]] (often a [[Alkali metal|Group I]] or [[Alkaline earth metal|Group II]] element) with a [[halogen]].
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Born–Haber cycles are used primarily as a means of calculating lattice energies (or more precisely enthalpies<ref group="note">The difference between energy and enthalpy is very small and the two terms are interchanged freely in this article.</ref>) which cannot otherwise be measured directly. The [[lattice enthalpy]] is the [[enthalpy]] change involved in the formation of an 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 applies [[Hess' Law]] to calculate 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 [[Chemical element|elements]].
 
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 first have to consider its [[bond dissociation enthalpy]] (see also [[bond energy]]). The energy required to remove one or more [[electron]]s to make a [[cation]] is a sum of successive [[ionization energy|ionization energies]]; for example the energy needed to form Mg<sup>2+</sup> is the first plus the second ionization energies of Mg. The energy changes when successive electrons are added to an atom to make it an [[anion]] are called the [[electron affinity|electron affinities]].  
 
The Born–Haber cycle applies only to fully ionic solids such as certain [[alkali halide]]s. Most compounds include covalent and ionic contributions to chemical bonding and to the lattice energy, which is represented by an extended Born-Haber thermodynamic cycle.<ref>H. Heinz and U. W. Suter ''Journal of Physical Chemistry B'' 2004, ''108'', 18341-18352.</ref> The extended Born–Haber cycle can be used to estimate the polarity and the atomic charges of polar compounds.
 
==Example: Formation of lithium fluoride==
[[File:BornHaberLiF.PNG|350px|thumb|right|Born–Haber cycle for the standard enthalpy change of formation of [[lithium fluoride]]. ΔH<sub>latt</sub> corresponds to U<sub>L</sub> in the text.]]
 
The enthalpy of formation of [[lithium fluoride]] (LiF) from its elements lithium and fluorine in their stable forms is modeled in five steps in the diagram:
 
# Enthalpy change of atomization enthalpy of lithium
# Ionization enthalpy of lithium
# Atomization 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, <math>\Delta\text{H}_{\text{f}}</math>.
 
<math>\Delta\text{H}_{\text{f}} = \text{V} + \frac{1}{2}\text{B} + \text{IE}_{\text{M}} - \text{EA}_\text{X} + \text{U}_\text{L}</math>
 
*V is the [[enthalpy of sublimation]] for metal atoms (lithium)
*B is the bond energy (of F<sub>2</sub>). The coefficient 1/2 is used because the formation reaction is Li + 1/2 F<sub>2</sub> → LiF.
*<math>\text{IE}_{\text{M}}</math> is the [[ionization energy]] of the metal atom: <math>\text{M} + \text{IE}_\text{M} \to \text{M}^+ + \text{e}^-</math>
*<math>\text{EA}_\text{X}</math> is the [[electron affinity]] of non-metal atom X (fluorine)
*<math>\text{U}_\text{L}</math> 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.<ref>Moore, Stanitski, and Jurs. ''Chemistry: The Molecular Science.'' 3rd edition. 2008.  ISBN 0-495-10521-X. pages 320-321.</ref>
 
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
<math> 0 = - \Delta\text{H}_{\text{f}} + \text{V} + \frac{1}{2}\text{B} + \text{IE}_{\text{M}} - \text{EA}_\text{X} + \text{U}_\text{L}</math>
which is equivalent to the previous equation.
 
==See also==
*[[ionic crystal]]
*[[ionic compound]]
*[[ionic liquid]]s
 
==Notes==
{{reflist|group=note}}
 
==References==
{{reflist}}
 
==External links==
*[http://www.youtube.com/watch?v=FD85Hetrg1Q ChemGuy on the Born-Haber Cycle]
 
{{DEFAULTSORT:Born-Haber cycle}}
[[Category:Solid-state chemistry]]
[[Category:Thermochemistry]]

Latest revision as of 13:44, 9 January 2015

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