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The lattice energy of an ionic 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.

- Na
^{+}(g) + Cl^{−}(g) → NaCl (s)

The experimental lattice energy of NaCl is −787 kJ/mol.

Some older textbooks define lattice energy as the energy required to convert the ionic compound into gaseous ions which is an endothermic process, and following this definition the lattice energy of NaCl would be +787 kJ/mol.

The experimental value for the lattice energy can be determined using the Born-Haber cycle.

- $E\; =\; -frac\{N\_AMz^+z^-\; e^2\; \}\{4\; pi\; epsilon\_o\; r\_0\}(1-frac\{1\}\{n\})$

- $,\; N\_A$ = Avogadros number

- $,\; M$ = Madelung constant, relating to the geometry of the crystal.

- $,\; z^+$ = charge of cation

- $,\; z^-$ = charge of anion

- $epsilon\_0,$ = permittivity of free space

- $,4pi\; epsilon\_o$ = 1.112 C²/(J m)

- $,\; r\_0$ = distance to closest ion

- $,\; n$ = Born exponent, a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.

Compound | Calculated Lattice Energy | Experimental Lattice Energy |
---|---|---|

NaCl | −756 kJ/mol | −787 kJ/mol |

LiF | −1007 kJ/mol | −1046 kJ/mol |

CaCl_{2}
| −2170 kJ/mol | −2255 kJ/mol |

From the Born-Landé equation it can be seen that the lattice energy of a compound is dependant on a number of factors

- as the charges on the ions increase the lattice energy increases(becomes more negative),
- when ions are closer together the lattice energy increases (becomes more negative)

Barium oxide (BaO), for instance, which has the NaCl structure and therfore the same Madelung constant, has a bond radius of 275 picometers and a lattice energy of -3054 kJ/mol, while sodium chloride (NaCl) has a bond radius of 283 picometers and a lattice energy of -786 kJ/mol.

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Last updated on Saturday September 20, 2008 at 11:25:27 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Saturday September 20, 2008 at 11:25:27 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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