Difference between revisions of "Born–Haber cycle"
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==Lattice enthalpy== | ==Lattice enthalpy== | ||
{{main|Lattice energy}} | {{main|Lattice energy}} | ||
| − | The lattice enthalpy of an [[ionic compound]] MX is the enthalpy change for the reaction<ref group="note">The lattice enthalpy is conventionally defined as the production of gaseous ions so that it is positive for all solids.</ref> | + | The lattice enthalpy Δ<sub>latt</sub>''H'' of an [[ionic compound]] MX is the enthalpy change for the reaction<ref group="note">The lattice enthalpy is conventionally defined as the production of gaseous ions so that it is positive for all solids.</ref> |
:MX (cr) → M<sup>+</sup> (g) + X<sup>−</sup> (g) | :MX (cr) → M<sup>+</sup> (g) + X<sup>−</sup> (g) | ||
| − | It cannot be measured directly, as the ions cannot be sufficiently separated in the gas state: in practice, all ionic compounds vaporize to covalent molecules. | + | It cannot be measured directly, as the ions cannot be sufficiently separated in the gas state: in practice, all ionic compounds vaporize to covalent molecules. However, the enthalpies of formation of each of the ions separately are known: the [[enthalpy change of atomization]] for the element concerned plus the [[ionization energy]] for cations or the [[electron affinity]] for anions.<ref group="note">As measured, ionization energies and electron affinities are [[internal energy]] changes and not [[enthalpy]] changes. However, the difference is small enough to be ignored in these applications.</ref> |
| + | |||
| + | {| | ||
| + | |- | ||
| + | | colspan=3 align=center | Na<sup>+</sup> (g) + Cl (g) + e<sup>−</sup> | ||
| + | |- | ||
| + | | Δ<sub>f</sub>''H''[Na<sup>+</sup> (g)] || || Δ<sub>f</sub>''H''[Cl<sup>−</sup> (g)] | ||
| + | |- | ||
| + | | Na (g) + Cl (g) || || Na<sup>+</sup> (g) + Cl<sup>−</sup> (g) | ||
| + | |- | ||
| + | | Δ<sub>f</sub>''H''[Cl (g)] || rowspan=5 | || rowspan=5 | −Δ<sub>latt</sub>''H''[NaCl (cr)] | ||
| + | |- | ||
| + | | Na (g) + ½Cl<sub>2</sub> (g) | ||
| + | |- | ||
| + | | Δ<sub>f</sub>''H''[Na (g)] | ||
| + | |- | ||
| + | | Na (cr) + ½Cl<sub>2</sub> (g) | ||
| + | |- | ||
| + | | −Δ<sub>f</sub>''H''[NaCl (cr)] | ||
| + | |- | ||
| + | | colspan=3 align=center | NaCl (cr) | ||
| + | |- | ||
| + | |} | ||
==Notes and references== | ==Notes and references== | ||
Revision as of 10:20, 12 April 2011
The Born–Haber cycle is a particular application of Hess's law to deduce the changes in enthalpy for reactions involving gaseous ions, particularly the determination of lattice enthalpies.[1] It is named after the German scientists Max Born (1882–1970) and Fritz Haber (1868–1934).
As with other applications of Hess's law, the Born–Haber cycle relies on the fact that enthalpy is a state function, that is that the change in enthalpy between two states of a system is independent of the path taken to change the state. In a Born–Haber cycle, the path is cyclical, with the initial and final states being identical, so ΔH = 0. This allows a single unknown enthalpy change along the path to be calculated by reference to the others. Born–Haber cycles can also be constructed for other state functions, such as internal energy, entropy and Gibbs energy.
Lattice enthalpy
The lattice enthalpy ΔlattH of an ionic compound MX is the enthalpy change for the reaction[note 1]
- MX (cr) → M+ (g) + X− (g)
It cannot be measured directly, as the ions cannot be sufficiently separated in the gas state: in practice, all ionic compounds vaporize to covalent molecules. However, the enthalpies of formation of each of the ions separately are known: the enthalpy change of atomization for the element concerned plus the ionization energy for cations or the electron affinity for anions.[note 2]
| Na+ (g) + Cl (g) + e− | ||
| ΔfH[Na+ (g)] | ΔfH[Cl− (g)] | |
| Na (g) + Cl (g) | Na+ (g) + Cl− (g) | |
| ΔfH[Cl (g)] | −ΔlattH[NaCl (cr)] | |
| Na (g) + ½Cl2 (g) | ||
| ΔfH[Na (g)] | ||
| Na (cr) + ½Cl2 (g) | ||
| −ΔfH[NaCl (cr)] | ||
| NaCl (cr) | ||
Notes and references
Notes
- ↑ The lattice enthalpy is conventionally defined as the production of gaseous ions so that it is positive for all solids.
- ↑ As measured, ionization energies and electron affinities are internal energy changes and not enthalpy changes. However, the difference is small enough to be ignored in these applications.
References
- ↑ Atkins, P. W. Physical Chemistry, 4th ed.; University Press: Oxford, 1990; pp 49–52. ISBN 0-19-855283-1.
External links
 |
See also the corresponding article on Wikipedia. |
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