User:Milton Beychok/Sandbox: Difference between revisions

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== Vapor pressure of solids ==
[[Image:Vapor Pressure of Liquid and Solid Benzene.png|thumb|350px|Vapor Pressure of Liquid and Solid Benzene]]


All solid materials have a vapor pressure which, for most solids, is very low. Some notable exceptions are [[naphthalene]], [[ice]] and  [[dry ice]] ([[carbon dioxide]]). The vapor pressure of dry ice is 5.73 MPa (56.5 atm) at 20 °C which would cause most sealed containers to rupture.
Due to their often extremely low values, measurement of the vapor pressure of solids can be rather difficult. Typical techniques for such measurements include the use of [[thermogravimetry]] and [[gas transpiration]].
The vapor pressure of a solid can be defined as the pressure at which the rate of [[sublimation (physics)|sublimation]] of a solid matches the rate of deposition of its vapor phase.
There are a number of methods for calculating the sublimation pressure (i.e., the vapor pressure of a solid). One method is to  calculate sublimation pressures <ref>{{cite journal |author=Bruce Moller, Jürgen Rarey and Deresh Ramjugernath |title=Estimation of the vapour pressure of non-electrolyte organic compounds via group contributions and group interactions|journal=J.Molecular Liquids|volume=143 |issue=1|pages=52-63|date=2008|id=|url=}}</ref> from extrapolated liquid vapor pressures if the [[heat of fusion]] is known. The heat of fusion has to be added in addition to the [[heat of vaporization]] to vaporize a solid. Assuming that the heat of fusion is temperature-independent and ignoring additional transition temperatures between different solid phases the equation, the sublimation pressure can be calculated using this version of the [[Clausius-Clapeyron]] equation:
:<math>ln\,P^S_{solid} = ln\,P^S_{liquid} - \frac{\Delta H_m}{R} \left( \frac{1}{T} - \frac{1}{T_m} \right)</math>
:{| border="0" cellpadding="1"
|-
|align=right|where:
|-
!align=right|<math>P^S_{solid}</math> 
|align=left|= Sublimation pressure of the solid component at the temperature <math>T<T_m</math>
|-
!align=right|<math>P^S_{liquid}</math>
|align=left|= Extrapolated vapor pressure of the liquid component at the temperature <math>T<T_m</math>
|-
!align=right|<math>\Delta H_m</math>
|align=left|= Heat of fusion
|-
!align=right|<math>R</math>
|align=left|= [[Molar gas constant|Universal gas constant]]
|-
!align=right|<math>T</math>
|align=left|= Sublimation temperature
|-
!align=right|<math>T_m</math>
|align=left|= Melting point temperature
|}
gives a fair estimation for temperatures not too far from the melting point. This equation also shows that the sublimation pressure is lower than the extrapolated liquid vapor pressure (ΔH<sub>m</sub> is positive) and the difference increases with increased distance from the melting point.

Revision as of 22:20, 9 December 2008

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