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Vapor pressure of solids

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 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 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:

$ln\,P_{solid}^{S}=ln\,P_{liquid}^{S}-{\frac {\Delta H_{m}}{R}}\left({\frac {1}{T}}-{\frac {1}{T_{m}}}\right)$

where:

$P_{solid}^{S}$	= Sublimation pressure of the solid component at the temperature $T<T_{m}$
$P_{liquid}^{S}$	= Extrapolated vapor pressure of the liquid component at the temperature $T<T_{m}$
$\Delta H_{m}$	= Heat of fusion
$R$	= Universal gas constant
$T$	= Sublimation temperature
$T_{m}$	= 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_m is positive) and the difference increases with increased distance from the melting point.