User:Milton Beychok/Sandbox

Vapor pressure of solids

Vapor Pressure of Liquid and Solid Benzene

Equilibrium vapor pressure can be defined as the pressure reached when a condensed phase is in equilibrium with its own vapor. In the case of an equilibrium solid, such as a crystal, this can be defined as the pressure when the rate of sublimation of a solid matches the rate of deposition of its vapor phase. For most solids this pressure is very low, but some notable exceptions are naphthalene, dry ice (the vapor pressure of dry ice is 5.73 MPa (831 psi, 56.5 atm) at 20 degrees Celsius, meaning it will cause most sealed containers to explode), and ice. All solid materials have a vapor pressure. However, due to their often extremely low values, measurement can be rather difficult. Typical techniques include the use of thermogravimetry and gas transpiration.

The sublimation pressure can be calculated from extrapolated liquid vapor pressures (of the supercooled liquid) if the heat of fusion is known. The heat of fusion has to be added in addition to the heat of vaporization to evaporize a solid. Assuming that the heat of fusion is temperature-independent and ignoring additional transition temperatures between different solid phases the equation

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

with:

$P_{solid}^{S}$	= 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
$R$	= 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 grows with increased distance from the melting point.