Hi Jalal,

primarily, the temperature of the system: as temperature increases, the number of molecules having enough energy to split from the liquid phase increseas, and pressure the vapour phase increases. If we considere pure water, the equilibrium between phases is describes by the Clausius-Clapeyron equation (or -in practice- by simpler, empirical equations, like

e_s(T)=e_s(0°C) * EXP[a * T / (b + T)]

where e_s(T) is the equlibrium (=saturated) vapour pressure (in kPa) at temperature T (degrees C), e_s(0) is the equoibirum pressure at 0°C (0.61078 kPa) and a and b are empirical parameters (17.269 and 237.3, respectively).

If you are not dealing with pure water, but with water interacting with a matrix (a porous media, soil...), or containing a solute, its state changes (its chemical potential -the "water potential", Psi_w, that would be zero for pure water) decreases, and the equlibrium vapour pressure above this energy-depleted liquid phase decreases as well.

The equation dealing with this is the "Kelvin equation":

e / e_s = EXP[(M_w * Psi_w) / (rho_w * R * T)]

where e is the actual vapour pressure, e_s is saturated vapor pressure above pure water at the same temperature, M_w is the molecular weight of water (0.018 kg/mol), R is the ideal gas constant (8.31 J K-1 mol-1 or 0.008314 kPa m3 mol-1 K-1), T is absolute temperature (K), and rho_w is the density of water (1000 kg/m3 at 20°C).

All this reasoning is in "pressure" terms. If you need vapour "density", the way is straigthforward.

Best,

Andrea

Hi Andrea,

Thanks for your reply. Would you please inroduce me a reference in which I can find these information and give it as reference?

Kind Regards,

Jalal.

Hi Jalal!

A general, very good reference on the thermodynamics of water is "Atmospheric Thermodynamics" by Bohren and Albrecht. That is a textbook which can give you many hints on this subject and the related ones, but also a very wider view of the topic.

A good text is also "Evaporation of water", by Jones.

If you are especially dealing with soil (Kelvin equation...), then I would strongly advice you to read an old (and almost completely forgotten) book on "Psychrometry in Water Relations Research" by Brown and van Heveren.

These are fascinating (and VERY important!) topics, but, in spite of that, they are often under-appreciated.

I sincerely hope this could help.

Greetings,

Andrea

There are at least two factors that can reduce the saturation vapor density.

a) When the liquid is not pure but contains solute. In that particular case the chemical potential of the liquid is reduced with the osmotic pressure times the molar volume. If you equate then the chemical potential of the vapor phase with the liquid, you will find a reduction in the vapor density.

b) In a porous material capillary effects could do a similar thing. When a liquid is present in tiny pores or is within a small wedge, the actual pressure in the liquid phase is below the atmospheric pressure. Again this leads to a reduction in the chemical potential equal to the capillary pressure times the molar volume. Following the same procedure as described under a) you end up with a lower vapor density.