Vapour pressure of small drops

Ostwald2 pointed out that, just as the vapour pressure of small drops of liquid is greater than that of large drops, so the vapour pressure and solubility of small solid particles is greater than that of large. The relation between the radius, surface tension, and vapour pressure or solubility of spherical particles is the same as that deduced in Chap. I, 15, for small drops. 

Nuclei, and often even colloidal particles, are so small that their thermodynamic properties may differ considerably from those of a corresponding macrophase, A wei knowm example cf this behaviour is the increased vapour pressure of small drops as given by the equation of W, Thomson... 

The vapour pressure of water in small drops is greater than that of water in mass, and the solubility of a solid is greater when in a state of fine subdivision than when in large pieces cf. Hulett, Z, physzkal. Ckem, 1901, 37, 385). The vapour pressure of small crystals is also greater than that of large ones (Pawloff, Z. physikaL Ckem, 8, 3x6). 

This is Kelvin s equation for the vapour pressure of a drop of radius R the second (approximate) form of whidi holds only if NjkT v Piy. It is inapplicable to drops containing only a few molecides since they have no uniform interior for whidi the calculation of p is meaningful. iW a drop of water of radius 1 mm, ln(p /p ) is lOA and for a drop of radios 1 pm, it is 10. Hence in a mist the very small drops evaporate and the larger drops grow. All are unstable with respect to the pool of liquid that ultimately forms. 

Equation (3) 15.VIIIL, shows that the vapour pressure over a drop of radius r=0 should be infinite, and it is necessary to explain how very small drops can begin to form at all in clouds. Aitken showed that they probably form over... 

The tendency of small drops of liquid to coalesce to large ones is manifested in an increase of vapour pressure with diminution of radius. The relation between vapour pressure and drop radius is easily calculated. When a small amount of liquid, volume dV, evaporates from a drop of radius r, the change in surface area is dA. We have... 

Here ns is the amount of substance of stationary liquid, pi is the saturated vapour pressure of the solute at temperature r. Bag is the mixture virial coefficient for solute 4- carrier gas interaction, Bcc is the virial coefficient of the carrier gas, Fjj is the partial molar volume of the solute at infinite dilution in the solvent, is the molar volume of pure liquid A, and pi and po are the column inlet and outlet pressures. The chemical potential at infinite dilution can be calculated by measuring the retention volume of an infinitely small sample for various inlet and outlet pressures and extrapolation to zero pressure drop across the column. Everett and Stoddart proposed using equation (33) to determine the mixture second virial coefficients. The precision in Bag from this method is nearly equivalent to the best static methods. The assumptions required to derive the above equation have been examined by a number of authors. - ... 

Note also the convention that the radius of curvature is measured in the liquid phase and is thus positive for a liquid drop but negative for a gas bubble. This means - see also later the Kelvin equation - that the vapour pressure of a liquid in a small drop is higher than for a flat surface but is lower in a bubble compared to a flat surface. 

Vapour pressure over a curved surface of liquid. The vapour pressure over a convex surface is greater than that over a plane and over a concave surfaoe it is less. The difference depends on the fact that condensation of vapour on a small convex drop of a liquid increases its surface... 

One consequence of this raising of vapour pressure is the well-known fact that water vapour will not condense in a dust-free (and ion-free) atmosphere, unless its vapour pressure considerably exceeds the saturation point. An 11 per cent, increase of vapour pressure would be required for condensation to drops of 10 6 cm. diameter when it is considered that a sphere this size contains about 140,000 water molecules, it is clear that the chance of so many coming together as to start drops of this size, or larger, is small some nucleus providing a less curved surface must be present if condensation is to occur anywhere near the usual saturated vapour pressure. 

A small but important class of atmospheric aerosol particles are the ice nuclei. These nuclei promote the freezing of water drops in clouds (see Fletcher, 1962). In this way they play a definite role in the formation of precipitation in mixed clouds containing both water drops and ice crystals. This kind of precipitation formation is due to the fact that the saturation vapour pressure over ice is smaller than over liquid water. In this way ice crystals grow by condensation while drops tend to evaporate. Thus, if human activity emits ice nuclei to the atmosphere the precipitation distribution can be modified. Results of measurements show that in the vicinity of steel works and aluminum foundries the concentration of ice nuclei active at a temperature of — 20 °C is unusually high. It is believed that this is caused by the presence of some metal oxides in the air (Pruppacher, 1973). More recent studies on ice nuclei also showed that lead compounds (e.g. Pbl 2) in exhaust gases of vehicles also have ice nucleating ability. It is believed, however, that anthropogenic ice nuclei cannot play an important role, except in local scale processes (see Pruppacher, 1973). 

The Philippines can be characterised as tropical islands with only minor fluctuations of temperatures and partial water vapour pressure during the day or year. Mean maximum temperatures normally do not exceed 31°C, and never drop below 23°C. Pd values can be found in the range of 25.0-33.0 hPa. All of the islands belong to Koppen Group Am just a small part of the northern island Luzon is characterised by Group Aw. 

---