The Vapor Pressure of Small Drops.

Gibbs did not consider the Kelvin equation for the vapor pressure of small drops for the obvious reason that it does not constitute chemical equilibrium. The Kelvin equation represents true equilibrium between vapor and a flat surface of liquid water, where the liquid is under a pressure greater than the vapor by any assigned value AP. For example, in a closed vessel in the presence of an inert, slightly soluble gas such as air a definite equilibrium exists which will be re-established if displaced by the transfer of water from the liquid phase to the vapor or vice versa. For equilibrium between vapor and small drops as described by the Kelvin equation this is no longer the case. For a given partial pressure of vapor a drop must be of a particular radius. A drop which is slightly larger will grow by condensation, and a drop which is slightly smaller will evaporate. The situation does not even correspond to unstable equilibrium, since it does not satisfy the condition AF = 0 so far as free surface energy is concerned. Gibbs' pointed out that the production of a drop of the required size from the vapor in the Kelvin equilibrium required an increase in free energy equal to one-third the surface free energy. The vapor in quasi-equilibrium with the drop has an additional free energy per mole 2 'yV0/r, where y is the surface tension and r is the drop radius. But the free surface energy of a mole of water in the form of drops is 3 7yV0/r, as will be shown later. Incidentally, free surface energy can only be of significance when the equilibrium involves the creation or disappearance of surface. This only happens when the liquid phase is subdivided into small drops. The equilibrium between a vapor and small drops is not a simple affair. Provided that the drops do not exceed a certain size, such an equilibrium is possible, but it necessarily involves a whole gamut of drop sizes and concentrations. Fortunately, we need consider only one particular drop size at a time in discussing the equilibrium. We shall proceed to discuss the range of conditions under which such equilibrium can exist. Before actually formulating the equilibria involved, it is necessary to consider the special thermodynamic properties which are possessed by small drops. Surface Energy.-The first of these is the free surface energy, which, expressed in ergs per square centimeter, is the surface tension. This is ordinarily assumed to be independent of drop radius, but this cannot be true down to the point where the radius becomes that of a single molecule and the drop vanishes. This problem has been considered first by Gibbs and later by Tolman2 and others, but no definite conclusions can be reached. What we are concerned with is not the validity of surface tension as a physical concept but rather the decrease in the free surface energy of the drop as the radius is decreased. From thermodynamics,