The osmotic data in relation to progressive hydration

When a concentrated aqueous solution of an electrolyte is gradually diluted there is reason to believe chat the amount of water in combination with the solute increasespari passu with the ionisation. This progressive hydration must be brought into the account in expressing tire conductivity and the osmotic data (in which term we include freezing point and vapour pressure data) in terms of concentration. In a recent paper it was shown that, the latest determinations of the osmotic pressures of sucrose solutions by Morse and his co-workers could be simply and accurately expressed in terms of the progressive hydration of the solute. For the correlation of vapour pressure lowering with osmotic pressure, there was used the approximate relation Obtained by the consideration of the equilibrium of a vertical column of liquid in contact with the pure solvent through a semi-permeable partition at the bottom and with the vapour of the solvent at the top. which contains as a factorρ , the mean density of the solution. In the application of the expressions to concentrated solutions of electrolytes it soon became obvious that the presence ofρ , so far from helping the approximation, only threw it. out, and the omission ofρ , or rather giving it a constant value unity, gave far more concordant results. In fact the errors introduced by the inclusion ofρ are much greater than the large experimental errors which occur in the measurement of the vapour of even concentrated solutions, whilst the errors whenρ is put equal to unity are considerably less than the experimental errors. The accurate measurement of the osmotic pressures of electrolytes has not yet. been achieved, but the theoretical relation between osmotic pressure and vapour pressure forms the connecting link which enables us to express the vapour pressure data for electrolytes in terms of progressive hydration in the simple formδp /p =i /(h -n ) without any density factor. It is, therefore, important to place the above result on a sound theoretical basis, since it appears to be of wide application in the study of electrolytes. The disappearance of the density factor is really a direct consequence of the relations developed by Callendar, but his development is obscured by the fact that he uses the term "osmotic pressure” in a sense which permits its magnitude to vary from point to point of a solution of uniform concentration and temperature. He speaks, for instance, of "the assumption made by Lord Berkeley and Mr. Hartley that osmotic pressure varies with concentration only, which appears from their experiments to be approximately true for some solutions.” It was pointed out in a recent communication that this “assumption” is strictly true for all solutions, if we define osmotic pressure, in accordance with the requirements of the vapour pressure theory, ns the liquid pressure under which the internal vapour pressure of the solution becomes equal to the vapour pressure of the pure solvent at the same temperature and under pressure of its own vapour only. From this definition the required relation can he deduced by considering the equilibrium of a small mass of solution of uniform concentration and pressure, instead of a column of solution of varying concentration and pressure. It. may be noted that, at the suggestion of Sir W. Ramsay, we avoid the use of the term "hydrostatic pressure,” and, in fact, the use of the term is out of place when deriving the relation from the consideration of a small mass of liquid which is mechanically compressed until its internal vapour pressure reaches a certain amount. Wo have to deal only with the liquid pressure at a point, which is a familiar conception. Tire idea of the internal vapour pressure at a point within a liquid is not so familiar, but it presents itself, for instance, in the conception of the equality of vapour pressures of ice and water in contact in a state of equilibrium. We may define the internal vapour pressure of a solution at a point as the pressure which would exist within a small sphere permeable only to the vapour of the solvent, placed at the point. This conception brings us into line with the “vapour sieve piston ” method by means of which Callendar established the relation Ud P =vdp , where U is “the rate of diminution of volume of the solution at a pressure P per unit of mass of solvent abstracted," andv is the specific volume of the vapour at pressurep . In Callendar's notation the value of U is U = 1/ρ – Cd (1/ρ )/d C, where C is the concentration in grammes of solute per gramme of solution. Examination of the densities of a number of aqueous solutions shows that we may with an inaccuracy of only about two or three parts per thousand take 1/ρ = 1/ρ w – BC, whereρ w is the density of the solvent (water) and B is a constant. This gives usd (1/ρ )/d C = –B, and therefore U = 1ρ w. That is to say within this limit of accuracy U is simply the specific volume of water. The accuracy attained by taking this value of U is considerably beyond that of the experimental vapour pressure determinations which are available.