tentials of constituent | in the two phases is then wi - w= RT in (4) ai To obtain a measure of this difference of the chemical potentials, use is made of the experimental fact that whena certain pressure difference is imposed across the barrier there will be no net passage of constituent | from phase A to phase where x is the so-called osmotic pressure. It is important to note that the osmotic ptessure multiplied by the partial molal volume of the constituent under consideration is equal to the difference between chemical potentials that obtained when the pressures on the two phases were equal. Nowhere does “the pressure of solute molecules” enter. Thelimiting law, or van’t Hoff law, of B. Experimentally, it is found that the pressure on phase B, Pg, must be greater than the pressure on phase A, P,. Equilibrium is established with respect to osmotic pressure is derived from Eq. 13 chemical potential, u’,,*,, of constituent 1 in phase A at the pressure P, is equal for Eq. 13 constituent | in this manner, and the by the use of simplifying assumptions. Theactivity, a, is the product of the mole fraction, N, and the mole fraction activity coefficient, {. We may then write x= Rt,Mi to the chemical potential, p’’, pg, of constituent | in phase B at the pressure Pp. Wehavenowtherelationships whe =ae,gtRT Ina: (5) and B's, pp = Bs, py t RT Ina’s (6) But equilibrium obtains; hence, Wie, SW". PR . (7) and woe, + RT Ina’, = Ho,ppt+ RT Ina”, Vi Nf" The convention that the activity of constituent 1 in phase A is unity is now applied. Equation 14 reduces to: tions of 4 with P. This variation is given by es . =V (10) molal volume of the constituent under consideration. For sufficiently small varia- tions of P—that is, if P, and P, differ by- a sufficiently small amount, and if the compressibility of the constituents may be neglected—we may write H9. by ~ Weg = Vil Pa - Pa) (11) From Eq. 11 and Eqs. 4 and 9, there follows immediately wi- w= Vi(Pe- Pa) =RT In = (12) whence 1 SEVTEMBER 1956 1 n Not” af" the present simplified system, we have NN”, +N’, = 1. Hence, N’”",f’, may be replaced by (1 — N’’,). We nowhave RT x=- In (1-N"s) (13) (16) The logarithmic portion is expressed as a series to give w= FE enor — AUN) | (17) Ic is now assumed that all terms in the expansion of degree higher than 1 may be neglected. Thus RT n= — - N", B ut me Ngee (18) (19) where n denotes number of moles. But n’’, is small compared with n’,; there- fore, we may write N”’,=n,/n”,. We then have RT t= > n 1 Vi na” (20) But n’”’,V, is simply the volume occupied by constituent | and may be written V,. Then n”,/V, is the mnolal concentration of constituent 2 and is denoted by C”,,. We have finally n= C0", RT Pa~ Pyne dn 22 The relationship is analogous in form to the simple gas law. However, this analogy does not require that the pressure difference x, experimentally determined, be the “bombardment pressure of the solute molecules against the barrier.” Indeed,if this were the case, the pressure “exerted” by the solute molecules against the barrier would have to be a negative bombardment pressure in order to accountfor the passage at equal hydrostatic pressures of the solvent from the pure solvent phase to the solution phase. It maybe pointed out that there is no justi- negative values. Use of the term osmotic pressure inthe where the subscripts T and n indicate that the temperature and composition remain constant, and whereVis the partial Conclusions If constituent 2 is present in sufficiently small concentrations, it may be assumed that Nf’, approaches N”, in value. In =- RT =i Vi, where 2°, pg and »°, », are determined by temperature and pressure. The system is considered to be isothermal, and we need be concerned only with the varia- librium with respect to constituent 1. 15 (15) = =In x= V, In —— NF", (8) (9) present system in orderto establish equi- fication or basis for the concept of negative pressure: pressure approaches zero From Eqs. 7 and 8 we have Upp ~U%s.e,= RT In (14) does no more than indicate the approximaterelationship between the concentration of constituent 2 and the pressure difference that must be imposed in the (21) This is van't Hoffs limiting haw of osmotic pressure. [Cis an approximation, It as the molecular density approaches zero, but pressure does not and cannot assume sense of the “pressure of the solute against a membrane permeable only to the salvent” cannot be justified either on theoretical or on experimental grounds see, for example, 6, 8, 9). On occasion, the conventent: operational designations, * Ssolvent and “sa. lute,” have been used with the implications of fundamental ditferences an properties. It will be noted that these designations have been avoided in’ the derivation givenhere. In a svstem suchas is considered here, “solvent” would desig- nate constituent | and “solute” constituent 2, But the meaning of such designations would be simply that the barner is permeable to constituent | and not per- meable to constituent 2. The designations would be reversed if a barrier permeable to constituent 2 but not to constituent | were used. A system frequently considered in physiology is that formed by the plasma, the capillary walls, and the in- terstitial fluid. In a simplified form of the system, water would be the solvent, the plasmaproteins the solute, and the capillary walls the barrier. In such a simplified system, the osmotic pressure of the plasma as determined in the laboratory provides a measure of the effect of the proteins on the properties of water, The term osmatic pressure is in itself misleading. [t is probable thac this has contributed to the confusion surrounding the meaning of the terin. As we have noted, osmotic pressure as experimentally determined is a pressure difference and not an absolute pressure. The experimental implications have been retainedin, for example, the terms freezing- point de pres473