236 



NA TURE 



[August 19, 1909 



Artificial membranes of sufficient fineness to be imperme- 

 able to such substances, as , sugar in solution, were first 

 prepared by Traube by means of precipitated pellicles of 

 substances like copper-ferrocyanide. The first quantitative 

 measurements of osmotic pressures of considerable magni- 

 tude were made by Pfeffer with membranes of this kind 

 deposited in the pores of earthenware pots fitted with 

 suitable manometers for indicating the pressure developed. 

 Pfeffer found that when a semipermeable vessel, filled with 

 sugar solution, was immersed in water, the membrane 

 being freely permeable to water, but not to the dissolved 

 sugar, the solution absorbed water through the membrane 

 by osmosis until the internal pressure reached a certain 

 magnitude sufficient to balance the tendency to absorption. 

 The osmotic pressure developed in the state of equilibrium 

 was found to be proportional to the strength of the solu- 

 tion, and to increase with rise of temperature at the same 

 rate as the pressure of a gas at constant volume. A few 

 years later van 't Hoff, reviewing these experiments in 

 the light of thermodynamics, showed that the osmotic 

 pressure of a dilute solution should be the same as the 

 pressure exerted by a number of molecules of gas equal 

 to those of the dissolved substance in a space equal to 

 the volume of the solution, that it should be the same for 

 all solutions of equal molecular strength, and that osmotic 

 pressure followed the well-known laws of gas-pressure in 

 all^ respects. This most important generalisation was 

 hailed as the first step to a complete kinetic theory of 

 solution, and the osmotic pressure itself has generally 

 been regarded as due to the bombardment of the sides of 

 the semipermeable membrane by the particles of solute, 

 as though they were able to move freely through the solu- 

 tion with velocities comparable to those of the molecules 

 of_ a gas. Such a view would not now be seriouslv main- 

 tained, but tlje fascinating simplicitv of the gas-pressure 

 analogy has frequently led io the attempt to express every- 

 thing in terms of the osmotic pressure, regarded simply, 

 but inaccurately, as obeying the gaseous laws, and h.is 

 done much to divert attention from other aspects of the 

 phenomena, which, in reality, are more important and 

 have the advantage of being 'more easily studied. It was 

 very soon discovered that the gaseous' laws for osmotic 

 pressure must be restricted to very dilute solutions, and 

 that the form of the laws was merelv a consequence of 

 the state of extreme dilution, and 'did not necessarily 

 mvolve any physical identity between osmotic pressure and 

 gas-pressure. .Many different lines of argument might be 

 cited to Illustrate "this point, but it will be sufficient to 

 take some of the more recent experimental measurements 

 of osmotic pressure by the direct method of the semi- 

 permeable membrane. 



Morse and Frazer in 1005 succeeded in preparing ferro- 

 cyanide membranes impermeable to sugar, and capable of 

 withstanding pressures of more than 20 atmospheres. 

 They_ operated by Pfeffer 's original method, allowing water 

 to tiitluse into the solution in a porous pot until the 

 maximum pressure was developed. There are manv serious 

 experimental and manipulative difficulties which ;he authors 

 carefully considered and discussed in applying this method, 

 but they succeeded in obtaining very consistent results.' 

 As a first deduction from their investigations they con- 

 sidered that they had established the relation that the 

 osmotic pressure of cane-sugar was the same as that 

 exerted by the same number of molecules of gas at the 

 same temperature in the volume occupied by the solvent, 

 and not in the volume occupied by the solution. In other 

 words, the osmotic pressure of ' a strong solution was 

 greater than that given by van 't Hoff's formula for a 

 dilute solution in proportion as the volume of the whole 

 solution exceeded the volume of the solvent contained in 

 it. It was a very natural extension of the gas-pressure 

 analogy to deduct the volume occupied by "the sugar 

 molecules themselves in order to arrive at the space in 

 which they were free to move. Unfortunatelv, the later 

 and more accurate series of measurements by the same 

 experimentalists at 0° C. and 5° C. gave near'lv the same 

 osmotic pressuresas at 24° C, and would appear to show 

 either that there is little or no Increase of osmotic pressure 

 with temperature, and that the pressures at 0° C. are 

 much greater than those given by their extension of the 

 NO. 2077, VOL. 81] 



gas-prcs-sure analogy, or that one or other of the series 

 of experiments are in error. 



About the same time Lord Berkeley and E. J. Hartley 

 undertook a series of measurements of the osmotic pressures 

 of solutions of various kinds of sugar at 0° C. by a 

 greatly improved experimental method, which permitted 

 the range of pressure to be extended to upwards of 100 

 atmospheres. Instead of allowing the solvent to diffuse 

 into the solution until the equilibrium pressure was 

 reached, they applied pressure to the solution until balance 

 was attained. The method of Lord Berkeley and Hartley 

 possesses several obvious advantages, and it is impossible 

 to study the original memoir without being convinced that 

 they have really measured the actual equilibrium pressures 

 with an order of certainty not previously attained or even 

 approached. The pressures found were in all cases greatly 

 in excess of those calculated from the gas-pressure of the 

 sugar molecules in the volume occupied by the solution 

 (according to van 't Hoff's formula for dilute solutions), 

 or even in the restricted volume occupied by the solvent 

 (according to Morse and Frazer's assumption). 



Lord Berkeley endeavoured to represent these deviations 

 on the gas-pressure analogy by employing a formula of 

 the van der Waals type, with three disposable constants.' 

 Out of some fifty formulae tested, the two most successful 

 were those given in Table I. The constants A, a, and b 

 were calculated to fit the three highest observations for 

 e.ach solution. Values calculated by the formulae for the 

 lower points were then compared with the observations at 

 these points, with the results given in Table I. for cane- 



T.vBLE I. — Osmotic Pressures of C.-\ne-sug.ar Solutions. 



Osmotic Pressures calculated hy various Formulae. 



C 



Vant 't Hoff ^'^J^'^ ^""^ Lord B, (i) Lord B. (2) 

 r razer 



Do. oliserved 

 Lord B. 



35-6 ... 53-2 



27-6 ... 37-4 



197 ■■■ 24-4 



II-2 ... 133 



6S-4 ... 677 .. 



4S0 ... 43'4 •• 



277 ... 25-4 .., 



I4'6 ... I2'2 



67-6 ... 67-5 



437 ... 410 



268 ... 268 



I4'I ... 140 



Lord Berkeley's equations : — 



{.\h'-P + a/2>-){v-/i) = 'RT . . . (i) 

 {Ai'v + F -a/v'-){z'-6} = RT ... (2) 



sugar. It is at once evident that, even with three 

 constants, the gas-pressure analogy does not represent the 

 results satisfactorily within the limits of error of experi- 

 ment. Moreover, with three constants the equation can- 

 not be interpreted, so that the gas-pressure analogy becomes 

 useless as a working hypothesis or as a guide to further 

 research. On the vapour-pressure theory, to be next 

 explained, the results are much better represented, as I 

 shown in column C, with but a single constant, and that I 

 a positive integer with a simple physical meaning. 



Vapour-pressure Theory. 



On the vapour-pressure theory, osmotic equilibrium 

 depends on equality of vapour-pressure, and not on an 

 imaginary pressure which the particles of the dissolved 

 substance would exert if they were in the state of gas at 

 the same volume and temperature. The vapour-pressure 

 of any substance is a definite physical property of the 

 substance which is always the same under the same con- 

 ditions of pressure and temperature and state, and is easily 

 measured in most cases for liquids and solutions. Equality 

 of vapour-pressure is one of the most general, as well as 

 the simplest, of all conditions of physical equilibrium. 

 Ice and water can only exist together without change 

 under atmospheric pressure at the freezing point 0° C., 

 at which their vapour-pressures are the same. Below the 

 freezing point the vapour-pressure of water is greater than 

 that of ice. Either is capable of stable existence separately 

 within certain limits, but if the two are put in com- 

 munication, the vapour, being mobile, passes over from 

 the water at higher pressure to the ice at lower pressure 

 until equality of vapour-pressure is restored by change of 

 temperature, or until the whole of the water is converted 

 into ice. 



In the case of ice and water, equality of vapour-pressure 

 can also be restored by a suitable increase of pressure. 



