August jq, 1909] 



NATURE 



This is the well-known phenomenon of the lowering o( the 

 freezing point by pressure. By considering the equilibrium 

 of water and vapour in a capillary tube, Lord Kelvin 

 showed that the vapour-pressure of water, or any other 

 liquid, was increased by pressure according to a very 

 simple law, the ratio of' the increase of vapour-pressure, 

 dp, to the increase of pressure, dP, on the liquid being 

 simply equal to the ratio of the densities of the vapour 

 and liquid, or inversely as the specific volumes, v and V. 

 This relation, which may be written VdP = i;df, is merely 

 a special case of Carnot's principle, and was deduced by 

 assuming the impossibility of perpetual motion. Assuming 

 a similar relation to apply to ice, Poynting showed that 

 when a mixture of ice and water was subjected to pressure, 

 the vapour-pressure of the ice must be increased more 

 than that of the water (since the specific volume of ice 

 is greater than that of water). Consequently, some of 

 the ice must pass over into water, and the temperature 

 must fall until the vapour-pressures are again equal. The 

 lowering of the freezing point by pressure, as observed by 

 Lord Kelvin, and calculated by James Thomson, agrees 

 precisely with that deduced as above from the condition 

 of equality of vapour-pressure. 



Similar considerations apply to the equilibrium between 

 a solution and the pure solvent, or between solutions of 

 different strengths. To take a simple case, the vapour- 

 pressure p' of a sugar solution is always less than the 

 vapour-pressure />' of water at the same temperature, and 

 the ratio />"//>' of the vapour-pressures depends simply on 

 the concentration of the solution, diminishing regularly 

 with increase of concentration and being independent of 

 the temperature. If separate vessels containing solution 

 and water are placed in communication at the same 

 temperature by a tube through which the vapour has free 

 passage, vapour will immediately pass over from the 

 water to the solution in consequence of the pressure differ- 

 erice, and will condense in the solution. The immediate 

 effect is to produce equality of vapour-pressure by change 

 of temperature. This takes only a few seconds. The 

 vapour-pressure then remains practically uniform through- 

 out. As diffusion proceeds and the temperature is slowly 

 equalised, the water will gradually distil over into the 

 solution, but the process of diffusion is so infinitely slow 

 compared with the equalising of vapour-pressure that the 

 final attainment of equilibrium would take years unless 

 the solution were continually stirred. 



The reason why equality of vapour-pressure is so 

 important as a condition of physical equilibrium is that 

 the vapour is so mobile and so energetic as a carrier of 

 energy in the form of latent heat. The first effect is 

 generally a change of temperature, but if the temperature 

 is kept constant there must then be a change of concen- 

 tration. Thus if two parts of the same solution are main- 

 tained at different constant temperatures, the concentra- 

 tions will change so as to restore equality of vapour- 

 pressure, if possible. Thus in a tube of solution the two 

 ends of which are maintained at different temperatures, 

 the dissolved substance will appear to move towards the 

 hotter end. What really happens is that the vapour, 

 which is the mobile constituent, moves towards the colder 

 end. If the tube is horizontal, with a free space above 

 the liquid for the vapour, this transference will be effected 

 with extreme rapidity. In fact, it will be practically 

 impossible to establish an appreciable difference of tempera- 

 ture until the transfer is effected. If the vapour has to 

 diffuse through the solution in a vertical column healed 

 at the top, the process is greatly retarded, but the final 

 effect is the same, and can be readily calculated from the 

 relation between the vapour-pressure and the concentra- 

 tion. 



In explaining the production of osmotic pressure as a 

 necessary consequence of the laws of vapour-pressure, there 

 is one difficulty which, though seldom expressed, has un- 

 doubtedly served very greatly to retard progress. How 

 can an insignificant difference of vapour-pressure, which 

 may not amount to so much as one-thousandth part of 

 an atmosphere in the case of a strong sugar solution at 

 0° C, be regarded as the cause of an osmotic pressure 

 exceeding loo atmospheres, or 100,000 times as great as 

 itself? The answer is that the equilibrium does not 

 depend at all on the absolute magnitude of the vapour- 



NO. 2077. VOL. 81] 



pressure, but only on the work done for a given ratio of 

 expansion, which is the same in the limit for a gram- 

 molecule of any vapour at the same temperature, however 

 small the vapour-pressure. Indirectly, the smallness of 

 the vapour-pressure may have a great effect in retarding 

 the attainment of equilibrium, especially if obstructive in- 

 fluences, such as other vapours or liquids, are present. 

 Thus mercury at ordinary temperatures in the open air 

 is regarded as practically non-volatile. Its vapour-pressure 

 is less than a millionth of an atmosphere, and cannot be 

 directly measured, though it may easily be calculated. 

 When, however, we take mercury in a perfect vacuum, 

 such as that of a Dewar vessel, the presence of the vapour 

 is readily manifested by its rapid condensation on the 

 application of liquid air in the form of a fine metallic 

 mirror of frozen mercury. The least trace of air or other 

 gas in the vacuum will retard the condensation e.xcessively.^ 

 Under the conditions of an osmotic-pressure experi- 

 ment we have solvent and solution in practical contact, 

 separated only by a thin porous membrane. It will facili- 

 tate our conception of the conditions of equilibrium if we 

 imagine the membrane to be a continuous partition pierced 

 by a large number of very fine holes of the order of a 

 millionth of an inch in diameter. If the holes are not 

 wetted by the solution or the water, the liquid cannot 

 get through unless the pressure on it exceeds 100 atmo- 

 spheres, but the vapour has free passage. If the solvent 

 and solution are under the same hydrostatic pressure the 

 vapour-pressure of the solvent will be the greater, and 

 the vapour will pass over into the solution.^ Since the 

 surfaces are practically in contact, no appreciable differ- 

 ence of temperature can be maintained. If the solution 

 is confined in a rigid envelope, so that its volurne cannot 

 increase, the capillary surfaces of the solution will rapidly 

 bulge out as the vapour condenses on them, and the 

 pressure on the solution will increase until condensation 

 finally ceases, when the vapour-pressure of the solution is 

 raised to equality with that of the pure solvent. The 

 osmotic pressure is simply the mechanical pressure-difi'er- 

 ence which must be applied to the solution in order to 

 increase its vapour-pressure to equality with that of the 

 pure solvent. If any pressure in excess of this value is 

 applied to the solution, the vapour will pass in the opposite 

 direction, and solvent will be forced out of solution. The 

 osmotic work required to force a gram-molecule of the 

 solvent out of the solution is the product of the osmotic 

 pressure P by the change of volume U of the solution 

 per gram-molecule of solvent abstr.acted. In the state of 

 equilibrium of vapour-pressure, this osmotic work PU 

 must be equal to the work which the vapour could do by 

 expanding from the vapour-pressure p' of the pure solvent 

 to the vapour-pressure p" of the solution. Neglecting 

 minor corrections, we thus obtain the approximate relation 



PU = R9 1og(/)7/'")-' 

 From this point of view the osjnotic pressure of a solu- 

 tion is not a specific property of "the solution in the same 

 sense as the vapour-pressure, or the density, or the con- 

 centration, but is merely the mechanical pressure required 

 under certain special conditions to produce equilibrium of 

 vapour-pressure when neither the temperature nor the con- 

 centration are allowed to vary. One might with almost 

 equal propriety speak of the " osmotic temperature " of 

 a solution, meaning by that phrase the difference of 

 temperature required to make the vapour-pressure of the 

 solution equal to that of the pure solvent. The observa- 

 tion of the elevation of the boiling point of a solution 

 above that of the pure solvent is a familiar instance of 

 a special case of such a temperature difference. It is just 

 as much a specific property of the solution as the osmotic 

 pressure, and would only require a perfectly non-conduct- 

 ing membrane for its p'roduction. No one would regard 

 the rise of boiling point as being the fundamental property 

 of a solution in terms of which'its other properties should 

 be expressed. By similar reasoning osmotic pressure 

 should not be regarded as existing per se in the solution, 

 and as being the" cause of the relative lowering of vapour- 

 pressure and other phenomena. This point of view does 

 not detract in any way from the reality and physical 



1 Obtained by Integrating U<!'P=mi'/. Planck, " Thermodynamik," also 

 Zcit. Phys. Clietli., xli. 212, 1902, and xlii. 584, 1903. 



