72 



SCIENCE 



[Vol. XIX. No. 470 



the molecules of water more readily than those of a salt. 

 For certain theoretical investigations we may conceive a 

 ''half permeable" wall with openings so small that the 

 water alone can penetrate. As a filter separates a solution 

 from the insoluble residue, so the half-permeable wall is to 

 transmit the solvent, while preventing the passage of the 

 dissolved salt. No material has been found fully possessing 

 this ideal property; but theoretical deductions have already 

 been confirmed by experiments with clay cells, the pores be- 

 ing partly closed with a film of insoluble precipitate. If 

 a solution tills such a cell, while fresh water surrounds it, 

 the contents soon show a considerable pressure, which is 

 measured by a manometer. This phenomenon is called '" os- 

 motic pressure," and we may have several conceptions of its 

 cause. Either tliere is an attraction between the unlike 

 molecules in the brine and the fresh water, so that the latter 

 flock in where the salt is imprisoned (as ducks fiy to the de- 

 coy) until the internal pressure arrests the flow; or the os- 

 motic pressure may be due to the aggregate force of impact 

 of the many moving molecules; this is the view generaJy 

 taken. 



The several properties that have just been considered re- ' 

 quire numerical expression, but these numbers are wonder- 

 fully related to each other and to the doctrine of the conser- 

 vation of energy. For example, consider the relation of 

 osmotic pressure to vapor pressure. Let a cell with half- 

 permeable wall, connected with a vertical tube be fllled with 

 solution, and immersed in a tank of pure water; the whole 

 arrangement being placed under a bell jar in vacuum. Un- 

 der osmotic pressure the solvent will enter the cell until a 

 certain pressure is reached, as determined by the height of 

 the liquid in the vertical tube. Evaporation will take place 

 at the same time, both from the surface of the solution in the 

 tube and from the solvent in the tank, at their respective 

 levels, until the jar is filled with vapor. X condition of 

 equilibrium will eventually be reached, for otherwise we 

 should have perpetual motion. On the half-permeable walls 

 of the porous cell we have an inward and an outward pres- 

 sure, whose difference is measured by the height and density 

 of the solution in the vertical tube. On the surface of the 

 two fluids we have a vapor pressure, the difference being 

 measured by the same height and the density of the vapor in 

 the hell jar. The former value is the osmotic pressure, the 

 latter is the diminution of vapor tension caused by adding 

 Ihe solid to the solvent; and these two values stand exactly 

 in the ratio of the densities of solution and vapor. By other 

 thermo dynamical considerations a relation is traced between 

 osmotic pressure and the change in freezing point, electrical 

 conductivity, etc. 



Important analogies between the physical properties of 

 gasses and those of dissolved bodies are pointed out by van't 

 Hoff; the laws of Boyle, G-ay-Lussac, and Avogadro all 

 have their counterparts in the phenomena of osmotic pres- 

 .sure. 



First. Boyle's law says that the pressure of a gas is in- 

 versely proportional to its volume; that is, that as the quan- 

 tity of any gas in a given volume is increased or diminished 

 the pressure changes in the same ratio; so, the osmotic 

 pressure of many solutions is found to vary directly as the 

 concentration. 



Second. Gay-Lussac's law may be expressed by stating 

 that the gaseous pressure varies directly as the absolute 

 temperature; the same is true of osmotic pressure. 



Third. Avogadro's law implies that two gases, at the same 

 temperature, will have equal pressures when the masses of 



equal volumes are proportional to the molecular weights. 

 The same is true for osmotic pressures in equivalent solu- 

 tions of different comparable substances. To calculate the 

 osmotic pressure conceive the solvent to be absent, while the 

 solid occupies the same space as gas; the hypothetical gase- 

 ous pressure, as determined by the three fundamental laws, 

 is then equal to the osmotic piessure required. Conversely, to 

 determine the molecular weight of a dissolved body, we may 

 find the osmotic pressure and calculate as for a gas; practi- 

 cally, the depression of freezing point is the physical prop- 

 erty usually measured. 



In a word, the three fundamental laws of gaseous matter 

 are found to be true of dissolved matter simply by substi- 

 tuting osmotic pressure for gaseous pressure, while even the 

 anomalies and limitations so long recognized in gases and 

 vapors find their counterparts in solutions. Can we find 

 identity of cause when there is almost identity of result? In 

 a gas matter is in a far more dilute condition than in ordi- 

 nary solids or liquids; the intermolecular spaces are evi- 

 dently far greater than the space occupied by the molecules 

 themselves. The same is true in a dilute solution of salt, 

 only here the intermolecular space is largely occupied by the 

 water. In both cases, motion is indicated by the phenomena 

 of diffusion. In both cases, each moving mole'.-ule is endowed 

 with kinetic energy, and the sum of the vis viva of all the 

 molecules exactly accounts for the laws of pressure. The 

 formulas used to unfold the kinetic theory of gases may be 

 applied without change to a kinetic theory of solutions. In 

 a jar of hydrogen, the molecule darts hither and thither at 

 the rate of a mile a second, asking for no support save other 

 molecules, from which it rebounds. If hydrogen mixes 

 with the denser vapors of paraffin, it will still exert its own 

 pressure upon the walls of the vessel, as though it were 

 alone. Our salt is less ethereal. The molecules are heavier. 

 They move more sluggishly. Very slowly do they rise, as 

 though climbing with painful effort upon an unsteady ladder 

 of water molecules. Yet, with the aid of the half-permeable 

 wall, their pressure is fouiid to be just what it should be on 

 the kinetic theory, if the salt alone occupied the space in 

 absence of water. 



Anomalies and limitations have always been mentioned. 

 There is no " perfect " gas. none that exactly fulfils the fun- 

 damental laws, but hydrogen, which most nearly agrees with 

 the " ideal gas" in its properties, is not compressed to one- 

 tenth its volume by ten-fold pressure, but occupii'S a little 

 more than one-tenth volume. Here, the molecules them- 

 selves may be considered as incompressible bodies occupying 

 too great a fraction of the whole space to be left entirely out 

 of account. A modification of Bowie's law assumes that the 

 total intermolecular space varies inversely as the pressure. 

 In most gases and vapors, however, the deviation is in the 

 opposite direction. As the molecules approach each other 

 their mutual attraction is manifested, for the volume becomes 

 less than required by Boyle's law. The piston of a Corliss 

 engine, which glides so beautifully to and fro, in obedience 

 to valve and governor, is impelled by the bombardment from 

 an army of vapor molecules, each one following its own 

 impulse almost untrammelled in the go-as-you-please contest; 

 yet some mutual attraction is manifest, for the steam exerts 

 a little less pressure iipon the piston than -would an ideal 

 gas under like conditions. So, osmotic pressure, instead of 

 increasing directly as the concentration, may increase a little 

 less rapidly. There is a well-known body whose vapor den- 

 sity has long been recognized as abnormal. 



Ammonium chloride, when converted into vapor, is found 



