OSMOTIC PRESSURE 



157 



the amount of acid in the solution is constant, and consequently the number 

 of collisions of the molecules of sugar with the molecules of the acid will 

 be proportional to the osmotic pressure of the sugar molecules. In other 

 words, the velocity of the reaction will be proportional to the osmotic pressure 

 of the sugar molecules." As we have seen, in fact, the actual volume occupied 

 by the sugar molecules must be taken into account, as was pointed out by Cohen 

 (1897). 



HYDRODIFFUSION 



Substances in solution always wander from a place of higher to one of lower 

 concentration. This is known 

 as "diffusion" or "hydro- 

 diffusion," and, according to the 

 kinetic theory, is brought about 

 by the constant movement of 

 the molecules. 



The phenomena were investi- 

 gated by Graham (1850), who 

 showed that the rate varied 

 with the nature of the sub- 

 stance. Later investigations 

 showed that the rate was 

 inversely proportional to the 

 size of the molecule, and directly 

 proportional to the difference of 

 concentration between the two 

 places between which diffusion 

 was proceeding. 



In fact, the law is completely 

 analogous to that sometimes known 

 as Newton's Law of Cooling or, more 

 generally, "Law of Velocities." Any 

 process, which is on the way to an 

 equilibrium, becomes slower and 

 slower as the final state gets nearer. 

 The driving force becomes less and 



chemical reactions as well as to the -~.Or ~ 



transfer of heat, the flow of water 

 along a tube connecting two cylinders 

 of water, and so on. 



FIG. 50. SCHEMA TO ILLUSTRATE OSMOTIC WORK. 



The cylinder (C) has an accurately fitting piston, and is closed 

 below by a membrane semi-permeable as regards the solute in 

 S. The solution inside the cylinder becomes more concen- 

 trated than that outside when the weight is placed on the top 

 of the piston. To do this, the piston with the weight falls, 

 thus doing work. 





In the case of diffusion, the 

 driving force is identical with 

 osmotic pressure in solutions, 

 and is completely analogous to 

 the equalisation of differences of 

 density in gases. In the latter, 

 however, the process takes place 



very rapidly, while in a liquid it is very slow, owing to the enormous friction 

 with which the moving molecules are met in the case of liquids. 



It is interesting to calculate this friction from the osmotic pressure and the rate of diffusion, 

 as can be done in a way analogous to Ohm's law. According to Nernst (1911, p. 152), 

 it requires a force equal to the weight of 6*7x109 kg. to drive one molecule (342 g. ) of 

 cane-sugar through water with a velocity of 1 cm. per second. We realise somewhat how 

 slow a pure diffusion process must be. The following experiment described by Graham 

 (1850, p. 462 of the Collected Edition) is instructive. A glass cylinder, 11 in. high, was filled 

 to one-eighth of its capacity with a saturated solution of calcium bicarbonate, which also 

 contained 200 gr. of sodium chloride in 8 cub. in. The jar was then filled completely with 

 distilled water in such a way as not to disturb the lower layer, covered with a glass plate, 

 and left to stand in a uniform temperature for six months. Samples of different strata were 

 then removed by a syphon, and it was found that equality of concentration had not been 

 attained, even in so long a time. The ratio of the concentrations of the sodium chloride in 



