328 



HEAT. 



gradually diluted a point is at last reached at which the protoplasm tends 

 to fill the cell again, or the osmotic pressure of the contents of the cell 

 equals that of the solution. De Vries called the solutions at this stage 

 isotonic. The same cells could be used for solutions of different salts, and 

 he found that equimolecular solutions of similar salts are isotonic. 



Van t'Hoff s Application of Thermodynamics. 



In 1885 Van t'Hoff (Phil. Mag., xxvi., 1888, p. 81) 

 pointed out that the osmotic pressure of sugar solution 

 as obtained by Pfeffer was the same as would be exerted 

 by the sugar in the gaseous form at the same density. 



Thus at 14 a 1 per cent, solution of sugar, or -^-r-^, ^ a 







top-in 



solvent. 



J/L 



solution 



FIG. 185. 



gramme molecule should produce a pressure 



D 22-3/ 14 \ na 

 F= ( l + - ) x 76 cm. ot mercury. 

 o4 2t\ 2iioJ 



= 52-2 cm. 



almost exactly that found by Pfeffer. 



Van t'Hoff also showed that in the variations of the pressure with 

 temperature as found by Pfeffer the pressure is proportional to the 

 absolute temperature. He then applied thermodynamic reasoning to 

 show that in any case the osmotic pressure is proportional to the absolute 

 temperature if a certain assumption is made which will appear in the 

 course of the proof. He used the conception of a semi-permeable mem- 

 brane which will allow the 

 solvent to pass, but which 

 is impermeable to the solute, 

 even though no such mem- 

 brane may have been found / 

 in practice. dp 



The following is equiva- 

 lent to Van t'Hoff's work. 

 Suppose that we have a 

 cylinder containing a quantity 

 of solution with osmotic pres- 

 sure p, separated from the 

 pure solvent by a semi-per- 

 meable piston, A, as in Fig. 

 185. If there is a pressure p 

 on the piston A so that the 

 solution is under excess pres- 

 sure equal to the osmotic 



pressure, there will be equilibrium between solvent and solution through 

 the membrane, and the piston can be moved either way reversibly. 



Let us take the piston through a reversible cycle represented on the 

 diagram, Fig. 186, by ABCD, where abscissae represent volumes, ordinates 

 osmotic pressures, i.e. pressures by the piston on the solution. Beginning 

 at temperature 6 at A, allow MN = dv of solvent to flow into the solution, 

 the temperature being maintained at by the addition of heat H. Then 

 allow a f urther flow of solvent, with no further addition of heat, represented 



volumeM 



FIG. 186. 



