148 PRINCIPLES OF GENERAL PHYSIOLOGY 



proposition, ayant rapport a la grandeur absolue de cette pression, et n'etant, 

 en realite, autre chose qu'une extension de la loi d'Avogadro. 



3. " Loi. d'Avogadro pour les Solutions. La pression exercee par les gaz a une 

 temperature determined, si un rneme nombre de molecules en occupe un volume 

 donne, est egale a la pression osmotique qu'exerce dans les memes circonstances 

 la grande majorite des corps, dissous dans les liquides quelconques." 



At normal temperature and pressure one gram-molecule of a gas occupies a volume of 22 '4 

 litres, so that if one gram-molecule of a solid be dissolved in 22'4 litres of water, its osmotic 

 pressure should be one atmosphere, as may also be seen from the following consideration. 

 To compress one gram-molecule of a gas to the volume of one litre, which is the volume 

 occupied by any solute in what is known as molar concentration, requires, by Boyle's law, 

 a pressure of 22 - 4 atmospheres. 



Let us take an example from one of Pfeffer's experiments. A 4 per cent, solution of cane- 

 sugar gave at 15 an osmotic pressure of 208'2 cm. of mercury. By Gay-Lussac's law, 



273 

 supposing it to apply, this would be, at 0, 208'2x 4 =197-4 cm. mercury. One gram- 



i *> 1 * 



molecule of the sugar weighs 342 g., so that the number of litres of a 4 per cent, solution 



34'^ 

 required to contain 1 gram-molecule is ' = 8'55. Hence its osmotic pressure should be 



76 x- = 199 cm. mercury, a very close agreement, considering the difficulty of the measuiv 



8*55 

 ment. 



This example will serve to show the justification of van't HofFs point of view. 

 The experiments of De Vries on isotonic solutions, referred to in the preceding 

 chapter, gave further confirmation of its correctness. 



Before proceeding further, we must insist on the fact that the theory was only 

 intended to apply to dilute solutions. For the present purpose we may define 

 dilute solutions as being those in which the number of molecules of the solute is 

 so small in proportion to those of the solvent that any effects due to the mutual 

 action of the molecules of the solute, to their actual volume, or to combination 

 with the solvent, in the sense of hydration or solvation, may be neglected. 



When we come to concentrated solutions, these factors have to be taken into 

 account, as van't Hoff himself (see Cohen's book, 1912, p. 282) pointed out with 

 reference to the treatment of the question from the kinetic point of view. In fact, 

 the osmotic pressures of such solutions are found to be higher than the simple gas law 

 would lead us to expect, the deviations becoming greater as the concentration rises. 



The most important work on concentrated solutions is that done by Morse 

 and his collaborators in the United States (1901, etc, summary in 1914) and 

 by Berkeley and Hartley in England (1906, 1). These experiments were 

 made on solutions of cane sugar. A further series of measurements on calcium 

 ferrocyanide was made in 1908 by Berkeley, Hartley, and Burton. As to 

 the interesting methods employed by these observers, the reader is referred to 

 the monograph by Morse (1914) and that by Findlay (1913). The preparation 

 of the copper ferrocyanide membrane is of especial importance. 



In the endeavour to find a formula which applies to concentrated solutions, as well as to 

 dilute ones, it is obvious that, by the introduction of a sufficient number of empirical constants, 

 this would not be difficult. On the other hand, if a physical meaning can be given to the 

 constants introduced, although it may not, for the present, be possible to determine them by 

 an independent method, such an expression is to be preferred. For this reason, in the 

 following pages, I have adopted the point of view of van der Waals (1881) and, as regards 

 details, that of Otto Stern (1913). This treatment consists in the application of the ra der 

 H'ttti/.*' i nuation of state to solutions, and it must not be supposed that no other point of view is 

 possible. The point of view of the doctrine of energy, or thermodynamics, for example, as 

 given by Findlay (1913), leads to a logarithmic formula and affords results which are, of course, 

 cogent if based on correct foundations, but it does not seem to me to help us far in under- 

 standing the factors at work. Nernst (1911, p. 155) appears to be of the same opinion. It is 

 pointed out by Arrhenius (1912, p. 6) in reference to the selection by van't Hoff of the thermo- 

 dynamic method, that, at that time, the kinetic theory was not so manageable as the former. 

 Boltzmann, however, brought the kinetic theory into favour again by reducing it to an 

 application of the theory of probabilities. The application of the kinetic theory to liquids 

 will be found discussed in Nernst's book (1911, pp. 212-219). 



The simple general gas law 



PV = RT 



