600 Mr. L. Ve&ard : Contributions to 



When the terms found for • — - and — 2 are introduced 

 into equation (11 a) a very simple calculation gives 



M1^iT)|£ = _ c(1 + c) |p. K . . . (lit) 



In this way it appears that we can obtain a determination 

 of the concentration gradient by help of the thermodynamic 

 condition of equilibrium. The result is therefore independent 

 of every hypothesis as to the internal constitution of the 

 solution. The formula cannot, however, be considered exact 

 in a mathematical sense. In the course of the development 

 we have taken it for granted that the fluid is incompressible, 

 and that the molecule volumes do not change greatly with 

 the concentration ; which, however, very nearly corresponds 

 to real cases. 



In our term for the concentration gradient, we have 

 still to consider the function /i(c,_^,T). Hitherto we have 

 only mentioned that it is a function characteristic for both 

 substances and closely connected with the external thermo- 

 dynamic potential . In the work by Duhem above mentioned * 

 the function is found for solutions in which the concentration 

 is small, L e. for so-called Dilute Solutions. 



Furthermore, van Laar f, starting out from van der Waals's 

 equation of state, has established a more general equation 

 which is approximately applicable also to concentrated 

 solutions. 



Instead of /i(c, p, T) we shall, however, introduce a 

 quantity which is more spontaneously accessible to our con- 

 ception — namely, the Osmotic Pressure. Not that the 

 solution as such can, properly speaking, be ascribed to an 

 osmotic pressure ; but let us suppose that solution and solvent 

 are in equilibrium on the two sides of a semipermeable 

 membrane. The difference of hydrostatic pressures on the 

 two sides of the membrane — the osmotic pressure it — is now 

 connected with the function f x in the following simple 

 manner : 



M0,p,T)-f l (c, 1 >,T)=l-7r. . . . (13) 

 Po 



p is the density of the pure solvent since we have, 

 throughout the development, calculated with mass units. 



* Duhem, Mecanigue Chimique, tome iii. livre vi. p. 44. 

 f See J. J. van Laar, Sechs Vortrage iiber das thermodynamische 

 Potential, 1906, p. 85. 



