Mr Vegard, On some general Properties, etc. 275 



On some general Properties of Mixed Solutions. By L. Vegard, 



Universitets-stipendiat of Christiania University. 



[Received 9 June 1909.] 



Introduction. 



§ 1. The object of the following paper Avill chiefly be to 

 generalise some results concerning properties of solutions, which I 

 have given in a previous paper*. The results found in this paper 

 were, in short, the following : 



I. Determination of the variation of concentration in a binary 

 solution exposed to any field of gravity. 



(a) Applying a purely mechanical equilibrium condition, it 

 was proved that the concentration in the equilibrium state must 

 be constant along an equipotential surface and have its greatest 

 slope in the direction of the force. 



(6) The concentration gradient Avas found from the condition 

 that a small volume element acted on by gravity shall be in 

 thermodynamic equilibrium. The result found holds good for 

 any concentration and without regard to the volatility of the 

 compounds. 



(c) In the case in which the osmotic pressure is known as a 

 function of concentration, the concentration gradient can be found. 

 Numerical calculations were carried out for cane sugar under the 

 assumption that the osmotic pressure follows the gas laws. In the 

 case of electrolytes, the equation had to be slightly modified, and 

 the calculation was carried out for potassium hydrate. 



II. (a) Using the conception of osmotic pressure, some very 

 interesting relations were found connecting the concentration 

 gradient with the variation of osmotic pressure with hydrostatic 

 pressure. These relations Avere : 



,^ , 1 (d'7r\ dc dir 



(1) P-Po=K[Tcl,d^>^Pdp' 



,^. 1 /d'7r\ dc dir 



(2) p-p„= XT + Po^ ' 



K\dc Jp^ dn ^ dpa 



(3) ^J^{l+^J^ 

 dpo dp\ dpo 



p is the density of the solution at pressure p; Pq that of the 

 solvent at p^; ir = p — po — osraoiic pressure, p and jy^ being the 



* "Beitrage zur Theorie der Losungen." Christiania Vid. Selsk. Skr. No. 8, 

 1906. Phil. Mag. [6] 13, p. 589, 1907. 



