156 PROCEEDINGS OF THE AMERICAN ACADEMY. 



in the solution there are still n gram molecules of something different 

 from the Bolvent itself.* 



All the general laws of solutions may be derived thermodynamically 

 from either of two empirical equations, each of which, moreover, may be 

 derived from the other. The first is the law of van 't IIotF, 



n R T 



n = -pr-, CD 



where Fl is the osmotic pressure of a solution containing n gram molecules 

 of a solute in a volume V. 

 The second maj be written, 



ii^*i= " . (i 2 .) 



or. more strictly, 



^ = ^. (12 1,, 



In < 12 a) // ami /// represent the number of gram molecules of solute and 

 solvent respectively; ij/x and if/ a denote the escaping tendencies of the 

 solvent from the pure solvent and the solution respectively; in i 12 In d\p 

 represents the change in the ex-aping tendency of the solvent, due to -In 

 gram molecules of the solute. In order to make the equations entirely 

 definite it is necessary to give the function \p, or the escaping tendency, 

 a meaning less vague than that which sulliced on page l Is, by defining 

 the actual value of ij/ for some one condition of each substance. There- 

 lore the escaping tendency of a perfect gas will be defined as equal to its 

 gas pressure, and the escaping tendency from most actual gaseous phases 

 will be approximately the partial gas pressure. 



Equation (12b) Bimply unites in one general equation the law of 

 Raoult for the lowering of vapor pressure, the law of Nernsl for the 

 lowering of solubility, and less directly the law for the depression of the 



* It is probable that, in some cases, " association " with the solvenl takes place 

 and in others thai it does not A crystal containing water of crystallisation seems 

 in mi way different from any other double salt, and since it lias often been shown 

 that double salfa nch In sniuiioii.it i> probable that water enters into 



many molecular COmpOUnda m solution. Thui it -e. in- probable that when a Ball 



forms a number of solid hydrates, all these compounds and others whose solubility 

 i- neater are present In solution In proportions varying continuously with concen- 

 tration and temperature. <>n the other hand, it ii • ictr< mely unlikely that when a 

 substance like hydro lissolves in water s chemical combination of any kind 



takes pis 



