156 PROCEEDINGS OP THE AMERICAN ACADEMY. 



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

 from the solvent 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 Hoff, 



nRT 



n = -^, (11) 



where 11 is the osmotic pressure of a solution containing n gram molecules 

 of a solute in a volume V. 

 The second may be written, 



^^-^^^- ^ (12a) 



» 



ij/i n -\- m 



or, more strictly, 



d\b dn , , 



In (12 a) n and m represent the number of gram molecules of solute and 

 solvent respectively ; \px and i//o denote the escaping tendencies of the 

 solvent from the pure solvent and tiie solution respectively; in (12 b) d\p 

 represents the change in the escaping tendency of the solvent, due to dn 

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

 definite it is necessary to give the function i/^, or the escaping tendency, 

 a meaning less vague than that which sufficed on page 148, by defining 

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

 fore 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 (12 b) simply unites in one general equation the law of 

 Raoult for the lowering of vapor pressure, the law of Nernst 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 solvent takes place 

 and in others that it does not. A crystal containing water of crystallization seems 

 in no way different from any other double salt, and since it has often been shown 

 that double salts exist as such in solution, it is probable that water enters into 

 many molecular compounds in solution. Thus it seems probable that when a salt 

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

 is greater are present in solution in proportions varying continuously with concen- 

 tration and temperature. On the other liand, it is extremely unlikely that when a 

 substance like hydrogen gas dissolves in water a chemical combination of any kind 

 takes place. 



