430 0. L. Speyers — Molecular Weights of Liquids. 



different, and so their volumes, within an infinitesimal differ- 

 ence, are each one half the original volume, as has been shown 

 by Konowalow.* As we pass on downwards below the criti- 

 cal temperature, the compositions of the two phases diverge, 

 the divergence sometimes increasing indefinitely, sometimes 

 diminishing at lower temperatures with promise of forming 

 later on a homogeneous liquid with a second set of critical 

 quantities, f 



Let a x be the activity factor of liquid 1, m x its normal molec- 

 ular weight, w x its mass in the phase under consideration. 

 Let t° be below the critical value. From 1 we get 



, _ w x ' pj , „ w" p" 

 ci = — _ T . . -, and ct = ,. T » . # . (3) 



Since two phases are present, w/ and N/ as well as p are vari- 

 able with t and so 



da,' _ \ _J f u>i P^Pt'-Pt'dp* P* N/tftg/— fg/^N/ -! 



dt P-P: 'fn^XPi-P* dt N 2 ' dt J 



where dpj /dt is the differential coefficient of the vapor tension 

 of the solution in the immediate neighborhood of the value 

 Pit dp 2 /dt, that of the pure solvent in the immediate neigh- 

 borhood of the value p 7 . With the exception of 



Pt d pj-p*' d p* and fly<fto 1 i -M 1 '<?N a i 



dt dt 



the signs of all the quantities are positive. For dilute solu- 

 tions we shall put dp 2 '/dt from the solution, approximately 

 equal to dpj/dt from the pure solvent. That is, we shall assume 

 that dp//dt from the dilute solution is quite close to what we 

 should get were we to differentiate the vapor tension from the 

 pure solvent in the immediate neighborhood of the numerical 

 value p 2 '. We do this because we find that in dilute solutions, 

 while the vapor tension curve of the solvent is depressed 

 numerically it is not altered in character, and because we seek 

 the sign of the first quantity rather than its numerical value. 

 With this understanding we find 



PtdpJ—Pi'dPi ^Q 

 dt ^ 



for water, methyl alcohol, i butyl alcohol, amyl alcohol, i amyl 

 alcohol, i butyric acid, carbon disulphirle, benzene, and chlor- 

 benzene, and probably for all dilute solutions. Its numerical 



* Drude's Ann., x, 360 (1902). 

 f Ostwald, Lehrb. ii, 670 (1902). 



