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VIII. Partial Pressures in Liquid Mixtures. 

 By William Edward Story *. 



LAST summer Professor Rosanoff called my attention to 

 an investigation of the partial pressures in certain 

 binary mixtures that he was making by the application of 

 the Duhem-Margules equation to experiments carried on in 

 the Chemical Laboratory of Clark University /and to analogous 

 applications that had been made by others. The mathematical 

 aspect of the problem interested me ; I studied it carefully 

 and found that it was possible not only to improve the method, 

 from a mathematical point of view, by the use of more 

 convergent series than those heretofore employed, but also to 

 extend it to mixtures of any number of components. Inci- 

 dentally it appeared that the coefficients of the new series are 

 more readily calculated from actual observations than those 

 of the former series, that Raoult/s law holds for any number 

 of components, that this law is an immediate consequence of 

 the Duhem-Margules equation, and that Margules' formulse 

 for the partial pressures in a binary mixture involve no as- 

 sumption other than those involved in the equation just 

 mentioned. The present paper describes my method in 

 general, and its application to binary and ternary mixtures 

 in particular. 



Contents. Page 



1. Physico-chemical assumptions 97 



2. Mathematical formulation of the assumptions 98 



3. The Duhem-Margules equation 102 



4 Raoult's Law 106 



5. General solution of the Duhem-Margules equation. . . . 107 



6. Special method for binary mixtures 118 



7. Ternary mixtures 116 



1. This investigation is restricted exclusively to such a 

 liquid mixture and its variations as satisfy the following 

 conditions : — 



a. All variations of the mixture shall take place iso- 



thermally, that is at a constant temperature. 



b. Each component shall have a vapour, and therefore a 



pressure of its own. 



c. The partial pressure of any component of the mixture at 



the temperature in question shall depend solely on 

 the composition of the mixture — that is on the molar 

 proportions of the several components, — and shall 

 vary continuously when the composition varies con 

 tinuously, being finite for all compositions. 

 * Communicated by the Author. 

 Phil. Mag. S. 6. Vol. 20. No. 115. July 1910. H 



