56 PROCEEDINGS OF THE AMERICAN ACADEMY. 



or of equal simplicity containing the fugacity instead of the vapor 

 pressure. Let us proceed to the determination of the laws according 

 to which fugacity changes with changes in the variables upon which 

 the condition of a substance depends, considering in the present paper 

 only those systems which are composed of a single chemically simple 

 substance. 



III. 



Influence of Temperature and Pressure on the Fugacity. 



Let us consider two' phases of a substance at the same temperature 

 and pressure, but not necessarily in equilibrium with each other. A 

 solvent may be chosen in which both phases are soluble without molecu- 

 lar change, and to so slight an extent that the saturated solutions may 

 be regarded as infinitely dilute. In such a case the solubility of each 

 phase is governed by the following equation, which may be obtained 

 directly from equations (2) and (3), 



/cHn_n\ _Q_ 



\ 9T ) P R T 2 ' 



in which II is the osmotic pressure of the saturated solution and Q the 

 reversible heat of solution (that is, inclusive of the osmotic work). We 

 may write for the two phases, 



{-JT-) P = RT* aud VJT-) P = RT» ° r COmbimng > 



Qx - Q, (9) 



1t no 

 91a u 2 



9T 



RT 1 



Q x — Q 2 may be conveniently replaced in the following way. Let one 

 gram-molecule of the first phase be dissolved in the solvent, this solution 

 then diluted or concentrated to the osmotic pressure II 2 , and then the 

 gram-molecule removed as the second phase. If these three steps be 

 done reversibly the heat absorbed in each will be respectively 



&, RT\u^, -<? 2 . 



The total heat change is a function only of the conditions of the two 

 phases, not of the path by which one passes into the other, and may be 

 designated by Q h2 , thus, 



