266 PKOCEEDINGS OF THE AMERICAN ACADEMY. 



by substituting for tbe activity tbe concentration of a saturated solu- 

 tion, and one for vapor pressure, by substituting for the activity the 

 concentration of the saturated vapor. 



The Influence of Pressure and Temperature upon the Activity 



OF A Simple Substance. 



Let us consider a pure substance in any state, — solid, liquid, or 

 gaseous, — and find the effect upon its activity : first, of a change of 

 pressure at constant temperature, and second, of a change of temperature 

 at constant pressure. Since the equations we are about to obtain are 

 special cases of equations IX and XII, of which a complete proof is 

 given in a later section, a less thorough derivation will here suffice. 



In the preceding paper a formula was obtained (equation 14) for 

 the influence of pressure on the fugacity of a pure substance, namely, 



ainf 



dF T RT 



where i/' is the fugacity and v the molecular volume. Combining this 

 equation with equation I of the present paper, we find, since BT i^ 



constant, 



'2 In A V 



RT' 



/a In A 



This is a perfectly general equation for the influence of pressure upon 

 the activity of a pure substance. Since the second member of this 

 equation is always a positive quantity, it is obvious that an increase of 

 pressure always causes an increase in the activity. 



In order to determine the influence of temperature, let us consider 

 a substance X, in contact with its saturated solution in an ideal solvent. 

 The solubility as measured by the osmotic pressure, 11, varies with the 

 temperature according to the well-known equation 



/ ainn \ 



<3 _ VI* 



RT 



which, since we are dealing with the ideal solution, can be shown to be 

 entirely exact. Q is the total heat absorbed when one mol of X dis- 

 solves reversibly in the ideal solvent. It is obviously the sum of three 

 terms, — the increase in internal energy, the osmotic work done, and 

 the work done against the external pressure, F. (According to one of 

 our fundamental assumptions the volume of the ideal solvent does not 



