266 PROCEEDINGS OP Tin: AMERICAS ACADEMY. 



by substituting for the activity the concentration of ;i saturated solu- 

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

 concentration of the saturated vapor. 



Tin: Influence of Pressure and Temperature upon the Activity 



of a Stmplb Substance. 



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

 ecus, — and find the effect upon its activity : first, ofachange 

 pressure at constant temperature, and second, ofachange of temperature 

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

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

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



In the preceding paper a formula was obtained (equation 1 h foi 

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



\ dP )t~ 



v 



where ti is the fugacity and r the molecular volume. Combining this 

 equation with equation I of the present paper, we find, since RT is 

 constant, 



( d M\ _JL. v 



V dP Jx RT 



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

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

 equation is always a positive quantity, it is obvious that an incr 

 pressure always causes an increase in the activity. 



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

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

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

 temperature according to the well-known equation 



/a In II \ 



§ , VI' 



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, ami 

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

 our fundamental assumptions the volume of the ideal solvent does not 



