270 



PROCEEDINGS OF THE AMERICAN ACADEJUY. 



ln[^(v-b)]-ln[^'{v>-h)] = 



2a 



+ -F 



2a 



v-b v'-b BTv BTv' 



From this equation, assuming that the van der Waals formula is true 

 and that the constants a and b are known for a given substance, the 

 activity of that substance can be found at the volume v when it is 

 known at any other volume, v'. At infinite volume the activity of the 

 gas, by definition, is equal to its concentration, which is the reciprocal 

 of its molecular volume. It is evident, therefore, that if in the above 



equation v' approaches infinity, ^' approaches — , or -; r, and the sec- 



v' v' — b 



ond, fourth, and sixth terms in the equation approach zero. Omitting 



these terms, therefore, and rearranging slightly, we have, 



ln^ = 



2a 



v-b BTv 



-\u{v- b). 



From this equation $ can be found for any gas at any volume, v, pro- 

 vided the formula of van der Waals holds, and the values of a and b 

 are known. Similarly any other empirical equation of condition may 

 be used. 



According to Amagat's experiments upon carbon dioxide at 60° the 

 molecular volumes of this gas at 50, 100, 200, and 300 atmospheres, are, 

 respectively, 0.439, 0.147, 0.0605, and 0.0527 liters. From these data 

 I have calculated the values of a and b at this temperature and found, 



a = 3.1; b = O.OU 



(pressure being expressed in atmospheres, volume in liters, and R con- 

 sequently having the value 0.0820). 



Substituting these values in the above equations, we obtain the 

 values for the activity of carbon dioxide at 60° given in the following 

 table : 



