12 ICEEDINGS OP THE AMERICAN ACADEMY. 



If v. ider the B] ial case of m whose volume is anchai 



by the reaction to which the equilibrium equation refers, then / : 0, 



and 



dT V A '" 1 " K ) ' R r ' l1 '' 



' il T — //. was Bhown to be con- 



t under the conditions which led to equations (1") and (12), when 



the conditions of equilibrium changed al constant temperature. In Bucb 



8 F 

 cases, therefore, — — =->- = 0, ami t h. ■ e«iiuit ion ln-comes 

 6 In A 



-/In A' U 



d T WT*' l "'" 



This equation applies to both homogeneous and heterogeneous equilib- 

 rium. When applied to the former il is identical with the well known 

 equation of van't Hoff, sometimes called the equation "isocbore." This 

 equation, however, has been used to express the change of equilibrium 

 with the temperature, m>t merely in those systems in which the reaction 

 canses no change in volume, but in general. That this use is justifi- 

 able in the cases for which equation (20) was developed may be readily 

 shown. For, in systems subject to moderate pressure, the only consider- 

 able isothermal changes in volume are those of the gaseous phase. The 

 volume of the gases is, at a given pressure and temperature, proportional 

 to the total number of gram-molecules of the various gases present. If, 

 during the reaction to which the equation refers, there is a change of n 

 gram-molecules iu the gaseous phase, thru the total change in volume is, 



„ nRT PV 



V= p , or -jr = nJi. 



8F 

 In the case under discussion, where r = 0, equation (18) may be 



written, 



rfl n A' 



/' V 

 Since — ,_- = n Ii, a constant, 



Jin K U 



dT " 11 T-' 



