LEWIS. — FREE ENERGY AND EQUILIBRIUM. 7 



If we represent by C^^ and C^^ the total heat capacity, when each 

 constituent remains at constant volume, in the initial and final states 

 respectively ; by H the total change in the various functions denoted by 

 «if^i, n2^2 7 etc.; by U the total change in the internal energy of 

 the svstem, then the equation may be written, 



,./ "'. 



V 2 ?/„ 2 n^ o — G 



A = RT\u ^ ""^'-' -ri -^^—^dT+HT+a (6) 



We have in this equation a perfectly general expression for the change 

 of free energy in any isothermal change, chemical or physical, in any 

 system, whether homogeneous or heterogeneous. The quantities con- 

 tained in the equation are all capable of direct experimental determination 

 with the exception of the quantity H, of which we only know that it is 

 not a function of the temperature, since it enters as the difference between 

 a number of integration constants each of which is indejiendent of the 

 temperature. The value of this function and the simple form that it 

 assumes in many important cases of equilibrium will be considered later. 



The form which equation (G) takes in the simple cases where all the 

 molecular species participating in the reaction are gases and dilute solu- 

 tions may be shown as follows. 



Equation (5), applying to the free energy of one of the simple con- 

 stituents of a system, is, 



(Si = - E Tluv - T r ^ d T + "^ T-^Wi+ ^, 

 differentiated with respect to volume, at constant temperature, 



J Tr. dv 1 dv dv ^ ^ 



dv V 



Since d ^ represents the work accomplished in a reversible change, 

 we may write 



d^ =z — p dv , V 



where p denotes the gas pressure or the osmotic pressure, as the case 

 may be. Then 



_, = _^_^ri,^,r+^a + ^^, (3) 



V J T^T dv dv dv ^ ^ 



Now we know that in the case of perfect gases and dilute solutions the 

 heat of free expansion and the heat of dilution respectively are zero. 



