lewis. — a new system of thermodynamic chemistry. 289 



The Relation of Activity to Free Energy and Thermodynamic 



Potential. 



It is interesting to see what relation the activity bears to certain 

 other quar^tities which have been previously used for a similar purpose, 

 especially the fi'ee energy of Helmholtz, which is itself intimately 

 related to the various thermodynamic potentials. 



The diminution in free energy which accompanies a given isothermal 

 process, that is, the maximum work which the process may accomplish, 

 is not a definite quantity until we define not only the process but also 

 the system which is to be considered. To illustrate, we may consider 

 a cylinder containing liquid and vapor, and a piston operated on by 

 a spring which exerts a force exactly balancing the vapor pressure. 

 When the piston moves out an infinitesimal distance, the decrease in 

 fi'ee energy of the water and vapor is equal to pdV, but on the other 

 hand the free energy of the spring increases by^x/F, so that the free 

 energy of the system comprising water, vapor, and spring does not 

 change. In general we shall depart from the most common usage and 

 consider the larger system, and we may therefore define the diminution 

 in free energy of a given isothermal process as the maximum work 

 which the process is able to accomplish, exclusive of the work done 

 against the external pressure or pressures. The negative of this quan- 

 tity, the increase in free energ}', we shall denote by A^'.-"-^ In a system 

 whose properties are determined when the temperature, the pressure, 

 and the compositions of the various phases are fixed, the general 

 condition of equilibrium is that, 



8(^ = 0. 



Let us now consider the change in free energy when one mol of a 

 given molecular species passes from one state where its activity is t", to 

 another state where its activity is ^'. This change may be effected as 

 follows : (1) Pass one mol reversibly from the first state into an ideal 

 solvent. The solution will have the osmotic pressure n and the vol- 

 ume V. (2) Change the concentration reversibly until the volume 

 becomes v' and the osmotic pressure reaches such a value, n', that the 



" The completely general definition of free energy is given by the equation, 



- A5 = Tr„„, + PJ\ + P\V\ H- . . . - Pj:, - P'„V\^ - • • . 



TFmax is the total work obtainable in the process in which system I, comprising 

 one portion of volume V, at pressure P^, another of volum.e Fo, at pressure Po- 

 etc., passes over into system II, comprising one portion of volume Vn, at pressure 

 P2, another of volume Po, at pressure P'o, etc. The free energy as thus defined 

 is identical with the thermodynamic potential, C, of Gibbs. 



VOL. XLIII. — 19 



