THERMODYNAMIC AL SYSTEM OF GIBBS 117 



We can distinguish between these possibilities by making use of 

 a proposition which we shall obtain in a later section,* viz., that 

 when t, p, and 1712 are constant, ni is an increasing function of 

 mi. We shall now consider two cases. 



(a) Mi Is Capable of Negative AsW ell As Positive Values. Thus 

 if we regard the hydrate FeCls • 6H2O (*Si) and anhydrous ferric 

 chloride {S2) as the components of a solution of ferric chloride 

 and water, the amount of ferric chloride will be negative in 

 solutions containing a smaller proportion of ferric chloride than 

 the hydrate itself and positive in solutions containing a greater 

 proportion. We may add the hydrate Si to solutions for which 

 the amount of ferric cliloride is either negative or positive. In 

 both cases ^ti is increased. Therefore ^ui must be a maximum 

 when the mass consists wholly of Si, i.e., when Wa = 0. There- 

 fore, if ?ri2 is capable of negative as well as positive values. 



( 



3, -«. 



p, t, mi 



when m2 = 0. 



(6) rrii Is Capable Only of Positive Values. For example, if 

 water {Si) and ferric chloride {S2) are regarded as the components 

 of the solutions, m^ cannot have negative values. The potential 

 of water {m) must increase when water is added to a ferric 

 chloride solution, and therefore decrease when ferric chloride is 

 added to the solution. Thus, in the limiting case when nh = 

 0, the value of the differential coefficient in (111) cannot be 

 positive. 



Gibbs points out that "if we consider the physical signifi- 

 cance of this case, viz., that an increase of rrh denotes an 

 addition to the mass in question of a substance not before con- 

 tained in it," there does not appear "any reason .... for supposing 

 that this differential coefficient has generally the value zero." Sup- 

 pose that we have a mass of water in equilibrium with ice. The 

 addition of a salt to the water will destroy the possibility of this 

 equilibrium at the same temperature and pressure and, if the 

 temperature and pressure are kept constant, the liquid will 



See page 167. 



