THERMODYNAMIC AL SYSTEM OF GIBBS 135 



If mi/ Ml = rii and mil Mi. = Ui, we have 



log 0:2' — log 0:2 = / — —-d log ori. 



(170) 



If Ni and A'"2 are the molar fractions of the two components 



ni d log Ni-\- riid log ^"2 = (171) 



and, subtracting this from (169), (170) is obtained in the form 



log (a^'/N^') - log (a./N,) = 



rai'/Ni' 

 Jm/Ni 



"^■dlogiai/Ni). (172) 



For example, Downes and Perman have determined the vapor 

 pressures of water over aqueous cane sugar solutions.* From 

 these measurements Permanf has calculated the activity 

 coefficients of water (Si) by (167) and those of cane sugar 

 (^2) by (172), takmg m/Ni = 1, when iV2 = 0. Table II gives 

 the values at 50°. 



TABLE II 



Activities and Activity Coefficients in Cane Sugar Solutions 



AT 50°C. 



22. The Lowering of the Freezing Point. Consider the 

 equilibrium of a solution of a solute >S2 in a solvent Si with a 

 soUd phase consisting solely of Si. We will denote the poten- 

 tials of Si in the solid, the pure solvent and in the solution at a 



♦ Trans. Faraday Soc, 23, 95 (1927). 

 t Ibid., 24, 330 (1928). 



