

962 Thermodynamiml Theory o, Ternary Mixtures. 

 By differentiation we obtain the equations 



and .... (70) 



S02O1, **/>, 0) = r j 2 ^ ^L -/ -7(To-T)J + -TjT- ^. 



.... (71) 

 In the case of a dilute solution these equations reduce to 



S i(*i,vM) = 7p|^ .... (72) 



and a f m #L dT 



o 2(5i>52ji?,^) = -^2-^- (73) 



The distinction between this equilibrium and that studied 

 under the heading " Solubility Influence " is arbitrary from 

 a theoretical standpoint, though practically it is very con- 

 venient. If for the moment we call the component which 

 freezes out C 2 , we may apply equation (43) . Since the heat 

 of solution {i. e. heat of fusion) is negative in all cases which 

 come under the head of " freezing," we see that the dilution 

 of the mixture with the component which freezes out raises 

 the freezing-point, and that therefore the simultaneous addi- 

 tion of the other components in the proportion in which they 

 exist in the mixture, lowers the freezing-point. 



The addition of one component may of course raise the 

 freezing-point. Reverting to the original assumption that 

 C is the component which freezes out, we see that the 

 further addition of Gj raises or lowers the freezing-point 

 according as So/ is positive or negative. 



The complete thermodynamical study of a ternary mixture 

 is not possible by means of freezing-point experiments since 

 only the two coefficients S i and S 02 can be evaluated. Thus 

 it is impossible to connect quantitatively freezing-point and 

 solubility data. We may, however, deduce a qualitative 

 relationship. It is evident from general considerations, that 

 if the further addition of C to a liquid mixture of C , C 1? 

 and C 2 in equilibrium with solid C 2 , precipitates C 2 (causes 

 more C 2 to dissolve), then the addition of C 2 to a solution 

 not too far removed from saturation raises (lowers) the 

 freezing-point. 



