Thermodynamic^. Theory oj Ternary Mixtures. 951 



We see from this table th&t the addition of alcohol to a 

 solution of sugar in a mixture of alcohol and water raises 

 the chemical potential of the sugar. Hence by equation (6) 

 the addition of sugar must raise the chemical potential of 

 the alcohol. Strictly speaking, equation (39) justifies these 

 statements for solutions only in the neighbourhood of satu- 

 ration. A little consideration will show, however, that the 

 statements are probably true over a considerable range of 

 values of the concentrations. Consider a mixture for which 

 ^ 1 = and s 2 =l*44. The chemical potential of sugar in the 

 mixture will be less than that of pure sugar. If alcohol be 

 added till ^ = '501, then the chemical potential will rise to 

 that of pure sugar. Of course the first addition might cause 

 the potential of sugar to fall, but it is reasonable to suppose 

 that a rise occurs over a considerable range of values of s h 

 if not from zero to *501. 



In a binary mixture, the two components exert a lowering 

 effect on each other's potentials. Hence in a ternary mixture 

 in which one of the components forms only a very small 

 proportion of the whole mass, the other two components 

 must exert a lowering effect on each other's potentials. 

 Thus in a system containing alcohol, sugar, and a very small 

 amount of v\ ater, the further addition of alcohol must lower 

 the chemical potential of the sugar. Hence as the numbers 

 in the first column are increased a point must be reached 

 when the numbers in the second column begin to increase. 

 This of course is simple common sense. When the solvent 

 medium is practically pure alcohol, the amount of sugar dis- 

 solved will be proportional to the amount of alcohol present. 

 In any system of this kind, if s 2 be plotted against s 1 the 

 curve is asymptotic to a straight line through the origin 

 whose slope measures the solubility of C 2 in d- 



If the addition of Ci lowers the solubility of C 2 in C , it 

 raises the potential of C 2 , and hence from equation (11) we 

 see that the addition of C 2 raises the potential of G v Hence 

 from equation (10) we see that the addition of C x lowers the 

 potential of C . If, however, the addition of Cj raises the 

 solubility, the addition of C 2 lowers the potential of C 1? and 

 hence from equation (10) we see that the addition of C 2 may 

 either raise or lower the potential of C . We will next, 

 therefore, find the condition which must be fulfilled with 

 respect to the solubility in order that the addition of C 2 may 

 raise the potential of C . 



From equations (10) and (39) we can deduce the equation 



3 R2 



