CHEMICAL THEOKY OF SOLUTIONS. PART I. 55 



of graphical representations in which x is taken as the abscissa 

 and the molare fractious as the ordinate. From equation (33) 

 Ave get by differentiation 



I 5^ * 5Ï "^ / 



because -^^ = C<^ by equation (32). 



dC 



"^ is positive for all values of .t because Cx is less than 



unity. At x = we have 



dCU 



{^\=' (^^) 



because O^ vanishes as x approaches zero, while at x = \ 

 Ca+Q = 1 and the differential coefficient becomes 



(4^)r(^y ^''^ 



where ((7a)i denotes the molar fraction of <Sa in the associated 



component in the pure state. 



d'C 

 The sign of the second differential coefficient , ./ is deter- 

 mined by that of the factors in the rectangular brackets, because 

 the other factors are necessarily positive. For small values of x 



