( 5'8 ) 



Chemistry". — "On the course of the x]nnoda] and the jihdtpoint 

 lines for binarij mixtures of normal suhstances." Hy J. J. 

 VAN Laar. (Third communication). (Communicated by Prof. 



H. A. LORENTZ). 



1. In my last paper') on tlie above mentioned subject I discussed 

 the general equations of the spinodal and the phxitpoint lines, viz. 

 RT = f (v, x) and F{v, x) := (derived in a previous communication ")) 

 for the special case />^ = />„, i.e. n^8, when rr denotes the ratio 



ot tiie critical pressures — , and & that of the critical temperatures — 

 Pi ^'i 



of the components. (The lii(jher critical temperature is always T^). 

 I started ti-om van der Waals' equation of state, where h was 

 assumed to be independent of r and T, while further in the quadratic 

 equations : 



\a = {l-,f- «, + -l,- (I-.,-) «,,, + X- a, 

 it was assumed that 



^. = \'. (i'l + ^'.) ■' «1. = y\ a, , • . • • (1) 

 which reduces the above expressions to 



U = (l-,.)^+.^-^ 



i« = ((l-.,;)j/«, +.''l/<g'. 



Henceforward we shall indicate by the name normal (binary) 

 mivAures such mixtures, the components of which are not only simple, 

 but where both the relations (J) may be considered as satisfied. 



. The discussion in (piestion led to the occurrence of tuKi separate 

 branches of the plaitpoint line (see plate loc. cit.), which present 

 a double point at a definite value of 6 (fig-. 4). If ^ < 2,89 

 (when ^1 = h^), we have the normal shape, represented in tig-. 2 ; if 

 ö]>2,89, we find the abnormal shape, represented in fig. 1, which 

 as yet has been only considered possible for mixtures, of which at 

 least one of the components is associating (abnormal). (C^H^ -\- CHjOH, 

 C,H, + H,0, SO, + H,0, Ether + H.,0). 



The possibility of a third case was also iirietly mentioned (see 

 fig. 3), examples of which lia\e been described inter alia by Küenen 

 (C, H, -f- C5H5OII, etc.) ; but this case was not further discussed, nor 

 the connodal relations and three phase equilibria, which, for the 



1) These Proc, .June 1905, p. lii. 



2) These Proc, April 1905, p. 646. 



