( 156 ) 



Physics. — ''The derivation of the /onna /a a'hich (jives the rehition 

 between the concentration of coe.vistint/ phases for hinary 

 mixtures" \\\ Prof. J. D. van der Waals. 



(Communicated in llic meeting oi' Juno 25, lOUi). 



Already in m\ niolccular tlicory (CoiU. 11, p. 10) 1 derived a 

 foriiiula for the conceiilration in coexisting phases of binary inixtnres. 

 This formula has the following form : 

 / db da I / db da 



1 X dx dx ] \ X dx dx 

 MRT I + MRT = MRT I -f MET 



I 1 — X V — b r )j I 1 — X V — b 



In the case tl)at the second phase is ;i i-arelied gasphase, tl 



.V 



second member is simplilied to MJiT I and \ve find : 



1 — X 



da dl> 1 



V 



'le 



1 — X. \dx dx } . . . . (1) 



X. 1 — X, {dx dx ] 

 IIT I ' ' =\ MRT 



Fi'om lliis 1 have (U-a\vn the concbision tlial I he circumstance that 

 two coexisling |)hascs have tlio same conceiilralion can oidy occur 



ax 



for mixliires, for which a niiuiniuiu value of the (pianlilv - occurs, 



bx 



and so a nnniiuiiui \ahie foi' (lie ci'ilical temperature. For the 



limiting case, >vitli exceedingly low \alnes of 7', the mixture for 



which — has a minimum value, would be exactlv the mixture, for 

 bx 



which the value of .v is the same in the two jthases; but for in- 

 creasing values of T this concentration shifts to the side of the 

 substance with the lowest value of the size of the molecules. (Cont. 

 II, p. 19 and p. 120). 



Afterwards I have derixed in "Ternary Systems" for equation (1) 

 the following equation: 



X, l-x,_ fdTk )_dpk 

 1— .I'l .^'2 I dx pk «-*■ 



which also holds only approximately for the case that the second 



phase is a rarefied gas-phase. For the derivation of (2) I have not 



directly used the equation of state, but I have considered the well- 



■P Tt-T 



known formnla for the vaponr-pressnre —1^=/ — — — as sulli- 



pk ^ 



ciently accurate for licpiid volumes which are not much smaller 



