Chemistry. — "In-, mono- and divariatit equiUbria." XXIll. By 



Prof. F. A. H. SCHKKINEMAKKKS. 



(Communicated at the meeting of March 24, 1 923). 



Equilibria of n components in // -|- J p/nise.i, lohen the qmoititi/ 

 of one of the components approaches to zero. The injiuence 

 of a neiv substance on an i'nva)'iant iu/nili/n-iuin. (Continuation). 



We write the isovolnmelrical reactiüii of an etjiiilibrium ^(.f.= 0): 

 }.,F^ + X^F,+ . . . . =0 2(XH)y^0 2:{XV) = Q. . (I) 

 and the isentfopical reaction: 



ti,F, + i,,F, + ....=OS(iiH) = 0:E{i,V)H>0. . (2) 



Consequently in reaction (1) are formed on addition of iieat and 

 in reaction (2) on increase of volume tiiose phases, which have a 

 negative reaction-coefficient. We have, therefore: 



2 (;.r) r = — ;i, .r, — x, x, — en -S' {hx)h = — ft, .», — fi, .r, — ,. . 



When we subtract botli reaction-equations (1) and (2) from one 

 another, after having multiplied the first one with fi, and the 

 second one with A,, then we find tlie reaction : 



(fi, X, — A, ft,) F, + (,t, A, — ;.. ft,) F, + ....= . . (3) 



wherein the change of entropy is ft, 2 {X H)]' 



and the change of volume is — A, 2 {hVh)- 



As (3) represents the reaction, which may occni- in the equilibrium 

 {F,) = F^-\- F,-\- . . ., we have 



Herein (-7^,) indicates the direction of curve (i*",) in the invariant 

 point. In the same way we find : 



^dTJ, - ;., • 2 (ft V)u ' 1.77' j. - ;, ^ (ft F)H '^'- ^'' '' 

 As we are able to deduce from (J) and (2) also the direction of 



temperature and pressure of the different monovariant curves, the 



P, 7'-diagram is, therefore, quantitatively defined. 



Now we add to the equilibrium a new substance X, which occurs 



19 

 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 



