Where now Sa molecules of acetic acid are possible, the relative 

 concentration T of the free acetic acid is: 



T —\ 



-kit 



The two relative concentrations which are of most importance 

 here, are those of the free fatty acid atid of the free glycerine, viz. : 



g = (l—e-hty . . (3) and T = l—e-ht . . (4) 

 from which follows: 



■<7=7" . . (5) 



or in words : 



In case of stagewise saponijicntion of an ester of a tri-vaknt 

 alcohol {lüith equivalent OH groups) and a univalent acid, the relative 

 concentration of the free alcohol, independent of time, is always 

 equal to the third power of the relative concentration of the f ree acid, 

 provided that no complications (as in case of saponification in emul- 

 sion), take place. 



When we saponify an ester of a trivalent acid and a univalent 

 alcohol, the reverse holds of course. 



The equations (3) and (4) may be derived from (1) and (2) by 

 putting p = q = 1. 



We may now apply our considerations also to the opposite case, 

 viz. the esterification of glycerine with the equivalent quantity of 

 acetic acid. 



In this case the reaction is bimolecular, as the reaction velocity 

 is not only dependent on the number of still unesterized OH groups, 

 but also on the number of molecules of free fatty acid. When we, 

 therefore, draw up equations of velocity as in the case of triglyce- 

 ride saponification, i e. when in our equations we only express the 

 number of free OH groups, which can become esierized, and not 

 the number of acetic acid molecules available to bring about this 



23 



Proceedings Royal Acad. Amsterdam, Vol. XX. 



