344 



course of the saponification (saponification in alcalic surroundings), 

 and it is now of importance more closelj to examine the ideal case, 

 in which such complications do not appear. 



Let us consider the saponification of triacetine in solution, and 

 let us assume that the three ester-groups are perfectly equivalent '). 

 Then the saponification takes place according to the following scheme : 



'B^ -^E 



ki ki ki 



(r) (x) (y) (s) 



In this A represents the triglyceride, B, C, and D the diglycerides, 

 E, F, and G the monoglycerides and H glycerine. Let the number 

 of molecules of each of these substances, present after a time t, be 

 represented by r, x, y, and .s-, in which x and y indicate the number 

 of molecules of the three di- resp. monoglycerides each taken 

 separate, and let the constant of velocity at the splitting off of each 

 fatty acid group be k-^. 



Then the equations of velocity are: 



dr 

 dt ' ' 



d.v 

 dt 



dy 

 dt 



ds 

 dt 



^k. 



■2k, 



2k j^ X — k^ I/, 



= 3^j y. 



Starting from a molecules of triglyceride, we may calculate from 

 this that the number of molecules of the different stages present 

 after a time t amounts to the values from column 2 of table 1. 



The relative concentrations (fraction of the total possible number 

 of molecules) of each of the glycerides is, therefore, represented by 

 the values from column 3 of table 1. The sum of these relative 

 concentrations is of course, always = 1. 



When we now finally calculate the number of molecules of acetic 

 acid {z) split off after the time i, we find from z = 3 {x -\- 2y -\- :i) : 



z = 3a(l — e— *iO. 



1) With regard to the validity of this assumption cf. § 3 and 4. 



