346 



esterification, the velocity constant k^ occurring in this equation 

 will in reality not be constant, but vary with fhe acetic acid con- 

 centration, hence with the time. 



The formulae for g and T, which we obtain by integration from 

 these equations of velocity, will then have no physical meaning in 

 themselves. If, however, k^ X t is eliminated, which is always pos- 

 sible, the equation obtained gives the connection existing between 

 q and T at any moment of the esteritication, and that independent 

 of tlie variation of k^. 



The equations of velocity drawn up like this for the esterification run : 



ds 



^ 3/: . s, 



dt 



dy 



— = k,s — 2k,y, 



• 



dx 



— z=.2k,y- k,. X 

 dt '^ ' 



'~ dr 



— = 3^, . X. 

 dt 



from which after integration and introduction of the relative con- 

 centrations, follows : 



g = e-^^i', and T = e-^^ and therefore g= T* 



We see, therefore, that g:= 7'' holds both for the reaction in 



saponifying sense and for that in esterizing sense. It follows from 



this that when the two reactions take place at the same time (i. e. 



when an equilibrium sets in) g = T^ holds likewise. 



This may be proved as follows: 



For the leaction of equilibrium holds: 



dg^_ dg^ -\- m dg ^ 



dT d7\ -f m dl\ 



dg^ dg^ 



when -— refers to the reaction in saponifying sense, and -^ to the reac- 

 dJ J d'J\ 



tion in esterizing sense, in which ??? is a quantity varying with the time. 



Because at any moment: 



^9 _ dg^ _3j» 

 dT, dT. 



also 



') We shall denote here and later the velocity constant in saponifying sense by 

 k^, that in esterising sense by k^. 



