188 



Mr. M. M. Pattison Muir on 



when k> 1, the minus sign is employed,, and the positive sign 



P P 



when k<1. The value of f is positive when Kjr > -^r* 



H Hi 



If it be desired to study the influence of time upon the course 



of the reaction, it becomes necessary to introduce the absolute 



velocity. If x be the amounts of A and B x decomposed to Aj 



and B in time t, then the amounts decomposed in an infinitely 



dx 



dt 



short time dt is dx, and the velocity is 



By further development, and by integration, the following 

 formula is found : — 



•£ h-3L 



a ± b 



log nat. (jS- . ^t_£) =^ («_ lXk-f). 



(3) 



where 



h 



__*(P + Qi) + P, + Q 



I 



From this equation it would appear that x attains the value 

 f only after an infinite time ; but the function in equation (3) 

 is of such a character that the difference between x and £ be- 

 comes so small after a comparatively short time, that it may 

 be disregarded in an experiment. 



The first special cases considered by Guldberg and Waage 



as illustrative of the systems now under examination is that in 



which A= acetic acid, B = water, A 1: == ether, Bj= alcohol. 



From the experiments of Berthelot and St. Giles it may be 



k 

 shown that-r- =4. 



kl 

 The values given in the following Table for f have been cal- 

 culated by the aid of equation (2). The secondary reactions in 

 this special case exert a considerable influence upon the primary 

 chemical change. 



Initial quantities of 



Quantity of acetic acid 

 decomposed. 



Acetic acid. 

 P. 



Alcohol. 



Qx 



Ether. 



Water. 



Observed. 

 t 



Calculated. 

 1. 





i 



2 

 4 

 1 

 1 

 1 

 1 

 2 



















1-6 

















 

 

 

 

 3 

 23 

 98 



0-665 

 0-828 

 0-902 

 0-858 

 0-521 

 0-407 

 0-116 

 0-073 



0-667 

 0-845 

 0-930 

 0-845 

 0-492 

 0-409 

 0-131 

 0073 



