180 VELOCITY OF REACTION, AND 



or if the substances concerned (A and B) are in equi-molecular con 

 centration a at the outset 



(2) 



The first equation (1) may be written 



dx 



i -- m - \ = * 

 (a - x) (b - x) 



1 / dx dx 

 and this 



on integrating this equation yields 



T log (b - x) - log (a - x) = kt + const. 



To obtain the value of the integration constant, we have when 

 t = that is, at the start of the experiment x = 0, for x is the amount 

 changed at time = , and hence when t = 0, x = 0. Therefore, substi- 

 tuting these values in above equation, we get 



-jjl log &-log a J=const., 

 and subtracting the two equations we obtain 



^fcflog ( ~ ) - lg (&-#) + log 6 - log flj = let, 



u . u . 1 b(a-x) 



whlchls 



giving for the velocity constant k 



I b (a - x) 



(a-b)t ' g a (b-xy 



The second equation (2) (above) may be written 



(a -^=kdt, 



or since dx = -d (a -x) 



d(a-x) 



