VELOCITY OF REACTION 83 



instead of & 9 we must put / [1 e, \ when the equation for 



2 \ l a /' 



velocity of reaction becomes 



This formula is too complicated for application to experimental 

 results on integration, but it includes all the observed experimental 

 cases, that is, it shows a stage when x is small where the reaction 

 is linear, a stage where the reaction is more rapid than the simple 

 logarithmic law demands, as in Henri's experiments, a stage show- 

 ing a falling off from the logarithmic values, as in the later stages 

 of the experiments of Armstrong and of Bayliss, a zero stage at the 

 equilibrium point, a reversed velocity, which also at the very end 

 tends to become linear. 



To make the investigation of the equation easier, 1 we may suppose, 

 since Henri found experimentally that the value of e was approxi- 

 mately unity, that e = e l = l, when the equation becomes 



a- 



x 2 . 



This may be written 



~ = ^ (a - x) + ^ [A?! (a - x) - Jc 2 a? 2 ], 



and in this form we may now investigate how the velocity, that 



dx 

 is, the value of ^-, will vary at different stages of the reaction. 



First, let the value of x be small compared with a as in the 

 earlier stages of the reaction, then x 2 and higher powers of x may 

 be neglected as small magnitudes of the second or higher orders and 

 the equation reduces to 



TV = /^ (a - x) + x . &J = ak r 



That is, the velocity of reaction is constant, and the curve expressing 

 it is linear. 



Secondly, for higher values of x (that is, later in the reaction), but 

 where x is not yet large compared to (a - x), since k 2 is small com- 



1 The same results follow with the formula as it stands, only the expressions 

 are more complicated. 



