ACTION OF ENZYMES 59 



Such reactions are termed mono-molecular, and include all those 

 reactions induced by enzymes, in which a single substance breaks up 

 into two or more, and the quantity of ferment active throughout the 

 reaction remains constant. 



No. 3. Where two substances on the left-hand side of the equation of 

 reaction react to form two (or more) 1 substances on the right-hand side. 



Here the velocity equation becomes 



%-k(a-x)(b-x) [I], 



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

 centration a at the outset 



fir*. 



!-*(-*)' [2]. 



The first equation [1] may be written 



dx 



7 r~/i v = K at. 



(a-x)(b-x) 



1 / dx dx \ 

 and this T I r~ - ) = k dt, 



a - o \o - x a-xj 



on integrating this equation yields 



- 7 flog (b - x) - log (a - x) J = kt + const. 



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

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

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

 tuting these values in above equation, we get 



= const -> 



and subtracting the two equations we obtain 



1 

 -^-T flog (a - x) - log (b - x) + log b - log a \ = kt, 



I b(a-x) 

 which is v Los h \ = kt. 



a-b 6 a(b-x) 



giving for the velocity constant (7c) 



1 ^ b(a- x) 



~ (a-b)t ' & a (b-x)' 



1 As before, the number of substances on the right-hand side has no effect 

 if these do not react back on the progress of the reaction from left to right. 



