312 PRIXC1PLES OF GENERAL PHYSIOLOGY 



molecules combine together to form one or more different ones. This is a 

 bimolecular reaction, since the change of concentration of two molecules must be 

 taken into account. What is the law here ? Take for a moment the kinetic point 

 of view and suppose that we increase the concentration of the one reacting 

 component, A, and leave the other, B, intact ; the rate is clearly proportional to 

 (A), using brackets to express concentration, since the number of times that a 

 molecule of B meets with one of A is proportional to the number of A to be met 

 with in a given space. Suppose that we increase (B), leaving (A) alone, then the 

 number of times collision takes place is proportional to (B) ; therefore, if both are 

 changed, the velocity of the reaction is proportional to the product of the 

 concentrations of the two molecules, or 



In practice, most cases of bimolecular reactions can be simplified for integration, 

 since the concentration of A and B can be made to change equally. In the 

 saponification of esters, say ethyl acetate, by sodium hydroxide, the equation is : 



~=k(a-x)(b-x), 



where a and b are the initial concentrations of ester and alkali, and x is the 

 amount of sodium acetate produced in the time t. If equivalent quantities of 

 ester and alkali are taken, this equation becomes 



dx 

 - dt ~k(a-x)\ 



since a = b. The integral of this equation is 



v . / v 



t a(a x) 



Hydrolysis of Gaiie-Sugar by Acids. This process can clearly be expressed as 

 a unimolecular reaction, since it is* completely accounted for, as regards its rate, 

 as the change of concentration of the one kind of molecule, cane-sugar. Applying 

 the formula to it, it is found that the constant k is the same at all stages of 

 the reaction. Indeed, as mentioned before, the determination of this velocity 

 constant has been used as a method of determining the hydrogen ion concentra- 

 tion of various acid solutions. 



Application to Enzymes. Suppose that cane-sugar is hydrolysed by the enzyme 

 invertase, instead of by acid. What sort of values of k do we obtain ? The 

 value of making measurements of this kind in the case of enzymes is that we 

 thereby obtain indications as to what to look for as causes of any divergence found, 

 and also, by the regularity of the time course of the divergence, we are able to 

 estimate the accuracy of the method of experiment adopted. 



In all cases where we are investigating the action of an enzyme on a single 

 substrate, as in the majority of hydrolytic reactions, we might expect to find that 

 the unimolecular equation is followed. In point of fact, in the case of invertase, 

 if we calculate the velocity constant by the unimolecular formula, we find that it 

 steadily rises as the reaction proceeds ; in a particular case, from '00058 to 

 0'00097 (Victor Henri, 1903, p. 55). Taking other enzymic actions, we find, on 

 the contrary, almost invariably, a decrease in the value of k. E. F. Armstrong 

 (1904, 1, p. 506) found it to fall from 0'0640 to 0'0129 in the case of lactase. 



We may now proceed to find what possible factors might have the effect of 

 diminishing the rate more than it should be, by mass action, on account of the 

 mere diminution in the number of molecules of the substrate, leaving, for the 

 present, the exceptional case of invertase. 



There are two things to be kept in mind with regard to this question. The 

 first is that there is every reason to suppose that all the reactions with which we 

 are dealing are reversible, and that there are two opposite reactions proceeding 

 simultaneously, so that the net result observed in any experiment is the difference 

 between the rates of these two reactions. Suppose that our reaction is the 



