ACTION OF ENZYMES AND CELLS 177 



where a is molecular concentration of single substance, b and c those 

 of substances into which it is converted, and x the change in concen- 

 tration in time t. If, as is usually the case, B and C are absent in the 

 beginning, and a still stands for the initial concentration of substance 

 A, then the equation obviously simplifies to 



~ = k l (a-x)-Jc 2 x* (4) 



3. For completeness we may add the formula deduced at length 

 above, for when two substances A and B react to form two others 

 C and D 



^ = &i (a-x) (b-x)-k 2 (c + x) (d + x). 



When initially a = b for A and B, and c=d = for C and D, then 

 the equation becomes 



-^^(a-x^-k^ (5 



The integration of the above equations of velocity is necessary 

 in order to obtain x, the quantity of the substance (or substratum) 

 changed in a given time t by the action of any catalyst, which is the 

 quantity usually observed in experiments on reaction velocity, and is 

 used to determine the constant or constants of reaction. Such integra- 

 tion is, however, difficult, and leads to complicated expressions for the 

 value of x, on account of the presence of the second member on the 

 right-hand side prefixed by the negative sign. Now this expression, 

 which introduces the difficulty, arises from the supposition that the 

 reaction is reversible ; it is the expression in the equation which repre- 

 sents the tendency of the substances to react in the reverse direction 

 from right to left instead of from left to right. 



Accordingly, if the degree of reversibility is small that is, if the 

 equilibrium point lies close up to the end point corresponding to the 

 substances being practically all converted into the forms represented 

 on the right-hand side of the equation of reaction the value of the 

 second expression on the right-hand side of the equation of velocity 

 becomes very small compared to the value of the first expression, and 

 may be neglected. That is, the reaction may be taken as running 

 irreversibly, and this is what is usually done in obtaining the equations 

 for the velocity of most reactions which concern us. 



This means that in those equations which run almost to com- 

 pletion, the value of the constant k is small compared to k l . Now 



12 



