56 VELOCITY OF REACTION, AND 



where a and b are the original molecular concentrations of the 

 substances A and B, and x the change in molecular concentration 

 at time t. This equation obviously takes the form 



2. For a single substance (A) undergoing conversion into two 

 substances (B and C), the common type of action of enzymes and 

 many other catalysts : 



dx 



-jj = &j (a - x) - k 2 (b + x) (c + x), 



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 



J-Ma-")-^ W- 



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

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

 (0 and D) 



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



When initially a = 5 for A and B, and c = d = Q for C and D, then 

 the equation becomes 



fJx 



=-*,(.-)- JfciP [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 integration 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 ex- 

 pression in the equation which represents the tendency of the 

 substances to react in the reverse direction from right to left 

 instead of from left to right. 



