CH. XXIV.] REACTION VELOCITY 329 



such enormous velocity as to be practically instantaneous. Ionic reactions take 

 place between the inorganic constituents of living cells, but such reactions 

 occurring as they do in a colloidal medium are somewhat slowed down, but even 

 so are completed in an immeasurably short time. The most important substances 

 (fats, carbohydrates, proteins) in living tissues are, however, not electrolytes, 

 and reactions between them are spoken of as molecular reactions, and occur so 

 slowly that it is possible to ascertain the rate at which they take place. Reaction 

 Velocity is defined as the quantity of the substance transformed, measured 

 in gramme-molecules per litre, which disappears in the unit of time (one minute). 

 When starch is transformed into sugar, or protein into amino-acids, there is only 

 one substance transformed, and such reactions which compose the majority of the 

 reactions in living cells are called unimolecular reactions , or reactions of the first 

 order. When, for instance, starch is changed into sugar by the action of an acid, 

 it is the starch alone which is altered ; the acidity undergoes no diminution. 

 Similarly when the change is brought about by an enzyme, the starch only is 

 changed ; the enzyme is still present in its original quantity. Reaction velocity 

 is thus of special importance in a study of the changes produced by enzymes, and 

 these are the most frequent of all changes in living structures. 



Since the quantity of the substance acted upon is continually diminishing, the 

 velocity of the reaction cannot remain the same throughout, but must diminish 

 in a certain ratio. Suppose 20 parts out of 100 are transformed in the first 

 minute, there will be only 80 parts remaining at the commencement of the 

 second minute: 



100 - i|r = 80- 

 o 



Similarly at the commencement of the third minute we have only 64 left, 16 

 having disappeared : 



64. 

 In the fourth minute, 12-8 disappears and 51 '2 is left: 



64 - = 51-2; 

 5 



and so on. 



In order to express this in general terms, we may label the original con- 

 centration 100 by the symbol C , and for 80, 64, 51% etc., use the terms C lf C 2 , C 3 , 

 etc. . . . C t . The constant figure in the above example is i or 0*2. This may be 

 represented by k. The equations then run : 



C,-C t = C J ,or(Ul-*) = C 1 , 



Further C (l - Jfc) - C (l - k) x k = C 2 ; 

 or C (l-^-C 2 . 



Further C (l - k) 3 = C 3 . 



Finally C (l - ft)' = C;. 



If this is plotted out in the form of a curve, we obtain the curve known as a 

 logarithmic curve. 



In other cases the law is a different one, and we find that the reaction velocity 

 is not directly proportional to the quantity of reacting substance, but to the square 

 of this quantity. In all such cases, two substances are simultaneously changed 

 in their concentration. Such a process takes place in the decomposition of esters 

 (compounds of organic acids and alcohols), under the influence of an alkali ; here 

 not only is the amount of ester becoming less, but the alkali is also used up in the 

 formation of salts of the organic acid. Such reactions are called bimolecular 

 reactions^ or reactions of the second order. Certain reactions in living cells are of 

 this order, but reactions of higher orders still are not as yet known in living cells. 



We shall again have to return to the study of molecular reactions when 

 speaking of the action of enzymes. It will then be more convenient to study one 

 of the peculiarities they possess, namely, the phenomenon known as reversibility. 



