322 PRINCIPLES OF GENERAL PHYSIOLOGY 



the components, it is not to be supposed that it is a statical one. The two 

 reactions are still proceeding, the various molecules are continually changing 

 their partners, but, during the same time, the number of changes in the one 

 direction is equal to that in the opposite one. 



This conception of a dynamical equilibrium is of great importance, not only in 

 chemistry, but also in the physiology of the cell. The idea seems to have been 

 first clearly expressed by A. W. Williamson (1850). 



Before proceeding further, some additional remarks on the law of mas* action, 

 especially on its history, are required. Before the time of Berthollet (1799), it 

 was generally held that the course of chemical action had nothing to do with 

 the quantity of reacting matter. This chemist, however, pointed out how the 

 reaction 



CaCl 2 + Na 2 CO 8 - CaCO 3 -f 2NaCl, 



was reversed, on the shores of certain Egyptian lakes, by the presence of great 

 excess of calcium carbonate, so that the deposits of sodium carbonate were thus to 

 be accounted for. As he says, " an excess of quantity can compensate for a 

 weakness of affinity," and "the result of a chemical reaction depends not simply on 

 the strength of the affinities, but also on the amount of the active reagents " (p. 5 

 of the reprint in Ostwald's " Klassiker "). This point of view was not accepted 

 for more than half a century. In 1850 Wilhelmy applied mass action in a 

 quantitative manner to the hydrolysis of cane-sugar by acid, and established the 

 fact that the rate of action at any moment is proportional to the amount of 

 substance undergoing change. Harcourt and Esson in 1856 obtained similar 

 results, but it is the great service of Guldbergand Waage (1864) to have formulated 

 and applied the idea in its full significance, and in a clear and systematic manner. 

 Nevertheless, their work remained for a long time unknown, so that the law of 

 mass action was developed independently by Jellet in 1873, and by van't 

 Hoff in 1877. 



To avoid possible confusion, it should be clearly understood that the masses 

 spoken of are concentrations, that is, mass in unit volume. Taking again the 

 kinetic point of view, we can see at once that it would not double the number of 

 effective collisions if we doubled the mass and the volume at the same time ; there 

 would still be only the same possibility of collision. We must ensure the 

 possibility of doubling the number of collisions by doubling the number of 

 molecules in the same space. 



Remembering that the composition of a system in equilibrium is determined 

 by the relative rates of two opposing reactions, we see how the law of mass action 

 is the basis, not only of chemical dynamics but also of chemical statics. 



Passing on to consider its application to the action of enzymes, let us see first 

 what is the effect of changing the concentration of one component of a reversible 

 reaction in equilibrium. Taking the familiar ester system, the rate of hydrolysis 

 is in proportion to the product of the concentrations of the ester and the water, 

 that is : 



v l = k l x (ester) x (water), 



that of the synthetic reaction is : 



v 2 = k.? x (alcohol) x (acid), 



using brackets as usual to express concentrations, and k { and k., are the two 

 velocity constants. Then, in equilibrium : 



Aj(ester)( water) = A; 2 (alcohol)(acid), or 



A;, (alcohol )(acid) , , . 



, and, as we saw before, 

 # 2 (ester)(water) 



k 



- l = K, the equilibrium constant. 



k. 2 



Put in this form, we see that if we increase one component, the result must 

 be to decrease its fellow, since the value of the fraction must remain unaltered. 

 Suppose we increase water, the value of the fraction can only be kept constant 



