ELECTROLYTES AND THEIR ACTION 185 



The law of mass action means that, other things remaining constant, doubling 

 the concentration of any one of the reacting substances doubles the rate of the 

 reaction, so that, if two are doubled, the rate is four times as fast, and so on. 

 The necessity of this fact on the kinetic theory is obvious. Thus, the rate at 

 which a reaction goes on depends on the number of collisions, per unit of time, 

 that occur between the reacting molecules. Clearly, if the number of one kind 

 of these molecules in a given space is doubled, the number of collisions is 

 doubled, and if, also, the number of the other kind is then doubled, this rate itself 

 will be doubled; so that the effect of doubling the concentration of both is to 

 multiply by the rate due to the increase of both, that is, by four. 



It is usual to express the concentrations of the reacting substances by the 

 use of brackets : thus the rate of the reaction : 



A + B:>C + D 



in which A and B react with the production of C and D, while C and D react 

 to form A and B, is expressed as : 



K(A).(B)^K'(C).(D) or 

 K(C) A .(C) B ^K'(C) C .(C) D 



A, B, C, D may stand for the concentrations of acetic acid, ethyl alcohol, ethyl 

 acetate, and water, and the formula would then read : 



K(C) Acid . (C) Alcohol ^ K'(C) Ester . (C) H.2O, 



where K and K' are the velocity constants of the two reactions respectively. We 

 note further that the ratio of these two quantities will define the composition of 

 the system in equilibrium ; if one reaction proceeds twice as fast as the other, 

 it will be clear that, in order to bring up the rate of the slower reaction to 

 that of the faster, as must be the case in equilibrium, the concentration of 

 the reacting substances in its case must be correspondingly increased. 



Now it was pointed out by Arrhenius that electrolytic dissociation must be 

 governed by the law of mass action. In order to understand its application 

 to this case, let us consider the ethyl acetate reaction in equilibrium, thus : 



(alcohol) (acid) = K (ester) (water), 



where K is the ratio of the two velocity constants of our previous formulae and 

 is known as the "equilibrium constant" and the names in brackets mean the 

 respective concentrations of these substances. Suppose that we increase the 

 concentration of any one of the components, it is easy to see that it involves 

 simultaneous changes in all the others ; for example, if we increase water, ester 

 is diminished, in order to maintain constant value of the product, and ester 

 cannot be decreased without increase of acid and alcohol. Perhaps the matter 

 will be made clearer if we put the equation given above into the form : 



^ _ (alcohol) (acid) 

 (ester) (water)' 



If water is increased, the value of the fraction may be kept constant by 

 increase of either alcohol or acid, but neither of these can occur without the 

 other nor apart from hydrolysis of part of the ester. 



Take next acetic acid in water ; the reversible reaction is : 



HA^H- + A' 



and, by mass action : 



K(HA) = (H-).(A') or K = 



K being the equilibrium constant. 



Put a = degree of dissociation, so that if a = CK5, half the molecules of the 



