EQUILIBRIA AND THEIR DISPLACEMENT 259 



case if we represent the concentrations of the ions by 

 (A) and (C) respectively, we have fc c oc (A)(C). For 

 example, if there are no ions of one type present there 

 can be no recombinations, and k c is zero. On the 

 other hand, doubling the number of either kind of 

 ion will double the number of collisions of this kind 

 of ion with the other. 



In the same way the rate at which molecules dis- 

 sociate will be proportional to the concentration of the 

 normal molecules. Thus k d oc(AC), where the brackets 

 represent the concentration of the substance included 

 by them. 



In equilibrium k d and k c are equal. Let the cor- 

 responding value of the concentrations be represented 

 by a subscript e. Then, since k d /k c = 1 we have 



(1) 



In this particular case the ratio K, which is called the 

 "equilibrium constant," is a constant expressing the 

 equilibrium conditions for ionization and is therefore 

 frequently called the " ionization constant." 



The idea that the rate at which a substance reacts 

 is proportional to its molecular concentration was 

 formulated in a law by Guldberg and Waage in 1864. 

 We may express it in a general form by saying that if 

 A and B are the reactants in a reaction which gives 

 the products C and D, then we may write the rate at 

 which the reactants disappear as ki(A)(B) or at the 

 equilibrium point as ki(A) e (B) e . Similarly if the 

 substances C and D may enter into a reverse reaction 

 then the rate at which they disappear is fe(C)(D) or 

 at the equilibrium point k 2 (C) e (D) e . At the equilib- 



