724 ACTIVITY COEFFICIENT OF THE HYDROGEN ION 



later, the velocity in this range of pH is proportional to the hydrogen 

 ion concentration. Also since the products formed are weak bases 

 we have the condition that'^ 



RNU2 + HCl ^ R NH,. HCl (1) 



and hence, when RNHz is large compared to Ch; (assuming complete 

 ionization of the HCl) 



k 



Ch = 



C/?NHs 



i.e., the hydrogen ion concentration and hence the velocity of the 



reaction will be inversely proportional to the amount of products 



formed. 



dx k' k' 

 Velocity = - = ^ Ch = = - 



This, as Arrhenius^^ pointed out is the condition which causes Schiitz's 

 rule since on integration it becomes 



X = k' Vr 



In Fig. 4 the results have been plotted against the square root of 

 the time and it will be seen that the experiment in which the hydrogen 

 ion concentration was 7iot kept constant (by means of buffers) obeys 

 Schiitz's rule very well; i.e., the amount of products formed is pro- 

 portional to the square root of the time. Reactions in which the 

 rate is inversely proportional to the amount of products formed 

 have been quite frequently observed. A very clear case which was 

 completely worked out and the mechanism verified experimentally 

 is that of the oxidation of oxalic acid by bromine studied by Richards 

 and Stull.^'* Similar reactions are discussed by Miiller.^^ The writer 



^" The complete equation would be 



+ HCl ;=^ A'NHj HCl ;=:i RNut + CI" 



iJNHa • ' J r - ^ 



+ H20^i?NH30H i?NH, + H"*" 



At the range of pH under consideration, however, the equilibrium may be repre- 

 sented approximately by (1). 



^■^ Arrhenius, S., Medd. Kong, vetsakad. Nohelinst., 1908, i. 



1^ Richards, T. W., and StuU, W. N., Z. physik. Chem., 1902, xli, 544. 



15 MiiUer, W., Z. physik. Chem., 1902, xli, 483. 



