Irreversible simultaneous linear reactions. 217 



velocity constants of the reactions involved. It will be seen that 

 equation (2) is of the form y = a(l — e~ bx ), so that the amount of 

 each product which has been formed varies with the time in the 

 same manner as we found experimentally for the rate of evolution 

 of carbon-dioxide from solutions containing oxalacetic acid phenyl- 

 hydrazone. 



By putting t = oo we find the final amount of C n produced is 



h n 



* = 2k *■ '' 



it is thus equal to the initial concentration of the original substance 

 multiplied by the ratio of the particular velocity constant con- 

 sidered to the sum of all the velocity constants. 



We see therefore that by determining the final concentrations 

 of the various products we can determine the values of the m 



fractions =■£- . If we substitute the values thus found in the 



equation (1), we obtain the absolute value of Xk n in terms of the 

 ratio of the concentration of the nth product at a time t, to the 

 initial concentration of the original substance, and of t ; so that 

 we can obtain the absolute value of %k n from a series of observa- 

 tions of the variation of the amount of any one of the substances 

 formed with the time. In this manner all the m quantities k n may 

 be completely determined. This method has been applied to the 

 case of the phenylhydrazone of oxalacetic acid (loc. cit., page 

 1157). 



Preliminary experiments show that the decomposition of oxal- 

 acetic acid itself in aqueous solution is more complicated than that 

 of its hydrazone ; products other than carbon-dioxide and pyruvic 

 acid are produced in increasing quantity as the concentration of 

 the acid solution is diminished. The authors are attempting to 

 apply this method to the investigation of this reaction. 



