34 GENERAL AND PHYSICO-CHEMICAL. 



example is the inversion of cane-sugar by means of acid. This reac- 

 tion is monomolecular because only the cane sugar is consumed. If 

 the concentration of the cane-sugar at the beginning is C moles, and if 

 x moles are transformed in t time, then at that time there are (Cx) 

 moles remaining. If dx indicates the quantity- which is transformed 



in dt time, then the reaction velocity is . According to the law 



dt 



of mass action this is at every moment proportional to the concentration 

 of the decomposing substance, -or 



f -*?-*). , a) 



For practical use this equation is integrated into the following: 



fc = -nat. log. - (2) 



t (_/ x 



If the theoretical considerations upon which this formula is based 

 are correct, then the x values determined by the polariscope after various 

 times must give the same figure for k. This is indeed the case. 1 k is 

 called the velocity coefficient (also velocity constant or specific reaction 

 velocity). If in the equation (1) Cx or the concentration of the still 



dx 



undecomposed cane-sugar =1, then the equation becomes -r k. from 



dt 



which it follows that k indicates the reaction velocity if the concentra- 

 tion of the substrate could be kept the entire time at = 1 . 



In these experiments k retains the same value. If in different experi- 

 ments the quantity of catalyst (acid) varies, then the obtained value 

 for k is proportional to the concentration of the H ions. This is so 

 prominent that the catalytic action of acids is due to the H ions (Ait- 

 RHENIUS 2 ) . Still irregularities occur as the anions of acids as well as 

 of salts present can under certain circumstances influence the action of 

 H ions (see page 70). 



FRANKEL 3 has recently studied the decomposition of diazoacetic ether under 

 the influence of different acids. The reaction is as follows: 



N 2 : HC.CO.O.C 2 H 6 -hH 2 0=HO.CH 2 .CO.O.C 2 H 5 +N 2 . 



1 See Poggend. Ann., 81, 413 and 499 (1850). 



2 Zeitschr. f. physik. Chem., 4, 226 (1889). 

 8 Ibid., 60, 202 (1907). 



