BETWEEN THE CONDITIONS OF A CHEMICAL CHANGE AND ITS AMOUNT. 217 



may call -4- the rate or velocity of chemical change, and the law may be thus stated : — 



" The velocity of chemical change is directly proportional to the quantity of substance 

 undergoing change." 



The constant a expresses the fraction of the substance which is changed in a unit of 

 time ; this fraction depends upon the other elements of the system, and upon its physical 

 conditions, such as temperature, density, &c. By varying each of these conditions in 

 succession, it is possible to detei-mine a as a function of them, and to predict the pro- 

 gress of the chemical change of a single substance, from its commencement to its com- 

 pletion, under any assignable conditions. 



This simple case of chemical change is of comparatively rare occurrence. Two 

 instances of it are recorded in the preceding pages (pp. 209 & 210, n= 3). It is necessary 

 therefore to investigate the modifications which the general law undergoes in the case 

 of complex reactions. 



Let us first take the case in which the chemical change consists of the reaction of two 

 substances, neither of which is present in the system in great excess. In the discussion 

 of this case we shall assume the general truth of the law of variation of the rate of 

 chemical action, which has been derived from experiments in which the constancy of 

 all the elements but one has been secured by taking them in excess. In fact we shall 

 assume that the truth of the law depends only upon the constancy of the elements, and 

 not upon their excess. Since, then, the velocity of change of each substance is propor- 

 tional to its quantity when the quantity of the other is constant, it follows that the 

 velocity of change is proportional to the product of the quantities when both vary. 

 Let a, b be the number of equivalents of the substances present in the system at the 

 commencement of the reaction, z the number of equivalents of each which has disap- 

 peared during a time x, then a—z, b—z are the number of equivalents remaining at the 

 end of that time ; hence 



~n{a-z){b-z), • (3) 



the solution of which is 



log(l-^)-log(l-3)=»(a-5)^, (4) 



an equation for determining the amount of chemical change, in this case, after the lapse 



of a given time. 



When the substances are originally present in equivalent quantities, a=-b, and (3) 



becomes 



-^=n{a-z)\ (5) 



the solution of which is 



nax (B\ 



z—a --r \y) 



nax+ 1 



The equation connecting the residue y with the time is in this case 



«=_^; (7) 



MDCCCLXVI. 2 H 



