CHEMICAL AFFINITY. 423 



the volume in which it is contained, and this enables us to 

 give an exact expression for a balanced action of any type. 



Suppose that we have two acids A and A 1 , with their 

 salts S and S\ and that A and S 1 are dissolved in such a 

 quantity of water that their active masses are each re- 

 presented by 1. Then, at the beginning of the action, 

 we have the two interacting to form the other pair A 1 and 

 S, the chemical equation being A + S 1 = A 1 4- S. 



After equilibrium has been reached, i.e., when the two 

 opposed reactions are balanced so that in a given time just 

 as much of the pair A, S 1 disappears as is produced in the 

 same time by the interaction of the pair A 1 , S, a certain 

 amount ^ of the original salt and acid will have been trans- 

 formed, so that their active masses are now no longer 1, 

 but 1 — ^. The rate at which these pass into the other 

 acid and base is proportional to the active mass of each, so 

 that we have — 



rate A, S 1 -> A\ S = /6(i - x ) (1 - x ), 



where k is a constant, expressing the amount of the re- 

 action in unit time when the concentration of each of the 

 reacting substances is unity. Now the active masses of 

 the second acid and base are \ and y. respectively, for just 

 as much of each of them has been formed as there has 

 disappeared of the others. We have therefore — - 



rate A 1 , S -> A, S 1 = k l x-x> 



where k l is the velocity constant of the second reaction. 

 But the amounts transformed in unit time are equal at the 

 point of equilibrium, so that we have — 



or K = - = X 3 



» ('-x) ! 



It is therefore easy from a determination of the amounts 

 of the various substances present at the point of equilibrium 

 to ascertain K the ratio of the velocity constants of the 

 opposed reactions. Julius Thomsen employed a thermo- 

 chemical method for determining the extent to which the 

 action of one acid on the salt of another had taken place. 



