4 PHYSICAL CHEMISTRY 



takes place with enormous rapidity and with the evolution of 

 heat, whereas the dissociation takes place slowly. As soon as 

 a molecule of water dissociates, its ions recombine to form 

 water. This combination takes place whenever a hydrogen ion 

 meets a hydroxyl ion. Hence, the speed of this reaction obeys 

 physical laws. 



Since ions of opposite charge combine when they meet, the 

 speed of the reaction depends on the rapidity of movement of 

 the ions and their number in unit volume, or concentration. 

 Since the ionic speed of the same ion at constant temperature 

 and viscosity of the solution is constant, the rate of reaction 

 depends on the concentration. This is called the law of mass 

 action. The behavior of the ions may be compared to men and 

 women in a cotillion. Each man has a chance of meeting each 

 woman. Similarly, each cation has a chance of meeting each 

 anion, and the numlber of chances of a cation meeting an anion 

 is the number of cations multiplied by the number of anions, in 

 unit volume. 



Since the concentration of the reacting substances changes 

 during the reaction, the rate of reaction changes, and is usually 

 negatively accelerated. The mathematical process by which the 

 rate at any particular moment is determined is called differentia- 

 tion (differential calculus). The rate is determined by the 

 amount of substance transformed, divided by the time. If the 

 rate were uniform we could find it by dividing the difference 

 in the amount of substance at the beginning and end of an ob- 

 servation period, by the difference in time at the beginning and 

 end of the period. But in an accelerated reaction the rate is 

 changing from moment to moment, and the rate at any particular 



time is expressed by the differential, — . Since the rate cannot 



dt 

 be measured in a moment, it is necessary to use the differential 

 calculus in order to estimate it. For our purposes, however, it 

 is not necessary to go through all of the mathematical reasoning, 

 but merely to use the formula supplied by the mathematician, 

 which varies according to the conditions of the reaction. 



In actual practice, ionic reactions are usually too rapid to be 

 measured. Even the point of equilibrium may sometimes be so 



