316 PHYSICAL CHEMISTRY 



that done in producing the same volume-change in a gas, which implies, 

 of course, that the ions and un-ionized molecules have in the presence 

 of each other normal osmotic pressures. On the other hand, the deri- 

 vation of the Mass- Action Law equation is based on cyclical processes 

 which necessarily involve the separate introduction and removal of 

 the un-ionized molecules and of the ions into or from solutions of dif- 

 ferent concentrations, and it further involves the assumption that this 

 introduction or removal of molecules or ions can be effected by the 

 application of an external pressure equal to that osmotic pressure 

 which each of them possesses in the mixture; that is, the possibility 

 is ignored that the separation of the molecules from the ions may 

 itself give rise to some new force, and may involve, consequently, 

 another quantity of work than that corresponding to the osmotic 

 pressure. The ionic theory would evidently predict a result of this 

 kind if an attempt were made to separate the positive ions from the 

 negative, even though their osmotic pressures when present together 

 were perfectly normal; and it is quite conceivable, even though the 

 reason for it be not apparent, that the separation of the un-ionized 

 molecules from the ions, with which they may be in electrical as well 

 as chemical equilibrium, should involve an abnormal quantity of work. 

 The assertion that the validity of the osmotic-pressure principle nec- 

 essarily implies that of the Mass-Action Law is therefore unwarranted 

 from a deductive standpoint; while the inductive evidence, pointing 

 strongly as it does to the substantial correctness of the former principle 

 and the complete inadequacy of the latter one, makes it highly pro- 

 bable that the separation of un-ionized molecules from ions does in- 

 volve the expenditure of other ivork than that corresponding to their 

 osmotic pressures. 



Since the ionization does not change with the concentration in 

 accordance with the Mass-Action Law, it is natural to inquire what 

 the law of its change is. This matter has been investigated from 

 an empirical standpoint by several investigators with the help of the 

 conductivity data. The results justify the statement of the following 

 principles : 



The un-ionized fraction of a salt as determined from the conductivity- 

 ratio is proportional to the cube root of its total concentration, or to 

 that of its ion-concentration, between -^Q-Q an d y 1 ^ normal, in the case of 

 both uni-univalent and uni-multivalent salts. That is, \ f = Kci, or 

 1 f = K(cf)*, where ?-is the degree of ionization, c the concentration 

 and K a constant. The first of these functions was proposed by Kohl- 

 rausch, the second by Barmwater. Owing to the relatively small 

 variation of the ionization, these two functions cannot differ much as 

 to their constancy, but on the whole the experimental data indicate 

 that the second function is somewhat more constant. The average 

 deviations of the actual measurements from the values corresponding 



