NOVEMBEB 4, 1904.] 



SCIENCE. 



581 



necessary the further conclusion that the 

 degree of ionization of salts, whether de- 

 rived from the conductivity-ratio or from 

 thermodynamic relations involving the 

 equality of the osmotic pressure constant 

 and the gas constant does not vary with the 

 concentration even approximately in ac- 

 cordance with the law of chemical mass 

 action. 



This empirical consequence of the funda- 

 mental hypotheses of the ionic theory has 

 led several investigators to raise a theoret- 

 ical objection to them, it being contended 

 that the laws of thermodynamics require 

 that the validity of these hypotheses in- 

 volves that of the mass action law itself. 

 This apparent inconsistency between the 

 inductive and deductive conclusions makes 

 it probable that some unproved, erroneoiis 

 assumption is tacitly involved in the theo- 

 retical derivation. -That there is in fact a 

 possible alternative, which has, I -believe, 

 been previously overlooked in the thermo- 

 dynamic discussions, will be evident from 

 the following considerations. The thermo- 

 dynamic relations between ionization and 

 freezing point, electromotive force, or heat 

 of solution involve only the assumption 

 that the work done in reversibly separating 

 water from a solution at constant concen- 

 tration is equal to 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 derivation 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 different concentra- 

 tions, and it further involves the assump- 

 tion 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 per- 

 fectly normal ; and it is quite conceivable, ' 

 even though the reason for it be not appar- 

 ent, 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 

 necessarily implies that of the mass action 

 law is, therefore, unwarranted from a de- 

 ductive standpoint ; while the inductive evi- 

 dence, pointing strongly as it does to the 

 substantial correctness of the former prin- 

 ciple and the complete inadequacy of the 

 latter one, makes it highly probable that 

 the separation of un-ionized molecules 

 from ions does involve the expejiditure of 

 other work 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 follow- 

 ing principles: 



The un-ionized fraction of a salt as de- 

 termined, from the conductivity ratio is 

 proportional to the cuhe-root of its total 

 concentration or to that of its ion-concen- 

 tration, between 1/2,000 and 1/10 normal, 

 in the case of ioth uni-univalent and uni- 

 midtivalent salts. That is, 1 — y = Ec^ 



