NOVEMBEE 10, 1911] 



SCIENCE 



627 



the un-ionized substances than to the prop- 

 erties of the ions. The divergence of tri- 

 chloracetic acid from the simple dilution 

 law may similarly be due to an inherent 

 property of the un-ionized acid, a single 

 cause being not improbably at the bottom 

 of both the great tendency to split into ions 

 in water and also the abnormal behavior 

 towards dilution. 



However that may be, I think the fol- 

 lowing reasoning goes far to show that the 

 non-ionized portion of the electrolyte is 

 that which is primarily abnormal in its 

 behavior, the ions acting in every way as 

 normal. The dilution formulas of Ostwald 

 or of van't Hoff are essentially equilibrium 

 formula. One side of the equilibrium rep- 

 resents the interaction of the ions to form 

 the non-ionized substance, the other side 

 represents the splitting up of the non- 

 ionized substance into ions. In order to 

 fix our ideas, we may consider a salt which 

 obeys the empirical dilution-formula of 

 van't Hoff. If Cu represents the molar 

 concentration of the un-ionized portion, and 

 Ci the molar concentration of each ion, 

 then according to van't Hoff's empirical 

 formula, 



e? 



— - ^const. 



If the law of mass-action were obeyed we 

 should have, on the other hand, Ostwald 's 

 dilution formula. 



According to this last formula, the activ- 

 ity of each substance concerned varies 

 directly as its molar concentration, and a 

 normal result is obtained on dilution. 

 According to van't Hoff's formula as 

 stated above, the activity of none of the 

 substances concerned varies directly as its 

 concentration; but since the constancy of 

 the expression is the only test of its accu- 

 racy, there are obviously other methods of 



stating the relation which will throw the 

 abnormal behavior either on the ions or on 

 the non-ionized substance. Thus, if we 

 write the equivalent form 



-— = const. , or - — ^ const. , 



the un-ionized substance is here represented 

 as behaving normally, and the ions ab- 

 normally; whilst if we write the formula 

 in the form 



—r^,=^ const., 



the ions are represented as behaving norm- 

 ally, and the non-ionized substance ab- 

 normally. Now it is very important that a 

 choice should be made amongst these three 

 expressions, all equivalent amongst them- 

 selves so far as the mere constancy of the 

 expression is concerned, as tested by meas- 

 urements of electrolytic conductivity. 

 Looked at from the kinetic point of view 

 we have in the first form, 



dt-'^"' 



di-"""' 



both direct and reverse actions abnormal. 

 In the second form, we have 



the ionization being abnormal and the 

 recombination normal. 



Now, if it were possible to measure di- 

 rectly the velocity of either ionization or 

 recombination, we should at once be able to 

 select the equilibrium formula which was 



