January 13, 1905.] 



SCIENCE. 



51 



same empirical equation describes the be- 

 havior of binary and of ternary electro- 

 lytes. This last fact appears to be fatal 

 to all explanations based on the assumption 

 that electrostatic effects are the disturbing 

 factors. While the mutual attraction or 

 repulsion of two ions or of three ions may 

 easily change the dissociation formula for 

 a binary or a ternary electrolyfe, it is very 

 improbable that the changes will be such 

 as to make two radically ditt'erent formulas 

 identical. Of course, the hypothesis of 

 hydrated ions gives us some leeway but 

 the outlook is not what it was five years 

 ago. It is too soon yet to say whether we 

 are merely to remodel the electrolytic dis- 

 sociation theory or whether we are to re- 

 place it by something else. My own opin- 

 ion is that reform is what is needed and not 

 revolution. It is evident, however, that 

 we have gone ahead too fast and that we 

 must test more thoroughly the premises on 

 which our conclusions are based. We know 

 of one error. The proportionality between 

 molecular weight and osmotic pressure 

 holds only for the cases in which the heat 

 of dilution is zero. This is stated clearly 

 in van't IToff's original deduction of the 

 van't Iloff-Raoult formula n/N = \og 

 p/p-,, but has been pretty generally over- 

 looked. Since the heat of dilution is rarely 

 zero in any actual case, our deductions as 

 to the molecular weights of solutes are 

 always somewhat in error. In the case of 

 the metals of the alkalies and the alkaline 

 earths dissolved in mercury, the lowering 

 of the vapor-pressure due to the heat of 

 dilution is practically equal to that due 

 to the molecular weight, and we therefore 

 have the surprising result that the appar- 

 ent molecular weight is only aboiit one 

 half the atomic weight. One of the first 

 things we have to do is to eliminate this 

 source of error in all cases. 



Another distressing feature in the quan- 

 titative physical chemistry of to-day is that 



the field which, it covers is daily growing 

 less. A tenth-noi'mal solution is now con- 

 sidered a concentrated one, and some people 

 are so extreme as to maintain that we can 

 not expect agreement between theory and 

 experiment for anything except infinitely 

 dilute solutions. To my mind a theory 

 which holds only for infinite dilution is 

 necessarily wrong. Here again one prob- 

 able source of error is easy to find. The 

 van't Hoft'-Raoult formula is deduced on 

 the explicit assumption that there is no 

 specific attraction between solvent and 

 solute. If this assumption is wrong, it is 

 reasonable to suppose that the error thus 

 introduced would become less as the con- 

 centration approaches zero. Under these 

 circumstances the van't Hoff-Raoult for- 

 mula might represent the facts at infinite 

 dilution without being a true formulation. 

 This is the case with another well-known 

 and important formula. The Helmholtz 

 and the Nernst equations, for the electro- 

 motive force of concentration cells are 

 identical for infinitely dilute solutions and 

 for these only. The Nernst equation 

 ignores the concentration of the undis- 

 sociated salt, while the Helmholtz formula- 

 tion does not. The two equations become 

 identical at the moment when the concen- 

 tration of the undissociated salt and the 

 disturbing factor due to it become zero, 

 that is, at infinite dilution. Since the 

 Helmholtz formula applies to all concen- 

 trations, the Nernst formula is necessarily 

 only approximately accurate. This has 

 been recognized explicitly by Planck, 

 though the point is often overlooked. It 

 is quite conceivable that the shortcomings 

 of the van't Iloff-Raoult formula may be 

 due in part to theoretical inaccuracies and 

 that we have laid too much stress on 'vari- 

 ations from the gas laws. ' 



If we introduce the conception of a 

 specific affinity between solvent and solute 

 in certain cases, notably those in which the 



