New Theories of Solution. 



359 



(fJb v ) to 



solution 



its 



molecular conductivity in an infinitely dilute 

 , i. e. in one where it is completely dissociated*. 



It' the dissociated proportion is a I = — J, then for every mole- 

 place, 



mginal 



cule which would be present if no dissociation took 

 there are now actually 1 + 2a molecules ; for each 

 molecule on dissociation becomes three, /. e. contributes two 

 additional molecules. We must, therefore, multiply the 

 freezing-point as deduced from the theory of osmotic pressure 

 by the factor i=l + '2a determined for each concentration. 

 Kohlrausch's results give us both //-„ and juu^. His estimate 

 of fj,^ for ^H 2 S0 4 as 370/10 7 Siemens units is admittedly 

 only a rough one, for the molecular conductivity for in- 

 finite dilution is difficult to determine in the case of many 

 acids and bases. It is quite definite, however, with salts ; and 

 by applying the dissociation theory we can deduce fi n for 

 ^H 2 S0 4 with great accuracy from fj, m for ^K 2 SG 4 , the differ- 

 ence between the values for potassium and hydrogen salts 

 being constant according to the theory. The number thus 

 obtained is 356/10 7 , and with it the accordance between experi- 

 ment and theory is complete. 



With respect to the deviations from constancy shown by 

 stronger solutions, Mr. Pickering states that on the osmotic- 

 pressure theory the depression of the freezing-point in their 

 case should be abnormally small. This conclusion is reached 

 from somewhat crude mechanical considerations regarding the 

 balance of attraction between the solvent and the dissolved 

 molecules (Journ. Chem. Soc. lvii. pp. 354, 355 ; Phil, Mag. 

 xxix. p. 500). The matter is not nearly so simple as Mr. 

 Pickering imagines. Even in the case of true gases (oxygen, 

 nitrogen, &c.) there is a deviation from Boyle's Law, first in 

 one direction and then in the other, as more and more gas is 

 compressed into a given volume. In a solution the relations 

 are much more complex, and it is impossible at present to 

 predict what the behaviour of any particular substance in 

 solution will be with regard to osmotic pressure (and the 

 freezing-point) when the concentration passes beyond certain 

 limits'!". Mr. Pickering commits a strange mistake when he 

 writes the following sentence (Chem. News, lxiii. p. 171) : — 

 " It is also remarkable that Professor Arrhenius should be so 

 anxious to show that strong solutions have an abnormally high 

 freezing-point, since he starts by telling us that according to the 



* Cf. Ostwald, Outlines of General Chemistry, p. 285. 

 f Information on this point will be found in a paper by A. A. Noyes, 

 Zeitschr. physikal. Chem. v. p. 53. 



