358 Dr. James Walker on the 



an independent judgment of his accuracy, shows his mean 

 .error in any one set of determinations to be many times 

 greater than his own estimate of it. The maximum deviation 

 exhibited by alcohol now falls within the magnitude of the 

 experimental error ; and thus Mr. Pickering's observations 

 must be looked upon as furnishing one more confirmation of 

 Blagden's Law and of van 't Hoff's theory. 



With regard to the other three solutions, they cannot be 

 expected to follow this simple law, if the theory of electro- 

 lvtic dissociation is true. The theory, however, when applied 

 in conjunction with van 't Hoff's expression for the molecular 

 lowering, given above, enables us to calculate the freezing- 

 point of dilute electrolytic solutions provided we know their 

 conductivity. Now very accurate determinations of the con- 

 ductivity of dilute solutions have been made by Kohlrausch, 

 and from these Dr. Arrhenius has been at the pains to calcu- 

 late the freezing-points of the solutions studied by Mr. 

 Pickering, in order that a comparison might be instituted 

 between the theoretical and the experimental numbers. A 

 table embodying the results is given in the B. A. Report, 1890, 

 p. 325 (Chem. News, lxiii. p. 148) , and from it will be seen that 

 the agreement in the case of weak solutions is as satisfac- 

 tory as could be wished for. Arrhenius has there indicated 

 the method of calculation, but it may be well that the matter 

 should be looked into in somewhat greater detail, so that it 

 may serve as an example of how such calculations are made, 

 and show on what exceedingly simple principles they rest. 



We find from van } t Hoff's formula that a normal aqueous 

 solution of a non-electrolyte, i. e. a solution containing one 

 molecular weight (in grams) per litre, freezes at — l o, 90. 

 But sulphuric-acid solutions conduct electricity readily, which 

 means, in the light of Arrhenius'' s theory, that the molecules 



are to a great extent dissociated into charged molecules H 



and S0 4 . Each original molecule on dissociation gives three 



+ + - 

 charged molecules (H 2 S0 4 = H + H + 80 4 ), which act, as far 

 as the freezing-point is concerned, exactly like any other 

 molecules. If the whole of the sulphuric acid in a normal 

 solution were thus dissociated, the freezing-point would be, 

 no t -l°-90, but -l°-90 x 3= -5°'70. We know, however, 

 that this is not the case, and that the dissociation varies with 

 the dilution ; so that it remains to determine the dissociated 

 proportion of the sulphuric acid at the various concentrations. 

 According to the theory this is given by the ratio of the 

 molecular conductivity of the substance in a given solution 



