226 ON A DIAGRAM OF FREEZING-POINT 



dilution, not much more trustworthy than their components.* 

 It is much safer, therefore, to base conclusions as to depression 

 constant on moderate dilution curves, although the conclusions 

 they admit of may not be so exact as we might wish. 



Discussion of the Curves. 



Electrolytes such as NaCl, HN0 8 , KOH, have 1 equivalent 

 in the single molecule, and 2 ions. If, therefore, they exist in 

 solution in single molecules, their curves should be normal 1 2 

 curves. If the molecules are all double or triple, the curves 

 should be 2 4 or 3 6 curves, provided the association does 

 not involve change in the mode of ionization. If it does, they 

 may be 2 2, or 3 4, 3 3, 32 curves respectively, according 

 to the change that may occur. If the molecules are single at 

 extreme dilution, but become double or triple as dilution dimin- 

 ishes, the curves should start as 1 2 curves, and undergo 

 the appropriate transformation. 



The electrolyte for which we have the most complete and 

 trustworthy data, is KC1. The LB B curve is based 

 on two series of observations in close agreement and 

 by a method exhibiting less divergence than the others. 

 Jones's runs a little to the right of it ; Abegg's a 

 little to the left. Both Raoult's and Wildermann's cross it, the 

 latter being somewhat steeper, the former less steep. Ponsot's 



* It follows that it is inadmissible to proceed as Raoult has done in determining 

 depression constants, (loc. cit. p. 658), viz., by selecting high dilution curves which are 

 in agreement, and applying extrapolation to a mean curve derived from them ; for such 

 procedure may mean the selection of observations made by methods which have char, 

 acteristic errors of the same sign. In fact, a mean curve based on observations whicn 

 agree well at low dilution, but disagree markedly at high dilution, would be likely to 

 give a better result, as more probably combining observations with small characteristic 

 errors of opposite sign. Raoult's procedure is open to other objections. For (1 ) his 

 curves of equivalent depression against total depression, make series of observations 

 appear to be in greater disagreement than they really are, and are thus not helpful in 

 making a judicious selection of observations to be used ; and (2.) extrapolation of such 

 curves not only gives a result affected by the average of the characteristic errors of the 

 observations used, but also neglects the possibility, in some cases the probability, that 

 owing to change in association and mode of ionization, the law of the change of curv- 

 ature may be very different beyond the limits of observation, from what it is within 

 these limits. 



