Freezing-point Depressions for Electrolytes. 513 



conclusions as to depression-constants 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 KC1, HN0 3 , KOH, have 1 equivalent 

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

 in solution in single molecules, their curves will be normal 

 1-2 curves. If their molecules are all double or triple, the 

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

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

 they may be 2-3 or 3-4, 3-3 or 3-2 curves respectively, 

 according to the change that may occur. If the molecules 

 are single at extreme dilution, but become double or triple as 

 dilution diminishes, 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 KOI. The LB-B curve (see main dia- 

 gram) is based for the most part on two series of observations 

 in close agreement and by methods exhibiting less divergence 

 than the others. Jones's curve runs a little to the right of 

 it ; Abegg's a little to the left. Both Raoult's and Wilder- 

 mann's cross it, the latter being somewhat steeper, the former 

 less steep. Ponsot's coincides with the lower part of it, but 

 in the upper part diverges to the left. In form the curve is 

 thus probably trustworthy ; but, being plotted with Barnes's 

 coefficients, it may be too high or too low. The R-W and 

 J-W curves (see inset), are not open to this suspicion, but at 

 the dilutions to which even their lower and more trustworthy 

 parts apply they may have begun to diverge unduly right- 

 wards. If the LB curve is plotted with Whetham's co- 

 efficients (extrapolated) it comes into a position (see LB-W 

 curve on inset) to the left of the R-W and J-W curves, the 

 usual relative position of the curves of these observers. 

 Loomis's own curve for somewhat greater dilutions than 

 those of the LB-W curve, when plotted with Whetham's 

 coefficients, coincides very nearly with the boundary-line of 

 the inset. Wildermann's is a little to the left of Loomis's, 

 and somewhat steeper. Both exhibit a slight rightward 

 bending, as do all the others. 



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 

 curvature may be very different beyond the limits of observation from 

 what it is within these limits. 



