HETEROGENEOUS EQUILIBRIA 237 



mined by the freezing point method are approximately seven per cent 

 greater than those determined by the conductance method. Comparison, 

 however, can be made only at two concentrations. The discrepancies 

 in the values appear to be greater than might be expected from any 

 possible errors in the assumed value of A . In the case of magnesium 

 sulphate, there is a marked divergence between the values of the ioniza- 

 tion as determined by the two methods. However, as the concentration 

 decreases, the ionization curves, as given by the two methods, approach 

 each other. 



Considering these results broadly, it may be concluded that the freez- 

 ing point and the conductance methods give values for the ionization 

 which fall very nearly within the limits of experimental error at concen- 

 trations approaching 10~ 3 normal for solutions of the binary salts, and 

 that in the case of solutions of salts of higher type the differences between 

 the values, as determined by the two methods, do not, in general, exceed 

 one per cent at low concentrations for salts of the uni-divalent type. 

 For salts of the di-divalent type, the discrepancies between the values, 

 as determined by the two methods, are markedly greater, lying in the 

 neighborhood of 5 per cent, and the same is true of lanthanum nitrate. 

 In general, however, in the case of salts of higher type, the divergence 

 of the values determined by the two methods diminishes as the concen- 

 tration decreases. 



Considering the results of freezing point determinations, it is a strik- 

 ing fact, the significance of which cannot be ignored, that, as the concen- 

 tration decreases, the molecular depression of the freezing point increases 

 and approaches a limiting value, which, in the case of salts of different 

 types, corresponds with the ionic structure of these salts and which is 

 in agreement with the fundamental ionic reactions assumed by the ionic 

 theory. So the value of i for the binary salts approaches a value of 2, for 

 ternary salts 3, for quaternary salts 4, etc. While the significance of the 

 agreement between the results of freezing point and conductance meas- 

 urements remains uncertain, the fundamental importance of the fact that 

 the limits approached in the two cases are substantially the same should 

 not be overlooked. 



The difference between the results by the two methods at the higher 

 concentrations are readily explainable, since the calculation of the num- 

 ber of molecules present in a mixture is based upon the assumption that 

 the laws of dilute solutions hold. Even in the case of non-electrolytes, 

 the laws of dilute solutions fail to hold at concentrations as low as 0.1 

 normal, and it is therefore a priori probable that the laws of dilute solu- 



