154 OX THE DEPRESSION OF THE FREEZING-POINT 



will be a little above that obtained from Loomis' values. As 

 mentioned above, the molecular depression increases as the solu- 

 tions become stronger. 



According to Van't HofFs theory the value of the molecular 

 depression should be 1.86. 1 Loomis found experimentally that, 

 with a large number of non-eleetrolytes in aqueous solutions, 

 the molecular depression was 1.86 for the dilute solutions. In 

 the case of the electrolytes used above, with the ionization coeffi- 

 cients determined by the conductivity method, the values of the 

 molecular depression are seen to be grouped around this value. 

 The divergence from this value may partly be accounted for by 

 the use of the doubtful values of the specific molecular conduc- 

 tivities at infinite dilution for 0, employed in the calculations of 

 the ionization coefficients. 



Mixtures of Solutions of Two Electrolytes. 

 Since equal volumes of simple solutions of two electrolytes, 

 having one ion in common, were mixed, and the molecules of 

 the electrolytes used dissociate each into two ions, expression (2), 

 as there was no change of volume on mixing, reduces to : 

 A = i[M lWl (1 +a,) + M 2 7i 2 (l +*,)] (4) 



in which n^ and 71 2 are the concentrations of the simple con- 

 stituent solutions. For the calculation of A the depression of 

 the freezing-point of the mixture by this expression, the n's are 

 known, the as are obtained by the modification of Prof. 

 MacGregor's method fully described in my former 2 paper, and 

 the M's in the manner referred to above. 



Results of the Calculations. 



Table V gives the data necessary for the calculation of the 

 depression of the freezing-point of mixtures of potassium 

 chloride and sodium chloride, and of sodium chloride and hydro- 

 chloric acid. It also shows the agreement of the calculated 

 with the observed values. The concentrations, molecular depres- 

 sions of the constituent solutions, and the depressions of the 

 freezing-points of the mixtures are expressed as in Table IV. 



1 Phys. Review, 9, 257, 1899. 



* Trans. N. S. Inst. Sci , 10, 124, 1899-1900. 



