370 SCIENCE PROGRESS 



determination. Even if the mobility of the ions were inde- 

 pendent of the concentration the ratio calculated from the 

 conductivity results would have only a limited value. It is 

 otherwise with the activity coefficient or the thermodynamic 



/y -1— 



degree of dissociation. This is taken as 7 = — for a binary 



° m 



electrolyte like KCl where a^ is the mean activity of the two 

 ions and m is the number of gram mols in one litre. This ratio, 

 of which a large number of values are given in the paper, may 

 be used to displace the degree of dissociation in the older 

 approximate formulae. 



Lewis shows that the activity coefficients, whether calculated 

 from the electromotive force, the vapour pressures of the 

 solute or of the solvent, distribution ratios, or freezing-point 

 data, possess the same value. Remarkable agreement is 

 obtained over a wide range of concentration. The results 

 with sulphuric acid are especially striking ; the activity co- 

 efficient of sulphuric acid (0-60 per cent.) is the same, 

 whether calculated from freezing-points, electromotive force or 

 vapour pressure data. Where the vapour pressure of the sol- 

 vent is employed it is necessary to derive the activity of the 

 solute <22 from the activity of the solvent a^. Lewis and Randall 

 (J.A.C.S., 1 92 1, 43, 233) have shown that 



f dloga^ = -f^d\oga,, 



where N, and Nj denote the mol fractions of the solute and 

 solvent and N^ -f Nj = i. For concentrated solutions this 

 furnishes a fairly satisfactory method of determining the 

 ratios of the activities of the solute between two concentrations. 

 The authors have developed the methods of determination 

 of the thermodynamic degree of dissociation from freezing- 

 point data. The vant' Hoff factor i is a quantity which 

 has been used in the interpretation of dilute solutions of 

 electrolytes. The relation (^— i) is not a measure of the 

 thermodynamic degree of dissociation, nor does it give any 

 valuable information regarding the thermodynamic properties 

 of the solute. The factor i merely gives the ratio of the lowering 

 of the activity of the solvent, to the lowering which would be 



produced by a normal undissociated substance. The activity of 



j^ 



the solute can be obtained from the relationship d log a^ — - — 



Km 



where h is the freezing-point lowering at the molality m and A, 



is the molecular lowering of any undissociated solute at infinite 



dilution. 



In the same paper Lewis has made a noteworthy generalisa- 



