Freezing-point Depressions for Electrolytes. 507 



volume, v, in the case of a gas. If pv is plotted against v, the 

 resulting curve is convex towards the axis of v, and passes in 

 general through a point of minimum value of pv. Hence if 

 PV, and therefore equivalent depression, be plotted against 

 V, we may expect to get curves of the same general form. 

 And experiment shows that in some cases at least we do. As 

 in the case of gases the variation of pv is ascribed to the mutual 

 action of the molecules and their finite volume, so in the case 

 of solutions the variation of PV is attributed to similar dis- 

 turbing influences. 



Owing to ionization the curve of an electrolyte will differ 

 from that of a non-electrolyte (1) because of the change thereby 

 produced in the number of the molecules (including free ions) 

 in unit of volume, and (2) because of the change produced in 

 the disturbing influences referred to. The former change is 

 doubtless the more important, and I shall assume the latter to 

 be negligible, for the present purpose. Now dissociation 

 increases continuously with dilution. If therefore association 

 of molecules does not occur, and if the mode of ionization 

 does not change, the equivalent depression must be increased 

 by the dissociation in a ratio which increases continuously with 

 dilution. The change produced in the curve by dissociation, 

 therefore, will be a shear parallel to the equivalent depression- 

 axis and increasing with dilution. The resulting curve will 

 consequently remain convex towards the axis of dilution, but 

 it will be less likely than the curve of a non- electrolyte to 

 exhibit the minimum point. 



If now we plot equivalent depression against ionization- 

 coefficient, instead of dilution, the result will be the same as 

 if we shortened the dilution ordinates of the various points of 

 the curve just mentioned, in ratios increasing with the dilu- 

 tion ; which process must leave the curve convex towards 

 what was the dilution-axis, but is now the ionization-coefficient 

 axis. 



If therefore no change occur in the association of molecules 

 or in the mode of ionization, the curve of an electrolyte on 

 the diagram must start at the intersection of its tangent line, 

 tangentially to that line, and bend away from it, as dilution 

 diminishes, to the right, possibly passing through a point of 

 minimum equivalent depression. We may speak of such a 

 curve as the normal curve for the tangent line corresponding 

 to the given conditions as to constitution in solution and mode 

 of ionization. 



If, the constitution of the electrolyte in the solution remain- 

 ing constant, the mode of ionization changes as dilution 

 diminishes, say in such a way that the molecules dissociate 



