212 ON A DIAGRAM OF FREEZING-POINT 



tangent lines for the electrolytes examined, on various assump- 

 tions as to constitution in solution and mode of ioniZation, and 

 for k= 1.85. They are indicated by the inscriptions 1 2, 2 3, 

 etc., the first figure in each giving the number of equivalents in 

 the molecule as it is assumed to exist in solution, and the second, 

 the number of free ions into which the molecule is assumed to 

 dissociate. Thus 1 2 is the tangent line for an electrolyte such 

 as NaCl, on the assumption that it exists in solution in single 

 molecules, each of which has therefore 1 equivalent, and disso- 

 ciates into 2 ions. If assumed to associate in double molecules, 

 with unchanged mode of ioni/ation, its tangent line would be 

 indicated by 2 4, and if the double molecules were assumed to 

 dissociate into Na and NaCl 2 , by 2 2. The line for H a S0 4 , on 

 the assumption that its molecules undergo no association, and 

 have thus 2 equivalents, and that they dissociate each into 3 

 ions, would be 2 3 ; and 4 6 would be its line if it associated 

 into double molecules, dissociationg each into 6 ions. 



In a few cases dotted lines have been introduced, to show 

 what the tangent lines would be with other values of k, 1.83, 

 1.84, 1.86, 1.87, the constant used in such cases being indicated. 

 The curve for any given electrolyte, must start at the inter- 

 section of its tangent line with the line : a = 1, to which point we 

 may refer, for shortness, as the intersection of its tangent line. 

 What its form will be, may be anticipated from the following 

 theoretical considerations : The equivalent depression in dilute 

 solutions of non-electrolytes, is proportional to the osmotic pres- 

 sure, P, and the dilution, V, which corresponds to the product of 

 the pressure, p, and the specific 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, in some cases at least, 

 that 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 attrib- 

 uted to similar disturbing: influences. 



