86 WORK OF J. N. PEARCE. 



The atomic volumes of the halogens chlorine, bromine and iodine, are approxi- 

 mately the same. If their ions are hydrated we should expect them to combine 

 with the same amounts of water, and, therefore, they should have migration velocities 

 of the same order of magnitude. This has been found to be the case. The atomic 

 volume of fluorine has not been determined, but from its position on the migration - 

 velocity curve we should infer that its atomic volume is smaller than that of the 

 halogens, and that its ion possesses a considerable degree of hydrating power. 



Further, it will be noted that the migration velocities of the halogens are almost 

 identical with those of the alkalis standing next above them in order of atomic 

 weights, whereas their atomic volumes are very much smaller. This leads us to 

 believe that the compensation, which brings about an equalization of the migration 

 velocities of the two groups, is due to the increase in volume of the alkali ions by 

 hydration. 



The silver ion alone, of all the metallic elements for which satisfactory data can 

 be found, presents an exception. It has a small atomic volume, and its salts crystal- 

 lize from solution without water. We should expect it to have but slight hydrating 

 power in solution, and it should, therefore, have a high migration velocity, but this 

 has been found to be slightly less than that of the halogens. 



According to the law of Raoult, the lowering of the freezing-point of a given 

 weight of solvent by a dissolved substance is directly proportional to the amount 

 of the substance dissolved, providing that substance is a non-electrolyte. In the 

 case of electrolytes the lowering produced by gram-molecular weights of the dis- 

 solved substances are greater than those produced by gram-molecular weights of 

 non-electrolytes. This abnormality in the case of electrolytes is explained by the 

 fact that an ion and a molecule lower the freezing-point to the same extent. 



The fact is that the freezing-point method gives us a relation between the amount 

 of solvent acting as such and the number of dissolved particles, whether they are 

 molecules or ions. 



Having determined the freezing-point lowering for any concentration of a given 

 electrolyte, it is an easy matter to calculate the amount of dissociation. For binary 

 electrolytes a is obtained from the expression a = i 1, where i is the van't Hoff i. 



For ternary electrolytes, a = , and for quaternary electrolytes a = . 



We have calculated the values of a from the molecular lowerings of all the solutions 

 studied, for the dilute solutions up to the concentration at which the molecular 

 lowering passes through a minimum. Beyond this concentration the molecular 

 lowering of the freezing-point increases, due to hydration, and, consequently, the 

 calculated dissociation would increase. For that reason the values of a have not 

 been calculated. 



In the case of every salt studied, without exception, the dissociation as calculated 

 from the freezing-point lowering is higher than the dissociation as calculated from the 

 conductivity measurements. 



This will be seen by comparing the values obtained for a in the tables representing 

 the freezing-point and conductivity measurements for each salt. 



