202 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



varies with the temperature and the concentration is not known. If 

 the absolute hydration of the ions is large, then it is to be expected that 

 the hydration will change at higher concentrations. It is possible, 

 therefore, that at concentrations below 1.2 normal the hydration of the 

 ions may be considerably greater than at the higher concentration. 



As we have seen in an earlier section, at higher temperatures the 

 conductance of the more rapidly moving ions approaches that of the 

 more slowly moving ions. At the same time, as we have seen, the con- 

 ductance of the more slowly moving ions changes almost in exact pro- 

 portion to the fluidity change of the solvent. It may be concluded, 

 therefore, that, at higher temperatures, the hydration of the more rapidly 

 moving ions increases and approaches that of the more slowly moving 

 ions, such as that of the lithium ion. It is probable, therefore, that as 

 the temperature increases the net transference of water diminishes, while 

 the absolute amount of water associated with the ions increases. 



3. Calculation of Ion Dimensions from Conductance Data. Lorenz 2a 

 has calculated the ion dimensions from the ion conductances, by means 

 of the Einstein-Stokes 2b equation. The values obtained for the ion 

 dimensions have been compared with those obtained by other methods, 

 as determined from the density of substances in a condensed state, assum- 

 ing close packing of the molecules. For ions containing a large number 

 of atoms, particularly large organic anions and cations, the calculated 

 values from the conductance data agree well with those derived by other 

 methods. In the case of the simpler ions, however, a similar agreement 

 has not been found. In the case of the alkali metals, for example, 

 lithium, which has the smallest atomic volume, has the lowest conduct- 

 ance, while caesium, with the largest atomic volume, has the highest 

 conductance. It has generally been assumed that the reversal in the 

 order of the conductance of the ions of the alkali metals is due to 

 hydration. 



Born 2C and Lorenz 2d consider that the Einstein-Stokes equation is 

 applicable even in the case of small ions and that the observed diverg- 

 ence is due to electrical interaction between the charge on the ions and 

 the adjacent solvent molecules. This electromagnetic frictional effect 

 is the greater, the smaller the volume of the ion. The total frictional 

 effect which the ion experiences is thus the sum of two effects, one of 

 which decreases and the other of which increases with decreasing ionic 

 diameter. The function which expresses the ionic resistance in terms 



2a Lorenz, Ztschr. /. Elektroch. 26, 424 (1920) ; Ztschr. f. pliys. Chem. 73, 252 (1910) ; 

 also, numerous articles in the Ztachr. f. Anory. Chem. 

 ab Einstein, Ann. d. Phys. 11, 549 (1905). 

 ac Born, Ztschr. f. Elektroch. 26, 401 (1920). 

 2d Lorenz, loc. cit. 



