162 CONDUCTIVITY AND VISCOSITY IN MIXED SOLVENTS. 



viscosity retards the velocity of the ions, but we think that the change in the 

 size of the ionic sphere, or the atmosphere which surrounds the ion, should also 

 be taken into account. The movement of the ion depends not only upon its 

 composition, but also upon its attraction for the surrounding solvent, which 

 causes an atmosphere of the solvent to be formed about the ion. Lithium is 

 an extremely slow-moving ion, or, in other words, one with a very large ionic 

 sphere. This atmosphere becomes larger with decreasing temperature. Thus, 

 we have evidence that the change in dimensions of the ionic spheres must be 

 taken into account in dealing with fluidity and, consequently, with con- 

 ductivity from the fluidity data of lithium bromide. The fluidity values are, 

 on the whole, small, due to the large atmosphere surrounding the lithium ion. 

 This atmosphere increases with decrease in temperature, and thus produces the 

 smaller fluidity values at the lower temperature. 



We should not, however, lose sight of the fact that if viscosity is in any way 

 dependent upon the attractions between the molecules, whenever there is a 

 contraction in mixing two solvents, as there is in the case of the alcohols and 

 water, then the molecules will be brought closer together and the attractions 

 will be increased between the molecules. It is obvious from this that we 

 should get a fluidity value different from that calculated from the law of 



averages. 



The statement was made above that fluidities are sometimes additive. 

 That is, the resulting fluidity of a mixture of two solvents is equivalent to the 

 sum of the fluidities of each solvent. Formulated, this would be 



(1) 



where < is the resultant fluidity, <, and < 2 the respective fluidities of the 

 components of amounts ki and k 2 . 



Jones and Bingham * have pointed out that this expression is similar to 

 the conception which we have in electricity, where the conductance of several 

 conductors, in parallel, is represented by the sum of their separate conduct- 

 ances. The conductance of a pair of conductors, of different material, is, 

 for a unit length, 



(o-j + <T 2 )C = CitTj + C 2 <T 2 



where o^ and <r 2 are the areas of cross section of the conductors, c l and c 2 their 

 respective conductances, and C the resulting conductance. 



By a simple mathematical deduction, Jones and Bingham have shown that 

 if fluidities are additive, viscosities can not be additive. They derived the 

 formula 



......... (2) 



1 Amer. Chem. Journ., 34, 481 (1905). 



