126 Conductivities and Viscosities in Pure and in Mixed Solvents. 



In 1909 Goldschmidt noticed that when weaker acids, such as tri- 

 chlorbutyric, picric, etc., were used as accelerators, the effect of water 

 on the reaction velocity could not be calculated by means of the 

 constant r = 0.15, but that a much smaller value had to be selected. 

 Under these conditions not only the ionized part of the double com- 

 pound alcohol-acid was acting as catalyzer (according to equation II), 

 but also the undissociated portion (as represented in equation I). 

 Consequently, the constant 0.15 was not wholly dependent upon the 

 relation between the ions, and could not be used to characterize the 

 equilibrium hydrogen ion-alcohol-water. Goldschmidt, therefore, de- 

 vised a new way of obtaining this equilibrium constant, namely, the 

 determination of the limiting conductivities of acids in absolute and 

 aqueous alcoholic solutions. 



The molecular conductivity of an acid in absolute alcohol at infinite 

 dilution is expressed by the well-known equation 



Vo=U + V (I) 



where u equals the migration velocity of the cation and v that of the 

 anion. (It is assumed that there are at least two kinds of cations in the 

 solution free hydrogen ions and the complex ions (C 2 H 5 OH, H) + ; 

 but since the ratio of these two must always be constant they may be 

 considered as one.) As soon as water is added, a new kind of ion is 

 formed (H 2 0, H) + . If the concentration of the water added be 

 17 mols. per liter, and the migration velocity of the ions (H 2 0, H) + 

 be u', the conductivity at infinite dilution, /z n , will be expressed by the 

 equation 



ju n = xu +(lx)u'+v (II) 



where x represents the fraction of a gram cation which is still present in 

 the original condition (as free or alcoholated hydrogen ion), and 1x 

 the fraction transformed into the hydrated ion (H 2 O, H.) + Therefore, 

 the equilibrium equation which expresses the distribution of hydrogen 

 ions between alcohol and water, is 



Xf] 



= r 



l-x 



whence 



and 1- 



Substituting these values in (II), we have 



and, since v =HQU, this reduces to 



= (M-tt')i? (HI) 



