DIFFUSION POTENTIALS 177 



It can readity be seen from this table that large values for u — v 

 can only result, when one of the ions is either a H-ion or an OH-ion. 

 Hence, the diffusion potential of two solutions of a binarv^ electrohie 

 whose concentrations are in the ratio of 1:10 have been calculated 

 for 18°C. to be as shown in table 26. 



This method of calculation is appHcable only when two solutions 

 of differing concentrations of one and the same electrolyte are in 

 contact. For all other cases, the calculation of the diffusion potential 

 is much more comphcated. 



The presentation of equations generally applicable to any solutions 

 containing any mixtures of electrolytes is a difficult and a still 

 unsolved problem. For the case where two solutions are in contact, 

 one of M^hich contains one electrolyte in concentration Ci (and the 

 velocities of its cations and anions are Ui and Vi) , and the other con- 

 tains a different electrolyte in concentration Co (whose ions have the 

 velocities of U2 and V2), the following general equation for tt has 

 been derived by Planck^: 



■K = 0.0001983 T log r 



where ^ is denned by the following theoretical equation : 



log log f 



f C2U2 — CiUi Cl r C2 — Ci 



C2V2 — f ViCi , C2 , , C; — f Ci 



log h log f 



Cl 



When the concentrations Ci and C2 are equal to each other, then 

 the calculation is simphfied considerably. Then, as can be readily 

 demonstrated, the value .t is easily calculated, and, for two solutions 

 of two different binary univalent electrolytes of the same concen- 

 tration Planck's formula becomes 



TT = 0.0001983 T log Hl±Z? 



U2 + Vl 



where ui and Vi are the velocities of the cation and anion, respectively 

 of the one electrolyte, and, correspondingly, U2 and V2 for the other 

 electrolyte. Thus from this formula we obtain, for example, the 



3 Planck, Wiedemanns Annalen 40, 561 (1890). 



