178 HYDROGEN ION CONCENTRATION 



figures in table 27 (for tt) for solutions of equal concentrations at 

 18°C. 



When more than one electrolyte are present in each of the two 

 solutions the following substitutions must be made in the above 

 formulas : 



UiCi substituted by u/ci' + Ui'd" + .... 

 U2C2 substituted by U2'c2' + U2"c2" + . . . . 

 ViCi substituted by Vi'ci' + Vi"c2" + . . . . 

 V2C2 substituted by V2'c2' + V2"c2" + . . . . 



where the subscripts 1 and 2 denote, as before, the two solutions in 

 contact, while the superscripts (', ", etc.) refer to the different kinds 

 of ions. 



Planck's equations (the first, general one, as well as the second, 

 special one) apply to the case where all electrolytes consist of two 



TABLE 27 



HCl, NaCl 0.0315 volts NaCl, KCl - 0.0044 volts 



HCl, KCl 0.0268 volts NH4NO3, KCl 0.0006 volts 



NaOH, NaCl - 0.0173 volts 

 KOH, NaCl - 0.0127 volts 



univalent ions. When all the ions present are n-valent then the 



potential amounts to -th of its value as shown by the equation. 



n 



But in cases where ions of different valences occur the calculation 



assumes great difficulties which have not yet been solved. 



The condition on which Planck based his calculations is that the 

 two solutions which are in contact should not be mechanically mixed 

 and that the above mentioned temporarily stationary concentration 

 gradient had been established. 



P. Henderson^ making a somewhat different assumption concern- 

 ing the connecting boundary between the two solutions, deduced for 

 certain conditions an equation which has the advantage over Planck's 

 of not being theoretically transcendental. Henderson assumed 

 that the connecting boundary is not the result of spontaneous diffu- 

 sion of the two solutions in contact, but that it ensues through a 



* P. Henderson, Zeitschr. f. physikal. Chem. 59, 118 (1907); 63, 325 (1908). 



