DIFFUSION POTENTIALS 175 



case, if it were not for the hindering effect of the electrostatic attrac- 

 tion operating between these oppositely charged ions. The more 

 rapidly diffusing H-ions would establish a flatter gradient, the Cl-ions 

 a steeper gradient. But the electrostatic attractions prevent this. 

 The H-ions are retarded by the Cl-ions, the Cl-ions are accelerated 

 by the H-ions, and an average diffusion gradient results. It is true 

 that the H-ions are slightly in advance, but only insofar as the 

 potential difference developed here permits it. Consequently the 

 more dilute solution becomes positively charged with respect to the 

 more concentrated one. The amount of such predominating H-ions 

 is extremely minute and is beyond chemical measurement, and it is 

 only recognized through the potential difference which develops 

 under these conditions. 



The values of this potential difference can be, according to Nernst,^ 

 calculated in the following way. Let us recall the two ends of the 

 tube the left end of which contains HCl in concentration ci, and the 

 right in concentration C2. Now these two ends are connected by an 

 external metal conductor. The immersed electrodes in this case are 

 assumed to have, for the sake of simplicity, equal and opposite 

 potential differences with respect to the solutions and thus counter- 

 balance each other. Then the E.M.F. of this chain is simply equal 

 to the diffusion potential r. The circuit is now kept closed until 

 F coulombs have passed through the transverse section of the tube. 

 Then the electric work x X F has been accomphshed in a reversible 

 manner. 2 The effect of this work is that a certain amount of H-ions 

 migrated from the stronger into the weaker solution and a certain 

 amount of Cl-ions migrated in the opposite direction; in fact a total 

 of 1 gram-ions had been transported. If the migration-velocity of the 



H-ions = u, and that of the Cl-ions = v, then of 1 mol of ions the 



u . v 



fractions — -; — of H-ions and — ; — of Cl-ions have migrated. The 

 u + V u H- V 



osmotic work to be obtained when 1 mol of H-ions passes from a 



solution of concentration Ci into one of concentration C2 is = 



Ci u u Ci 



RT In - : hence of — ; — moles H-ions the work is — ; — RT In — , and 

 C2 u -f- V u + V C2 



^ W. Nernst, Zeitschr. f. physikal. Chem. 2, 611 (1888); and especially in 

 Ibid. 4, 129 (1889). 



^ On the assumption that the period of time consumed in this experiment 

 is so short that the displacement of substances in the solution through mere 

 diffusion can be neglected. 



