CHEMISTRY: D. A. MACINNES 
527 
algebraic sum of the number of equivalents of ion that are carried across 
it from the concentrated to the dilute solution, in this case equal to 
fic — {1 — fic) = 2nc — 1. If we now make the assumption that the 
osmotic work involved in the transferring of a gram equivalent of posi- 
tive ion from a dilute to a concentrated solution is the same as the work 
necessary for the transfer of a corresponding amount of negative ion, 
we can obtain the electromotive force at the liquid junction by the sim- 
ple proportion : 
(ElF : EF = {2nc - 1) : luc or Ei = E (1 - l/2nc). (1 
This equation contains only the directly measurable quantities E and tic, 
and contains no assumption concerning the concentrations of the ions 
in the two solutions. 
A direct test of this simple equation is not possible; but an indirect 
one is afforded by the following considerations. The electrode-potentials 
of cells of the type Ag, AgCl (soKd) + MCI (Ci), AgCl (solid) +MC1 
(C2), Ag would be expected to be the same whether hydrogen or any one 
of the alkali metals is chosen for the radical M, if the concentrations of 
Ci and C2 are the same in each case and below about 0.05 normal. The 
sum of the electrode-potentials is determined by the difference of the 
osmotic pressures of the chloride ions in the two solutions; and this 
difference of osmotic pressure is, probably, nearly the same for dilute 
solutions of chlorides of ulnivalent cations at corresponding concen- 
trations, since the degrees of dissociation in dilute solution as determined 
by the conductivity method have been found to be nearly the same 
for these substances. If this is true, and if the assumption involved 
in the above-given expression for the potential at the liquid junction is 
correct, the sum of the electrode-potentials should be independent of 
the nature of the cation. This amounts to the assumption that the 
free energy of dilution of the chloride ion is the same whether hydro- 
gen, potassium, or sodium is the cation, since the process at the 
electrodes during the operation of a cell consists in the formation of one 
equivalent of chloride ion in the dilute solution and the removal of the 
same amount of chloride ion from the concentrated solution per faraday 
passed through the cell. Jahn's accurate work (loc. cit.) on concentra- 
tion cells with hydrochloric acid, potassium chloride, and sodium chlo- 
ride is, fortunately, well adapted to test these conclusions. 
Table I, which is self explanatory, gives the result of my calculations, 
ba^ed on Jahn's electromotive-force data, which are here given in 
millivolts. The transference-numbers are from Noyes and Falk's^ 
compilation. 
