84 
CHEMISTRY: J. H. ELLIS 
for it a new quantity, which may be regarded as the 'effective ion-con- 
centration' and which has been appropriately called by Lewis^ the ac- 
tivity of the ions. This quantity has been shown by Lewis to be ther- 
modynamically related to various other properties of solutions, thereby 
on the one hand increasing its practical significance and on the other 
affording independent means of evaluating it. 
The most general of these thermodynamic relations, one indeed which 
may well be regarded as the best practical definition of activity, is that 
afforded by the equation Fi — F2 = RT log (^1/^2) in which R is the 
perfect-gas constant and Fi — F2 represents the decrease in the free- 
energy of the system attending the transfer at the absolute temperature 
T of one mol of any substance (thus of an ion) from a solution of any 
concentration in which its activity is a 1 to another solution of any con- 
centration in which its activity is the free-energy decrease being 
defined in general to be equal to the maximum work W producible by 
the change in the state of the system under consideration diminished 
by the attendant increase in the product of its volume and pressure 
(that is, Fi - F2 = W - {P2V2 - piVi) ). 
The most direct way of determining the free-energy-decrease attend- 
ing the transfer of ions from one concentration to another, and thereby 
of determining their relative activities, is the measurement of the elec- 
tromotive force of cells in which such a transfer takes place; and it is 
with such a study of the ions of hydrochloric acid that this investigation 
deals. Namely, measurements have been made of the electromotive 
force at 18, 25, and 35° of cells of the form H2 (1 atm.), HCl (at various 
concentrations), Hg2Cl2 (solid) + Hg. If two such cells are considered 
to be placed in series in opposition to each other, the changes at the 
electrodes of the two cells compensate each other, and the net change 
in state when one faraday (f coulombs) of electricity passes through 
it is the transfer of 1 HCl or of 1 H+ and 1 CI" from one solution to 
the other. Considering the ions, we have therefore the relation: 
(E2 - El) F = 7^1 - 7^2 = 2 RT log (ai/a2), 
in which E2 — Ei is the difference in the electromotive force of two 
cells in which the acid has the free-energies F2 and Fi and its ions have 
the activities ^2 and ai, respectively. For ^2 and we may substitute 
^2^2 and aiCi in which a2 and ai are activity-coefficients (analogous to 
ionization-coefficients) representing the factors by which the concentra- 
tions C2 and Ci of the acid must be multiplied to give the activities of 
the ions. 
The mean corrected values of the observed electromotive force in 
