20 
CHEMISTRY: NO YES AND MacINNES 
Proc. N. a. S. 
pressures. We have recourse, therefore, to a simple thermodynamic 
relation between activity and electromotive force. This relation may be 
derived by considering the work or free-energy decrease attending the 
transfer of one mol of the substance (for example, of 1 HCl) from the solu- 
tion in which its vapor-pressure is pi to that in which it is p2- This free- 
energy decrease — AF is given by the familiar expression — AF = RT 
log {pi/ pi)' In this expression, in view of the above considerations, we 
may substitute for the vapor-pressure ratio the ratio (ai+ai~)/(a2+a2~) of 
the product of the activities of the ions, yielding the equation 
™ 4- ™ - 
— AF = i^riog 
a2+a2~ 
We thus obtain what may be regarded as a secondary, but more general 
definition or measure of activity. 
The simplest process from a theoretical standpoint (aside from that 
already described involving passage through the vapor phase) by which' 
a substance can be transferred from one solution to another is one in which 
this transfer is brought about in a voltaic cell. Thus in the case of hydro- 
chloric acid, we can cause a transfer of one mol of the acid from concen- 
tration Ci (activity ai) to concentration C2 (activity 02) by causing one fara- 
day (f coulombs) to pass through the cell 
H2 (1 atm.), HCl(c2), AgCl + Ag, HCl(^7i), H2 (1 atm.). 
The electromotive force K of this cell multiplied by the quantity of elec- 
tricity is, therefore, the work which can be obtained from the change 
in state under consideration, or the free-energy change attending it. That 
is, 
ai+ ai~ 1 ^^1^0:1"'' Oil~ 
AF = = RT log -^—^ = RT log 
ai C2'^a2^ 0:2 
It will be noted that in the last of these expressions there has been written, 
in place of the activities a of the ions, products ca, in which the quantity 
a, called the activity-coefficient, is evidently the factor by which the total 
concentration c of the substance must be multiplied to give the activity 
of the ion. 
By the use of this electromotive-force method the authors of this paper 
have, with the aid of their students, carried out a series of determinations 
of the activities of typical substances. Two of these researches, those on 
potassium chloride^ and on hydrochloric acid,^ have already been published; 
and two more, on lithium chloride and potassium hydroxide, will soon be 
described in detail in the Journal of the American Chemical Society. These 
last investigations were carried out, with the aid of grants from the Car- 
negie Institution of Washington, by Mr. J. A. Beattie and Mr. Ming Chow, 
respectively, using cells, with dropping amalgam electrodes, of the fol- 
lowing types : 
