364 
CHEMISTRY: S. J. BATES 
constant, and T is the absolute temperature, does not hold; for, if all 
of the molecular species entering into an equilibrium obey this law, the 
law of mass-action is a thermodynamic necessity. ^ 
In this paper is outlined and applied a method for determining the 
extent to which the ions and the undissociated molecules deviate from 
van't Hoff's law, that is, for determining the relation between the osmo- 
tic pressure of the ions or of the undissociated molecules and their con- 
centration. The significance of the results, particularly as applied to 
the calculation of the degree of ionization and to the validity of the law 
of mass-action, is discussed. 
Besides the laws of thermodynamics, the assumptions involved in 
these calculations are that (1) in a dilute solution of a di-ionic electro- 
lyte the osmotic pressure due to each of the two ions is the same, and 
that (2) the degree of ionization (7) is given by the conductance-vis- 
cosity ratio (Xr7/Xo7]o), the concentration of each ion then being Cy 
and that of the undissociated molecules C{\-y). These assumptions 
are generally accepted; they are, however, briefly discussed below. 
The total osmotic pressure (n) of a solution is due in part to that of 
each of the two ions and in part to that of the undissociated molecules. 
Since by the first assumption above stated, the osmotic pressure of one 
ion is equal to that of the other, the relation 11 = 211* -\- Hu follows. 
The principles of thermodynamics, together with the same assumption, 
lead for equilibrium in a solution of di-ionic electrolyte, to the relation^ 
26?n,/Q-Jn,/c, = o (1) 
If now Ci and Cu are calculated from conductance data, and if the total 
osmotic pressure of the solution be known (from direct measurements 
or from freezing-point determinations, etc.), there remain in these two 
equations but two unknown quantities Hi and 11^. 
The solution of these two equations gives for the rate of change of 
the osmotic pressure of the ions with their concentration the relation: 
^3 = 1/ , dWCi) y 
dCi [c 2-303 dlogCil 
The first term IT/C may be calculated directly from the data. The 
second term, which is small in comparison with the other, may be con- 
veniently evaluated by the graphic method of plotting values of 11/ d 
against those of log d and determining the tangents. Having cal- 
culated dlli/dCi for a series of concentrations, values of ILi/d may be 
determined by integration, either graphic or algebraic. 
