CHEMISTRY: S. /. BATES 
367 
pressure of the undissociated molecules and their concentration. In 
the case of potassium chloride these relations, one for the ions and one 
for the undissociated molecules, express the results for solutions between 
0.001 normal and 0.5 normal, so closely that the average difference 
between the total osmotic pressure of the solution calculated from them 
and that experimentally determined is but 0.10 percent. 
The behavior of the undissociated molecules of copper sulphate 
is remarkable in two particulars. First they show an almost constant 
deviation from van't Hofl's law from 0.001 normal to 0.02 normal. 
In the second place, while the bivalent ions are considerably more 
abnormal than are the univalent ions, the undissociated molecules of 
this salt obey van't Hoff's law much more closely than do those of the 
uni-univalent salts. 
H. Jahn^ and recently G. N. Lewis^ have considered it to be less reason- 
able to assume that (1) the concentration of the ions is proportional 
to the electrical conductivity of the solution, than it is to assume that 
(2) the concentration of the ions is proportional to their osmotic pressure 
or activity, that is, that the ions are normal or that they obey van't 
Hoff's law. Parallel to this latter assumption is the one that (3) the 
undissociated molecules are normal. The degree of ionization calcu- 
lated upon any of these three assumptions is different from that cal- 
culated upon the other two. That is, the acceptance of one compels 
the rejection of the others. 
It may be shown in another way that the experimental data are such 
that it is not possible for both the ions and the undissociated molecules 
of strong electrolytes to be normal. By combining the mass-action 
law relation, C]/Cu = K, and the differential equation derived from this 
with the thermodynamic equation (1) above, it can be shown, that the 
necessary and suflBicient condition that the law of mass-action hold over 
a certain concentration range is that at all concentrations dlli/dCi = 
dUu/dCu] that is, that the rates of change of the osmotic pressures of 
the ions and of the undissociated molecules with their respective con- 
centrations be the same. Since the mass-action law is not obeyed by 
solutions of strong electrolytes this relation does not hold, and the 
relation 11 = Ci^r cannot be true for both molecular species. The 
computation of the mol-number i from freezing-point data, and the 
calculation of the degree of ionization on this basis, assumes that both 
the ions and the undissociated molecules are normal. Since the result- 
ing values do not obey the mass-action law, the method is incon- 
sistent and theoretically incorrect. It has long been recognized that 
actual gases are not ^perfect' gases. Unfortunately the idea that in 
