CHEMISTRY: S. J. BATES 
365 
In order to determine the similar ratios for the undissociated mole- 
cules, the equation corresponding to (2) might be employed. In practice, 
however, it is more convenient to use a different method. By eliminat- 
ing K, Ci and Cu from Storch's equation, [C? /Cu = K], from the differential 
equation obtained from this and from equation (1), the relation 
dUjdCu= -dUi/dCi 
n 
is obtained. That is, having calculated values of dUi/dd and of n 
at any given concentration, by the methods which have been previously 
developed, 2 over a concentration-range, values of dUu/dCu may be de- 
termined, and hence by integration the osmotic pressure of the undis- 
sociated molecules may be calculated. 
The results of such calculations for a few representative di-ionic 
electrolytes for whose solutions reliable freezing-point data^ are avail- 
able are given in the table. They are given as ratios of the form 
dU 
— /RT, The deviations of these from imity show the degree of devi- 
aC 
ation from van't Hoff's law at the different concentrations. For most 
purposes the ratio dU/dC here considered is more useful than the 
integral ratio n/C; for it is the former ratio which is introduced into 
thermodynamic relations in order to derive the mass-action law, the 
electromotive-force equation, etc. Further, the differential ratio gives 
information of a more definite character regarding the properties of 
the solution at any given concentration than does the integral ratio. 
The value of the former depends only upon the properties of the solu- 
tion of the concentration in question, while that of the latter is influenced 
by, and to a great extent depends upon, the properties of the solutions 
of all concentrations from the infinitely dilute solution up to that in 
question. 
Values 
dlli 
of the Ratio 
dCii 
/ RT for 
the Ions 
Equivalents 
per liter 
LiCl 
NaCl 
KCl 
KNOs 
CuS04 
0.001 
0.996 
0.987 
0.927 
0.002 
0.993 
0.983 
0.919 
0.005 
0.990 
0.983 
0.990 
0.899 
0.01 
0.985 
0.986 
0.979 
0.983 
0.867 
0.02 
0.993 
0.983 
0.977 
0.972 
0.824 
0.05 
0.986 
0.980 
0.970 
0.946 
0.756 
0.1 
1.000 
0.973 
0.967 
0.926 
0.734 
0.2 
1.015 
0.963 
0.960 
0.888 
0.3 
1.046 
0.965 
0.958 
0.850 
0.5 
1.110 
0.967 
0.956 
