THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
149 
Let us now calculate the effective molecular freezing-point depression, not upon 
the total amount of water present but upon the amount of free water obtained from 
the above expression. The expression for the E.M.D. calculated in this way is 
py = _^_ 
N'(l +«)’ 
where N' is the number of gram-molecules of the solute in 1000 grammes of 
water. We have then 
1ST = 
lOOON 
w 
and 
D' = D. 
w 
1000 ' 
In the following table are set out the values of D resulting from Jahn s data (taken 
from the column “D calculated” in Table XXV.), together with the other data 
necessary for the calculation of D', the effective molecular depression of the freezing- 
point calculated on the amount of free water. It will be seen that we obtain a 
constant value for D ; , up to about twice decinormal solutions, the mean value of the 
constant being 1*867. 
Table XXVIIIa. 
N. 
i„. 
w. 
grammes. 
0-201 
5-794 
971 
0-151 
6-021 
977 
o-ioo 
6-289 
984 
0-076 
6-443 
987-5 
0-0504 
6-626 
991 
0-0378 
6-733 
993 
0*0254 
6-881 
995 
D. 
D'. 
Difference 
from mean. 
1-92. 
1-864 
-3 
1-91 
1-866 
-1 
1-90 
1-869 
+ 2 
1-89 
1-866 
-1 
1-89 
1-873 
+ 6 
1-88 
1-867 
+ 
1-875 
1-866 
1 
We may recapitulate the method by which the above figures are obtained. The 
ionic volumes measured in arbitrary units having only relative values were deduced 
from the corrected conductivity data. The factor y which was required to give us 
the absolute volume for a gramme equivalent of KOI in solution, with its combined 
water, was deduced from the viscosity data. The volume of free water so deduced, 
when applied to calculate the effective molecular freezing-point depression, gives us 
for this a constant value, which is in correspondence with the value obtained for 
non-electrolytes. We thus obtain a striking confirmation of the validity of the 
hypothesis and of the method pursued, and at the same time illustrate the dependence 
of the various physical properties considered upon the varying size of the hydrated 
ions caused by the varying amount of water with which they combine.* 
* The corresponding values for NaCl solutions give the constant as U860 for high dilutions, but for 
lower dilutions the value is too low, indicating over-correction. This may indicate that either the ionic 
volumes deduced for NaCl, or the value 0-030 for y, may be slightly too high. The larger ionic volume 
for the Na ion renders any error much more effective in disturbing the constant. 
