THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
143 
Now, in order to make a just comparison, we ought to consider the value for the 
E.M.D. in relation to the ionic volumes in the neighbourhood of the freezing-point. 
But the data at or near 0° C. necessary for making the comparison accurately do not 
exist. We have for KC1 and NaCl obtained the ionic volumes and the ionisation 
coefficients at 18° Cl, and it is probable that the ratios of these values will not be 
sufficiently different at 0° C. to vitiate our comparison, though the values themselves 
will be sensibly different. We will therefore make a comparison on this basis. 
(b) Freezing-point Depression a Linear Function of Ionic Volume. — Jahn (‘ Zeit. 
Phys. Chem.,’ 1904, 50, p. 136) gives a series of values of the molecular freezing-point 
depression for K.C1 and Nad which we will use as the basis ol our comparison. All 
his observations are taken in pairs, on solutions of nearly equal concentration. In 
most cases we have taken the mean of his duplicate observations, but in a lew cases 
the separate results are taken, in order to indicate the order of his maximum errors 
of observation. 
In the following tables are set out for KOI and Nad the following data :— 
N, the number of gram-molecules of the solute per 100 grammes ol water, 
h, the hydration, i.e., the number of gram-molecules of water per gram-molecule 
of solute, 
r, the radions, of which the cube is calculated from A, as described in 
Part III. (/), 
I„, the ionic volume, which in our units is equal to the sum of the cubes ol the 
radions x 10 6 , 
A/N, the molecular depression of the freezing-point as given by Jahn, 
a, the true ionisation coefficient at 18° C., 
D = A/N (l+a), the effective molecular depression ol the freezing-point. 
Table XXV.— Kd. 
N. 
0-3395 
0-3377 
0-259 
0-201 
0-151 
0-100 
0-076 
0-0504 
0-037-8 
0-02552 
0-02527 
h 2/3 . /' K 3 x 10°. r cl 3 x 10° 
0-03345] 
736 
0-03333J 
0-02790 2-870 
0-02357 2-981 
0-01945 3-092 
0-01483 
0-01231 
0-00938 
0-00774 
0-00596] 
0-00592J 
3-223 
3-298 
3-387 
3-439 
3-511 
2-561 
2 ■ 698 
2-813 
2- 929 
3- 066 
3-145 
3-239 
3-294 
3-370 
h- 
297 
568 
794 
021 
A/N. 
6-289 
443 
626 
733 
881 
261 
{\ 
l 
b 
337] 
344 / 
37 
385 
41 
472] 
457 J 
485 
50 
55 
547 ] 
562 J 
CL. 
0-727 
0-749 
0-769 
0-790 
0-819 
0-837 
0-863 
0-878 
0-896 
D - D 
observed, calculated. 
{hi!} 
1-93 
1-91 
1-90 
{ 1•90 } 
1-90 
1-88 
1-89 
n-87 1 
11 - 88 / 
94 
93 
92 
91 
90 
89 
89 
88 
1-875 
Difference. 
- 1 
+ 
± 
- 1 
- 1 
+ 1 
+ 
+ 1 
- 1 
+ 1 
