370 SOLUTIONS OF CERTAIN HYDROXIDES—MACGREGOR. 
volume of the solution is less than the volume of the water used 
in preparing it. If we treat the data of the above table graphi- 
cally, plotting expansion against percentage composition, we find 
that the contraction has its greatest value, about 0.0041 cu. cm., 
for a solution containing about 5.35 per cent. of the hydroxide, 
and that for all solutions containing less than 10.5 per cent. of the 
hydroxide the expansion is negative. 
The following table is based on Kohlrausch’s observations, 
which were made at a temperature of 15° C.: 
| 
Volume at 15°C.; 
. o| Volume of 1 
Percentage of | Density at 15 grm.of solution of solvent Expansion 
Naot in | (gre peru. For io" c, eu. [Weet sm Let] Gt. ci 
cm.) (cu. cm.) 
4.87 1.0552 0.9477 0.9521 —0.0044 
10.80 1.1222 0.8911 0.8927 —0.0016 
19.66 1.2224 0.8181 0.8041 +0.0140 
29.67 1.3337 0.7498 0.7039 +0.0459 
42.72 1.4685 0.6810 0.5733 +0. 1077. 
_ Kohlrausch’s observations, therefore, substantiate Thomsen’s 
result qualitatively, though the expansions calculated from them 
differ from those calculated from Thomsen’s to a greater extent, 
probably, than is accounted for by the difference in the tempera- 
tures of their solutions. The relation between expansion and per- 
centage composition, according to Kohlrausch, both for this sub- 
stance and for those considered below, is shown in PlateI. The 
curve gives, as the maximum contraction, 0.0045 cu. cm., and 
as the solution exhibiting this contraction one containing about 
6 per cent. of the hydroxide, and it gives about 12.3 per cent. as 
the limit of concentration within which the expansion is negative. . 
The above observations enable us also to determine the values 
of the expansion when the above solutions are prepared by add- 
ing sodium monoxide (Na,O) to water, if we assume that the 
oxide, when added to water, combines with a portion of the 
water to form the hydroxide. 
