Feb., 1953
PARTIAL MOLALVOLUMES OF Cd(N03)2A N D HzO IN CONCENTRATED SOLUTIONS 245
PARTIAL MOLAL VOLUMES OF CADMIUM NITltATE AND WATER I N CONCENTRATED AQUEOUS SOLUTIONS BY WARREN W. EWING AND CHARLES HOLMES HERTY,111 W m . H . Chandler Chemistry Laboratory, Lehigh University, Bethlehem, Penna. Received June 80. 19.51
Density measurements were made on watw sol$iops of cadmium nitrate over a concentration range of one to thirty molal a t five diffet,ctit.trmpcrntur~afrom 26 to 60 . A method based upon Archimedes' principle was used to determine the densities. From thc data obtained, apparent and partial mold volumes of cadmium nitrate and partial molal volumes of water were calculated. Empirical equations were used in the calculations, with the constants for equations determined by the least squares method.
Reports have been made, previously, 'from this Laboratory on properties of the cadmium nitratewater system. These include studies of the freezing point-composition relations and the vapor pressure-composition-temperature relations' and heat of solution relations.2 Data on the partial molal volumes of cadmium nitrate and of water in aqueous solutions are presented in this article. Only the concentrated solution range, 1 to 29 molal or 20 to 87% cadmium nitrate, is covered. The data are for the temperatures 25, 30, 40, 50 and 60'. These data were obtained by experimental determinations of the densities of the solutions, calculation of the apparent molal volumes of the cadmium nitrate from the densities, calculation of the partial molal volumes of cadmium nitrate from the apparent molal volumes, and finally by calculation of the partial molal volumes of the water from the partial molal volumes of the cadmium nitrate. Freshly boiled distilled water was used in making the solutions. The salt was a C.P. grade of cadmium nitrate which was recrystallized four times as the tetrahydrate. The concentrations of the solutions were determined by drying the solutions after the density determinations and calcining the nitrate to the oxide. The error in the,concentrations is estimated as j=0.02%. The solubility of cadmium nitrate a t 25" is about 6295.' Since the solutions are supersaturated above this concentration, considerable difficulty was encountered with recrystallization. This trouble was overcome by heating the solutions to 110' and filtering them through a steam jacketed, sintered glass plate. .These viscous solutions were forced through the filter plate by applying nitrogen pressure. The filtered solutions were then aged three days in a 110' oven. After slowly cooling they remained in the supersaturated state indefinitely . Density measurements were made by an application of Archimedes' principle. The apparatus and technique have been described p r e v i ~ u s l y . ~The apparatus was modified by raising the heating coil to a position j.ust above the bottom of the weighing bottle. This prevented bubbles of gas, which were formed by contact between the n-heptane and the hot wire, from being trapped under the bottom (1) W. W. Ewing and W. R. F. Guyer, J . Am. Chem. Soc., 60,2707 (1938). (2) W.W. Ewing, J. D Brandner and W. R. F. Guyer, ibid.. 61,260 (1939). (3) W. W.Ewing and R. J. Mikovsky, ibid., 72, 1930 (1950).
of t,he bott,le. This method gave a maximum deviation of -0.0003 g./cm.S in the determination of the density of water. Table I contains the experimental values of the densities of the solutions. Values of the apparent molal volumes, 9, were calculated by means of the usual equation
The method of least squares was applied to all values of 9 and the following equations were found to fit the data. TABLE I DENSITIES OF SOLUTIONS OF CADXIUM NITRATE Cd(NOa)z, % 00.000 19.747 20.455 31,149 41.221 43.076 50.654 54.313 60.665 61.560 155. 813 67.866 72.373 75.486 80.274 83.903 84.384 85.064 87.395
m
0.0000 1.0408 1,0879 1,9136 2.9723 3,2007 4.3417 5.0283 6.5233 6.7737 8.1424 8.9328 11.080 13.024 17.212 22.047 22.856 24.089 29.326
~$25"= 42.375
25' 0.9970 1.1524 1.1901 1.3208 1.4680 1.4977 1.6352 1.7080 1.8505 1.8731 1.9803 2.0360 2.1698 2.2684 2.4272 2.5666 2.5817 2.6114 2.7065
30' 0.9954 1.1798 1.1875 1.3177 1.4646 1.4937 1.6308 1.7033 1.8454 1,8681 1.9753 2.0305 2.1640 2.2628 2.4211 2.5594 2.5760 2.6052 2.6995
+ 6.4602m1/a 0.24785m
40' 0.9919 1.1746 1.1824 1.3113 1.4577 1.4860 1.6220 1.6941 1.8352 1.8581 1.9648 2.0198 2.1521 2.2517 2.4090 2.5468 2.5641 2.5929 2.6855
50' 0.9878 1.1692 1.1769 1.3049 1,4505 1.4782 1.6129 1.6850 1.8252 1.8482 1.9547 2.0094 2.1397 2.2403 2.3968 2.5338 2.5521 2.5501 2.6712
60' 0.9832 1.1637 1.1712 1.2983 1.4432 1.4705 1.6036 1.6756 1.8151 1.8381 1.9445 1,9990 2.1276 2.2280 2.3845 2.5209 2,5404 2.5672 2.0571
- O.O273O(ittiV'~
+ 5.8086mVr 0.11561m - 0.0RG583ms/z +40° = 45.301 + 5.1602mV: 0.0082Gm - 0.042521mVr +50" = 46.026 + 5.1636m'/a -
(2)
+30° = 43.648
0.06141m
+60° = 46.132
+ 5.5741mVr -
- 0.034592m8/:
(3) (4) (5)
-0.20870n~ - 0.019800~~*/~ (G)
In comparing the values of 4 calculated from the experimental densities by means of equation (1) with values of 4 calculated by means of equations (2) to (6) the root mean square deviations were found to be a t 25, 30 and 40°, 0.13 ml., at 50°, 0.14 ml. and at 60°,0.15 ml. In Fig. 1 the values of 4 from equation (1) are plotted as circles and the
246
WARRENW. EWING A N D CHARLES HOT~MER HERTY, 111.
72
VOl. 57
curves for equations (2) to (6) are plotted as solid lines. . Differentiation of equation (1) with respect to n2 gave the usual general equation for the partial molal volume of the solute -
Vz
68
= k
+ 3/2am'/z + 2bm + 5/2cma/z
(7)
where the constants are those in equat,ions (2) to ( G ) . The general equation for t,he partial molal volume of water then becomes .
-
V I = 0.01801G -- 1/2arn3/z - hm2 - 3/2cm5//z) (8)
0
64
Curves for the partial molal volumes of tthe salt and of water are plotted in Fig. 1. The first constants in equations (2) to (6) should not be taken as values of +o's, the apparent molal volumes a t infinite dilution, because these equations do not describe the behavior of these solutions in the very dilute range. This method of measuring densities does not give data for calculating 6's of sufficient accuracy for locating the curves to infinite dilution, Regarding the previous work on the partial molal volumes of calcium nitrate,3 Redlich has suggested in a private communication that, since the limiting law for low concentrations is well e~tablished,~ the theoretical coefficient, 9.664, of the square root term should be used in the 25' equation instead of our empirical coefficient, 6.3098. He plotted 6 - 9.664 m'/z versus m. Choosing three points on the smooth curve he obtained the equation
60
56
2d 52 .-
c .e c
s
$25" = 37.56
+ 9.G64in1/z - 0.624m - 0.0427ni8/i
(9)
instead of our equation $25" = 40.164
48
+ 6.3098m1/z + 0.6472m - 0.1903mP/z (10)
19
His root mean square deviations are 0.095 compared with" ours, 0.159. This procedure did not give satisfactory results when applied to the cadmium nitrate data. Consequently the constants in our equations are presented merely as empirical values applying only over the concentration range which was investigated. At 60' these solutions are undersaturated throughout the concentration range studied.' At the lower temperatures the solutions are supersaturated in parts of the concentration range. The continuity of the curves shows that there is no essential difference in the behavior of undersaturated and supersaturated solutions as regards volume relations.
18
17
(4) 0. Redlioh, TAMJOURNAL, 44, 619 (1940).
16
15 0
3-40 50 5 60
4
-
-
Fig. 1.-The partial molal volume of Cd(NOs)z and 1
2
3
4
5
6
H,O, (v2 and (NOa)z, (+).
VI),
and the nppnrant molal volume of Cd-
.'
