NOTES
820
Melting points were meawred as followe. About 10 ml. a 150 x 20 mm. loosely stoppered test-tube was warmed at 50" for ten minutes to erase the sample': thermal history, stoppered tightly and stored a t 0 f 0.01 for 20 hours. A Neoprene ball, dig 1.17, and diameter 0.5 cm. was inserted under the surface of the gel, the stopper replaced and the tube heated a t the rate of 5" per hour. The melting point was taken as the temperature at which the ball reached the bottom of the tube. The reproducibility of the method is about *0.3". af solution in
THERMAL DIFFUSION NEAR THE CRITICAL SOLUTION TEMPERATURE * BY L. J. TICHACEK A N D H. G. DRICEAMER Department of Chemisfru and Chemical Engineering, University of IlEinoie, Urbana, Illinois Received Janlurrlr Id, 1966
The thermal diffusion ratio CY for a binary system is defined by the flux equation -.F
JI
- pD
--c
[grad XI
- axl (1 - XI] 1 grad 2'1
(1)
Vol. 60
t ~ r e .Since ~ there is no necessity for the numerator to go to zero a t this point, CY should increase greatly in magnitude as we approach the critical solution temperature. To test this hypothesis thermal diffusion measurements were made on the system isooctane (2,2,4trimethylpentane) perfluoroheptane. The isooctane was Phillips pure grade. The perfluoroheptane was obtained from Minnesota Mining and Manufacturing Co. It was carefully redistilled and a cut boiling from 82.2 to 83" was retained. I n order to operate with a AT of 1 - 2 O , a special cell was designed as a modification of our standard cell.4 The cell is shown in Fig. 1, and is largely self-explanatory. The fritted glass was seated in a groove etched in the glass body of the cell and sealed in with sauereisen. The AT was measured using iron-constantan thermocouples. The cell is in many ways more useful than our standard cell. The results are shown in Fig. 2. Because of the small AT'S used, considerable scatter was inevi-
From the thermodynamics of irreversible processes it is possible to derive an expression for a2 where
0
- 7.0the Vi's are partial molar volumes, P is the average volume and Oi* is the heat of transport of component i. For our present purposes, the factor in the denominator XI bpccl/bXl is of most interest. In an ideal solution it equals RT. It approaches zero as one ripproaches the critical solution tempera-
- 6.0d.
- 5.0-
-
- 4.0- 3.0a
-7
-2.0-
I
6
I
I
- 1.0-
b
0
I
I
I
0
20
I
40 60 VOLUME FRACTION
I
80
I(
nC,Fl,.
Fig. 2.-Thermal diffusion ratio cy us. composition system n-perfluoroheptane (2,2,4-trimethylpentane).
table. X ( b p / b X ) can be written using ScatchardHildebrand theory.
bx;
= RT [I
x1
Fig. 1.-Glass walled thermal diffusion cell: 1, I , thermocouples; 2,2, sample taps; 3, sample tap scaling screw; 4,4, agitators; 5, fritted glass diaphragm, cemented in; 6, wall of cell chamber-glass tubing; 7,7, Teflon gaskets; 8,8, holes for connecting screws; 9, coolant takes. (1) This work was supported in part by the AEC. (2) L. J. Tiohacek, W. 5. ICmak and H. G. Drickamer, THIEJOURN A L , 60, 060 (1956).
where pi
"'"I
- VRTR
(3)
= volume fraction i
7 = average molar volume.
The subscript R refers to the value relative to the value at the C.S.T.
(3) J. H. Hildebrend and R. L. Scott, "Solubility of Non-Electrolytes," 3rd Ed., Reinhold Publ. Corp., New York N. Y.,1950, p. 253. (4) R. L. Saxton, E. L. Dougherty, Jr., and €1. G. Driokamer. J . Chem. Phya.. 11,1166 (1954).
NOTES
June, 1956
It can be shown that use of a Flory-Huggins type entropy correction would not affect the calculations materially for this system. If one assumes, quite rashly, that the heats of transport (and partial molar volumes) are independent of temperakire and rompmition in this range then relative values of (Y can be cnlculnted TI [1
-?SR1
T [I
-E;:]
-CY = a*
VR T R - A
(4)
Using Tc = 23.2’ ( V ~ ) C , F , ~= 0.45 as the best ~ 0.45 estimated values and using 25’ and ( P C ~ F , = as the fiducial state (A), the calculated ratios vary in the same manner as the experimental ratios, but considerably more rapidly with temperature and composition. If Tc were about 10-12°, the agreement would be substantially better, but there is no justification for using this latter value. TABLE I CALCULATED AND EXPERIMENTAL VALUESOF a T, C.
25 30 45 a Using Tc
PC,F~(
-
0.18 .45 .45
(a/aA)
erp.
0.21 .63 * 43
(a/aA)
oalcd.
0.036 .28 .10
/ a ~ (a/ar)a
0.17 .72 .42
loo.
Part of the discrepancy is probably caused by averaging properties even over 1-2” in a region where they vary rapidly with temperature, and by the approximate solution theory used. Doubtless the major error is the assumption that the heats of transport are independent of temperature and composition in this region.
82 1
very fragile and brittle. The resulting fragments were irregular with no apparent cleavage planes. The search for a single crystal was a hit-or-miss affair. The material was ground and sieved; particles that would pass a 50-mesh sieve but not a 100-mesh one were collected. These chunks were waled in capillaries of 0.2 to 0.3 mm. diameter and manipulated under a binocular microscope (36 X ) until an isolated fragment could be fixed in place by being jarred into a constricted portion of the capillary. Three suitable single crystals, isolated in this way, were mounted on a Weissenberg camera and photographed using Cu K a radiation. By chance the three rotation axes were [110], [loll and [Oll]. A facecentered orthorhombic cell was obtained from the Weissenberg patterns. More precise dimensions for this cell were then derived from a powder pattern taken with Cr K a radiation. These dimensions are compared in Table I with the data of Juza, Weber and 0pplz who chose a different orientation of the axes. Also listed in the tables are experimental densities and densities which we calculated for the two sets of data with 16 molecules per unit cell.
r
T ~ L E
CELLDIMENSIONS AND DENSITY OF SODIUM AMIDE This work a = 8.964 f 0.003 A. b = 10.456f 0.003 c = 8.073 f 0.003
Juxa. Weber and Opp*
b = 8.929ka c = 10.427
a = 8.060 Density (expt. 1 1.40b 1.39” (calcd.) 1.37 1.38 a Converted from kx. units; last digit in doubt. By flotation. By pycnometer.
*
Q
T H E CRYSTAL STRUCTURE OF SODIUM AMIDE1
The systematic absences correspond to certain special positions in space group Fddd--Dz42h. It was easy to show, as described elsewhere,‘ that the BY ALLANZALK~NAND DAVID H. TEMPLETON sodium and nitrogen positions are Uniuera‘ty of California Radiation Laboratory and Department of Chemistry, Livermore and Berkeley, California 16 Na in f): (0, y, 0; 1/4,1/4 y, 1/4) F Received January 7. 1966 16 N in [g): f (0,0, z ; 1/4,1/4,1/4 z ) F In a recent note, Juza, Weber and Oppzdescribed in agreement with Juza, Weber and Opp, taking the crystal structure of sodium amide. We stud- account of the different assignment of axes. A p ied the structure independently and arrived a t the proximate values of y and z from inspection of the same arrangement of sodium and nitrogen atoms, intensities were 0.15 and 0.25. The structure was but found slightly different values for the cell di- refined by onedimensional Fourier calculation of the electron density along (O,y,O) and (O,O,z). The mensions and atomic coordinates.3n4 Sodium amide was prepared by Dr. W. L. Jolly intensities used were obtained mostly ftom the best at the Livermore laboratory by the direct combina- set of Weissenberg patterns, which were for rotation of molten sodium and ammonia gas at 300°.6 tion about [Oll ], by visual comparison with a set of The resulting material was a fused yellowish mass standard exposures. Layers zero through three covered by a layer of unreacted sodium. The prod- were used. They were normalized to a common uct was removed from its crucible for investigation basis by means of equivalent reflections which fell in an argon-filled dry box. The yellowish white in different layers for this orientation. Figures 1 and 2 show the electron density along and opaque material when crushed was found to be (1) This research was performed under the auspices of the U. 8. the b- and c-axes, respectively. The parameters chosen, after a minor backshift correction, are y = Atomic Energy Commission. (2) R. Juza, H. H. Weber and K. OPP, Naturwisscnacha~fen, 42, 125 0.146 and z = 0.236, compared with 0.142 and 0.233 ( 1955). by Juza and eo-workers.2 The structure factors (3) A. Zalkin and D. H. Templeton, Abstracta, Summer Meeting calculated for this final structure using Na+ and N American Crystallographic Association, Pasadena, California, 1955. atomic form factors,6J were also used t o calculate (4) A. Zalkin and D. H. Templeton, U. S. Atomic Energy Commis-
*
sion Report UCRL-4557 (1955). (5) L. M. Dennis and A. W. Browne, “Inorganic Syntheses,” Vol. 1, McGraw-Hill Book Co., New York, N. T.,1939.
+ + ++
(6) “International Tabellen sur Beetimmung von Kristallstrukturen,” Vol. 11, Borntriiger. Berlin, 1935. (7) J. A. Hoerni and J . A. Ibers, Acta Cyst., 7 , 7 4 4 (1954).
