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 16 N in [g): f (0,0, z ; 1/4,1/4,1/4 z ) F Received January 7. 1966 In a recent note, Juza, Weber and Oppz described 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).
NOTES
822
Vol. 60
cluding zero ones, R is calculated as 26.5.8 The standard errors in y and x , by the method of Cruikshank,9 are 0.001 and 0.005, respectively. The complex shape ofthe anhedral crystal made absorption correction prohibitively difficult; this was not attempted, although it is recognized as an important omission. We calculate the following interatomic distances 2 Na-N
2 Na-N 2 Na-Na 1 Na-Na 1 N-N 2 N-N 4 N-N 2 N-N
2.44 A. (2.38, ref. 2) 2.49 (2.50, ref. 2) 3.05 3.06 3.81 3.88 3.99 4.11
The minimum nitrogen-nitrogen distance of 3.81 A. :s much longer than that of the weak hydrogen bo, ‘s in solid ammonia, 3.38 A. or the even shor, hydrogen bonds observed in other compounds.10 Thus there are no hydrogen bonds in this structure, as is also true of lithium amide.” Each sodium atom has four nitrogen nearest neighbors and vice versa. The four nitrogen neighbors have a nearly regular tetrahedral arrangement around the sodium atom as shown in Fig. 3A, but the four sodium neighbors of a nitrogen have a highly distorted tetrahedral arrangement as shown in Fig. 3B. These sodium atoms are concentrated toward one side of the nitrogen, and the packing in a model shows vacant holes on the opposite side of the nitrogen. It is suggested that the hydrogen atoms, being less negative than the nitrogen, will be located on the side away from the sodium neighbors, in positions described below. b r
I
0
I
I I I 0.2 0.3 0.4 0.5 b. density distribution along the b axis.
0.1
Fig. 1.-Electron
-Observed
---- Calculated (Includes temperature foctor correction for N , exp(-$ sin* e); B = 1.19 x lO-”l Calculated ( N o t corrected for temperature factor)
A B Fig. 3.-Coordination geometry in sodium amide: A, nitrogen configuration about sodium; B, sodium configuration about nitrogen.
0
0.1
0.2
0.3
0.4
0.5
C.
Fig. 2.-Electron
density distribution along the c axis.
electron densities, which are included in the figures for comparison. In order to get coincidence of the curves it was necessary to include a temperature factor, exp (--B sin2B/X2) with B = 1.19 X for nitrogen, but a factor of unity for sodium. For 126 reflections permitted by the reflection rules, in-
The sodium-nitrogen distances correspond to a radius of about 1.60 A. for the amide ion, corrected to coordination six by Zachariasen’slz method. This value is reasonable but not necessarily very significant because of the peculiar coordination geometry. Since the amide ion is isoelectronic with water, it is expected to have a bond angle slightly greater than a right angle. Thus the two hydrogen atoms must be in general positions related by the twofold axis, since special positions would require the molecule to be linear. With reasonable estimates of (8) A table of calculated and obssrved structure factors is avadablc upon request from the authors; i t i s also given i n ret. 4. (9) D. W. J. Cruikshank, Acta C r y s f . , 2, G5 (1949). (10) J. M. Robertson, “Organic Crystals and Molecules.” Cornel1 University Press, Ithaca. N. Y., 1953, p. 244. (11) R. J u r a and K. Opp, 2.anorg. allgem. Chem., 266, 313 (1951). (12) W. H. Zschariasen, “American Crystallographic Association Meeting Abstracts,” Pennsylvania State College, April 1950.
NOTES
June, 1956 the dimensions of the amide ion, we investigated the packing of the hydrogen atoms with those from the neighboring amide ions and with the neighboring sodium atoms. For reasonable interatomic distances free rotation is impossible. The best packing was achieved with hydrogen parameters x = 0.08
y = -0.03 z = 0.32
This arrangement gives for the minimum distances H-N H-H H-H
= = = H-Na =
1.01 A. (covalent bond, assumed) 1.6 A. (hydrogens of same amide ion, assumed) 2.3 A. (hydrogens of neighboring amide ions) 2.2A.
Figure 4 illustrates the hydrogen atom packing.
a
Fig. 4.-Hydrogen
823
tion of scavenger solutes, e.g., iodine, a t moderate concentrations in solution, but strongly dependent in gas phase decompositions. It appeared to us that the production of ethane in solution is an example of diffusion recombination such as we have studied in other systems and that a t higher concentrations of iodine a decrease in ethane yield should occur and be susceptible to treatment by our semi-empirical e q ~ a t i o n . ~ Acetyl peroxide, obtained as a 25% solution in dimethyl phthalate, by courtesy of the Buffalo Electrochemical Co., was decomposed at ca. 0.01 M in toluene a t 70 and 85". Initial concentration of peroxide was determined by i ~ d o m e t r y . ~Product gases were collected, measured and subjected to mass spectrometric analysis. I n several experiments, with and without added iodine, the first-order rate of production of carbon dioxide was verified. A rate constant of 1.53 X 10-6 set.-' a t 70" and an activation energy of 30.4 kcal./mole were obtained, in satisfactory agreement with previous work.6 The ratio of ethane to carbon dioxide was determined at iodine concentrations up t o 0.1 M . The ratio decreased with increasing iodine concentration but showed no measurable change with temperature. Since we have shown that carbon dioxide production is not affected by iodine, it follows that the efficiency of the ''cage" recombination of methyl radicals is being diminished by iodine. The diffusion-recombination equation previously developed has been applied to this phenomenon by taking 2C2H6/COz to be the efficiency of recombination of methyl radicals, W,(X). Figure 1 shows that log
T
packing in sodium amide.
Powder patterns of this material photographed a t approximately -120 and 160' indicated no structural change from room temperature. We are indebted to Dr. W. L. Jolly and Mr. Saul Siege1 for providing the pure samples and t o Dr. E. R. Bissell for the density measurements. .SI
DIFFUSION-RECOMBINATION I N DECOMPOSITION O F ACETYL PEROXIDE' BY JAMESR. NASH,WILLIAM H. HAMILL AND RUSSELL R. WILLIAMS, JR.
1 I
2
3
4
6
6
7
8
0
IO
Contribution from the Radiation Project, Department of Chemistry, University of Notre Dame, Notre Dame, Indiana Received January 9, 1966
(mole froction 4 )"' x 100. Fig. 1.-Decomposition of acet 1 peroxide in toluene solution; W = 2&Hs/C02.
It has been suggested by Levy and Szwarc2 and further demonstrated by Rembaum and Szwarc3 that ethane production in thermal decomposition of acetyl peroxide in various solvents results from a "cage" recombination of methyl radicals produced in dissociation of a single molecule of peroxide. The ratio CZ.&/CO~is independent of the concentra-
(1 - W , ( X ) ) is a linear function of (X12)'/zas indicated by the equation. Assuming that no primary (i.e., non-diffusive) recombination occurs, the intercept yields Pl (5.75 ypO)-' = 0.033 and the slope yields PIPz'/~ (3.24 y2) = 0.17, where y is the mean free distance of diffusion and pa the distance of
(1) Work supported in part by the U. S. AEC under contract At(ll-1)-38 and U. S. Navy equipment loan contract Nonr-06900. Presented at the 129th Meeting of the American Chemical Society, Dallas, Tex., April 8-13, 1956. (2) M . Levy and M. Szwarc, J . A m . Chem. SOC.,7 6 , 5981 (1954) (3) A. Rembaum and M . Szwaro, ibrd., 77, 3486 (1955).
(4) (a) J. C. Roy, R. R. Williams, Jr., and W. H. Hamill. ibad., 1 6 , 3274 (1954); (b) J. C. Roy, W. H. Hamill and R. R. Williams, Jr., ibad., 77, 2953 (1955). (5) C. D. Wagner, R. H. Smith and E. D. Petera, Ind. Enp. Cham.. Anal. Ed., 19, 976 (1947). (6) hf. Levy, M. Steinberg and M. Szwarc, J . A m . Chem. Soc., 76, 6978 (1954).
