NOTES
364
since all these derivations depend on the limiting values of the slopes a t infinite dilution, it is quite immaterial which function of the dielectric constant or solute mass is used. This is illustrated in the table, where it is apparent that for values of eI2 €1 up to 0.01, the slopes of the two dielectric functions are within 0.3% of each other, and that the same is true of the density and specific volume for density changes up to 0.002 g./ml. The more marked difference in slope between the density and specific volume is relatively unimportant, since such measurements are usually made with far more precision a t low concentrations than is possible in the case of the dielectric constant measurements, although in dilute solutions of highly polar molecules the reverse may be true. Thus, since the values of (e12 - l ) / ( e l z 2) usually have t o be calculated a t some stage anyway, and since the final expression for P2 is simpler, the following approach has been used in this Laboratory. We put
+
+
where x2 = N 2 / ( N 1 Nz), the mole fraction of solute. Similarly, for the density di2
By definition
= dr
+ bxz
+ x2P2 = -+ 21 XlMl + x2M2
+
A.
tl9
-
tl
0.000
.001 .002 .005
.01
- l)/(eir
+ 2)
A(ar
- l)/(r~z f -
A(m
2)
€1)
...
0.2980814 ,2982456 .2984097 .2989010 .2997199 A(ui
- vid/A(dia - d d 1.310 1.306 1.300 1.289 the ratios a / a
VI1
0.000 .001 .002
-
-
.
0.1642" .I641 .1639 ,1637
1,144951 1.143641 1.142335 .005 1.138434 .Ol 1.131990 a The numbers in this column also give and @ / b in Parts A and B, respectively.
dii
B.
- di
(ax
...
(6) e 2.2740, CIHE,25' from A. A. Maryott and E. R . Smith, Table of Dielectric Constants of Pure Liquids, Nat. Bur. Standards Circ. 514, August 10, 1951; d 0.87340 g./ml., C E H ~25O , from "International Critical Tables," Volume 111, McGraw-Hill Book CO., New York, N. Y.,p. 29.
-
THE STRUCTURE OF LIQUID ANTIMONY PENTAFLUORIDE
+
BY CHARLES J. HOFFMAN, BERTE. HOLDER AND WILLIAM L. JOLLY^ University of California, Radiation Laboratory, Livermore Site, Livermore, California Received August I d , 1867 ,
which on rearrangement becomes Pz = PI
+
di
--
+b ~ z
1
--
I
+ bxdi
The last equation is in a form suitable for passing to the limit, and we obtain, at zero concentration Pz =
- bP1
P I M Z+ allll
di
That this expression is equivalent to that proposed by Halverstadt and Ilumler, who used the ax2 and v12 = v1 , 8 2 2 , is linear forms €12 = €1 easily shown from the identities
+
(1 El
+
ax2
+
- 1 - €1 - 1
+ ax2 + 2
+ 2 + axr
El
and v1
+
m
2
=d
1 j
2
on obtaining similarly the limiting expressions Lim a 22-0
and
TABLE I LINEARITY COMPARISON; os. ( e12 - I)/( eI1 2) AND d1, vs. via; SOLVENT VALUESBASEDO N BENZENE AT 250°
dl2
€12
hence PI
Thus, since Halverstadt and Kumler have amply demonstrated the applicability of their equation, it follows that the present expression is equally applicable, and we have in addition somewhat greater simplicity of form and ease of calculation.
€12
P u = XlPl
P2 =
Vol. 62
3 a
+
= ___ (El 2)2
Antimony pentafluoride is an extremely viscous liquid a t room t e m p e r a t ~ r e ,suggesting ~ a high degree of polymerization. The fluorine nuclear magnetic resonance spectrum of the compound was examined in an attempt t o determine the molecular structure. Experimental Samples of antimony pentafluoride were vacuum-distilled into 3 mm. i. d. Pyrex tubes and sealed off in vucuo. The material analyzed 99.2% pure antimony pentafluoride; the melting point, 8.5", was comparable to values obtained recently for pure antimony pentafl~oride.~ A Varian V-4300 high-resolution spectrometer waB used a t a fixed frequency of 40 mc. and a magnetic field of 9980 gauss. The system was capable of at least five cycles resolution without sample spinning. Resolution of the peaks in the spectra was limted by the separations and line widths of the signals themselves rather than by magnetic field inhomogeneity. Chemical shifts of the fluorine resonances were measured relative to trifluoroacetic acid b.y sample substitution after calibration of the linear magnetic field sweep by an appropriate side-banding of the trifluoroacetic acid sample. The fluorine spectra for three temperatures (cu. -lo", room temperature, and ca. 80") are given in Fig. 1. The lower temperature spectrum is the most interesting and (1) The work described in this paper wae sponsored by the U. 8. Atomic Energy Commission. (2) Department of Chemistry, University of California, Berkeley, California. (3) A. A. Wolf and N. N. Greenwood, J . Chem. SOC., 2200 (1950). (4) C.J. Hoffman and W. L. Jolly. THIB JOURNAL, 61,1574 (1957).
I
.h
,
NOTES
March, 1958 indicates the existence of three non-equivalent sets of fluorine atoms in antimony pentafluoride within this temperature range. Detailed data for the low temperature spectrum are given in Table I. The chemical shift, 6," for the high temperature peak is 0.335.
365
a
TABLE I Low TEMPERATURE FLUORINE SPECTRUM O F SbFb Peak
Nominal total No. of resolved half-width, gauss lines
,.
A B C
*
8
7
0.065 .10
0.085 0.268
3
.10
0.528
Spin-spin splitting , cycles
Relative area
....
1
70f 10 130A 15
2 2
Discussion Any model which is proposed to explain the low temperature nuclear magnetic resonance spectrum of liquid antimony pentafluoride must be consistent with the existence of three non-equivalent sets of fluorine atoms in the over-all population ratio 1:2: 2. I n addition, the observed splittings must be satisfactorily explained. Various models can be used t o explain the nuclear magnetic resonance data, but it is believed that the one chosen is not only consistent with the high viscosity of antimony pentafluoride but is also reasonable with respect to theories of chemical bonding. The chosen model is pictured in Fig. 2. Liquid antimony pentafluoride is envisioned as a mixture of long chains of SbFs- groups, each group sharing two of its fluorine atoms with its two neighbors. The three groups of fluorine atoms are: type A (shared, or bridging fluorine atoms), type B (trans to type A fluorine atoms), and type C (trans to each other). It should be noted that the type A fluorine atoms are always cis to one another. The distances of the fluorine atoms from the antimony atoms are presumed t o increase in the order: type B, type C, type A. This order is the same as that of increasing ionic character for the individual Sb-F bonds. I n Fig. 2, the fluorine atoms have been arranged approximately octahedrally about each antimony, but an attempt has been made to indicate a tendency for a tetrahedral arrangement of type B and type C fluorines. The concept of shared or divalent fluoride ions is not without precedent. Brosset6 has shown that the compound T12A1Fs contains infinite chains of hexafluoroaluminate octahedra in which the two opposite (trans) corners are shared. Bystrom and Wilhelmi7 have shown that in CsSbzF7 the antimony atoms are surrounded by four fluorine atoms situated at the corners of an irregular tetrahedron. The two tetrahedra share one fluorine atom, so that Sb2F.l-groups are formed. It recently has been suggested that the 2 : l addition compounds of boron fluoride with triethylamine and with pyridine existing in solution as well as in the pure phase have single fluorine bridge structmes.8 I. Spectrum Interpretations in Terms of the Model.-Since the spin of the F19 nucleus is 1/2,
-
-
(5) 6 (Hi HTFA)/HTFAX 104,where Hi is the resonance field at 40 mo. for the peak in question and HTFAis the corresponding field for trifluoroacetic acid. (6) C. Broaset, 2.anorg. Cham., 236, 139 (1937). (7) A. Bystrom and K. A. Wilhelmi, Arkiu Kemi,3, 374 (1951). ( 8 ) H.C. Brown, P. F. Ftehle and P. A. Tierney, J . Am. Chem. Soc., 79, 2020 (1957).
r C
Fig. l.-F'g
--loo;
spectrum of antimony penta ioride a t (a) (b) room temperature; and ;) -80".
the nuclear magnetic resonance line for a particular set of fluorine atoms will be split into (n 1) peaks by neighboring fluorine atoms of another type. It has been assumed that due to strong nuclear quadrupole relaxation, the Sb-F spin-spin coupling is ineffective in splitting the fluorine lines. The proposed model does not have electric field symmetry a t the antimony nuclear site and can permit a strong relaxation interaction with the relatively large antimony quadrupole moment. The spin-spin coupling constants estimated from the measured splittings are: JAB= 70 -f 10 cycles, J A C < 30 f 10 cycles, and J B C 130 15 cycles. Peak A (Fig. 1) is split into a quintet 10 cycles by the type B with separations of 70 fluorines; these lines being further split by the type C fluorines overlap to make an unresolvable single broad peak. Peak B is split into a triplet with separations of 130 f 15 cycles by the type C fluorines and each of these lines, in turn, is split into a triplet of separations of 70 f 10 cycles by the type A fluorines. Since JBC = 2 JAB,two pairs of
+
*
366
.
NOTES
@
Antimony
0
FI uori ne
Fig. 2.- -Schematic chain structure of SbF5polymer.
n
w Antimony
0
Fluorine
Fig. 3.-Active
end of SbF5 chain.
lines overlap and a septet of 1:2:3:4:3:2:1 intensity distribution results. Peak C is split into a triplet of 130-cycle separation. by the type B fluorines. The splitting of this peak by the type A fluorines is unresolvable. The loss of detail in the spectra obtained a t room temperature and a t ca. 80” indicates that the fluorine atoms exchange at these higher temperatures. At room temperature, the average lifetime for the exchange between fluorines of type A and B is calculated to be about 2 X sec. and a t 80°, the average lifetime for any type of fluorine is less than see. 11. The Model in Terms of Electrostatics and Polarization.-It is assumed that all the Sb-F bonds are principally ionic bonds, with little covalent character. The distance between neighboring Sb+5ions is more than twice the Sb-F distance in the SbFe- ion not only as a result of cou-
Vol. 62
lombic repulsion of the Sb +&ions,but also because of the decreased covalent character in the bonds between antimony ions and the “bridging” fluoride ions. A “bridging” fluoride cannot form two bonds each with as much covalent character as that of a singly bonded fluoride. Figure 3 represents a terminal group of an SbF5 chain. This may be considered as a basic group which is capable of reaction with an acidic group (e.g., an SbFs monomer or the fluoride-deficient end of another SbF6 chain). It is proposed that a type (D) fluoride ion is a less basic site than a type (E) fluoride ion as its electron cloud has been attracted toward the central Sb+5ion more strongly than the others by virtue of a dipole induced in the SbC5 ion. This induced dipole in the Sbf5 ion is the result of a virtual positive charge in the direction of fluoride ion (F) and is caused by (a) the neighboring Sbf6 ion in the chain (which is not shown in Fig. 3), and (b) the fact that fluoride ion (F) is farther from the terminal Sb+5than the other five fluorides. Therefore the attachment of the acid group always occurs a t one of the cis fluoride ions (E); never a t the trans fluoride ion (D). 111. The Model in Terms of Atomic Orbitals.Although the bonds in an SbF6 chain are principally ionic, their fractional covalent character is of some importance. Antimony has available only four bonding orbitalsg (5s5p3), and yet it must form bonds with six fluorine atoms. The four bonds to the non-bridging fluoride atoms are more covalent in character than the other two, hence the most stable configuration will involve maximum utilization of the four available orbitals by these four bonds. Each of the three principal axes of antimony has available one and one-third orbitals for bonding (s’/~P). If the bridging fluorides are trans to each other, the one and one-third orbitals in the direction of their axis are misspent on what are necessarily very ionic bonds. However, if the bridging fluorine atoms are cis t o each other, it is then possible to utilize a full orbital in each of the . bonds trans to the bridging fluorides, and a total of only two-thirds of an orbital is misspent on the very ionic bonds. In the cis configuration, the fluorine atoms trans to bridging fluorine atoms are the most strongly bound to the antimony and hence closer to the antimony. The bridging fluorine atoms are the most weakly bound and hence are farthest from the antimony. Acknowledgment.-The authors wish t o thank Prof. K. S. Pitzer for his helpful discussions of the bonding in antimony pentafluoride. (9) The 5 d orbitals are theoretically available for ap3dZ hybridiza. tions, hut it ia unlikely that they participate appreciably.
CALCIUM AMMONIUM PYROPHOSPHATES BYEARLH. BROWN, WALTER E. BROWN, JAMESR. LEHR, JAMESP. SMITHAND ALVAW. FRAZIER Division of Chemical Development, Tenneasee Valley Authority, Wilson Dam, Ala. Received October 1% 1967
One amorphous and two crystalline phosphates of interest as potential fertilizer materials were prepared by ammoniation of products of the hy-
C ’
