NOTES
4688 in the vapor phase, but their relative instabilityl5 made observation of their spectra impossible by our techniques. By analogy to the phosphorus and vanadium oxotrihalides, the niobium oxotrihalides are expected to have a trigonal pyramid structure of symmetry CsVin the vapor phase. Molecules of this symmetry give rise to six infrared-active fundamental vibrations. The vibration v1 corresponds to the metal-oxygen stretching vibration. Being of symmetry class a1, it exhibits P, Q, and R branches. It is to this mode that we attribute the bands observed between 986 and 1000 cm-l. The band at 460 cm-l in the spectra of the vapors in the Sb-C1-0 systems can be attributed to v4, the metalchlorine stretching vibration of NbOC13, or to NbC15, which gives rise to an absorption band at 444 cm-I when observed in a nitrogen matrix at 5’K.lB I n Table I the known metal-oxygen stretching vibration frequencies for the phosphorus, vanadium, and niobium oxohalides and monoxides are presented. I n contrast to the phosphorus case, the metal-oxygen stretching frequencies in the niobium oxotrihalides seem to be nearly independent of the halogen substituents, decreasing by only’l3 cm-’ in going from the oxotrichloride to the oxotriiodide. Substituent effects on the metal-oxygen stretching frequency become less important in going from main group to transition element oxohalides and in going from lighter to heavier central metal elements. This conclusion is supported by data in a similar investigation of gaseous group VI OXOhalides.l7 Acknowledgment.
The cohesion energy as a function of volume has been studied by many investigators;’l5 over a small volume range the following form is employed
uc
=
-a 7
(1)
where UC is the cohesion energy, V is the molar volume, and a and n are constants dependent upon the nature of the particular liquid and upon the temperature. It was shown experimentally that, for a number of liquid substances, the exponent n has a value close to unity over a limited range of temperature^.'-^ For a uniformly expanded model, Benson4 derived a value of n = 2, but a value of 5.3 resulted in better agreement with experiment. For perfect liquids and hydrocarbons in the normal liquid range, Scott5 found a value for n equal to about 1.5 for nonisothermal conditions (along the vapor-liquid equilibrium curve). In this connection, we present our recently found results for normal aliphatic hydrocarbons (C&lJ and for carbon tetrachloride, tetrachloroethylene, benzene, thiophene, and pyridine. As is evident from Figure 1 (curve a), the change of the cohesion energy of hexane with temperature is more pronounced at temperatures near the melting point. This can be partially explained in terms of the more “solidlike” structure of liquids at these temperatures. A similar curve was obtained for the exponent n as a function of temperature (Figure 1, curve b), with the only exception that n reaches a constant value in a certain temperature range (T,=
This work was supported by the
U. S. Army Research Office, Durham, N. C. Dr. B. G. Ward and Miss H. V. Taylor performed some of the initial experiments. (15) H. Schhfer and E. Sibbing, Z . Anorg. Allgem. Chem., 305, 341 (1960). (16) R. D. Werder, R. .4.Frey, and Hs. H. Gunthard, J . Chem. Phys., 47,4159 (1967). (17) B. G. Ward and F. E. Stafford, Inorg. Chem., 7,2569 (1968).
Table I : Cohesion Energies Calculated from Experimental Data and from the Group Contributions Substance
c4
cs Ce (27 CS C9
ClO
Some Comments on Cohesion Energies of Liquids
c 1 1
ClZ Cl3
Cl, Cl5
by Vojtech Fried and Garry 13. Schneier Department of Chemistry, Brooklyn College of the City University of N e w Y o r k , Brooklyn, New Y o r k 11210 (Receizled J u n e 24, 1968)
The solution of many theoretical problems in chemistry requires knowledge of the cohesion energy of liquids. The energy-volume-temperature relations present an especially severe and sensitive test for a theory of liquids. T h e Journal of Physical Chemistry
-Tr Exptla
2.137 2.522 2.881 3.241 3.592 3.941 4.283 4.613 4.953 5.289 5.617 5.955
-
I O - ~ U c ,J mol-’ 0.6---Tr Calcd Exptl‘
2.190 2.534 2.878 3.222 3.566 3.909 4.253 4.597 4.941 5.285 5.629 5.973
-.
= 0.7-
1.927 2.255 2.571 2.885 3.192 3.486 3.772 4.058 4.338 4.617 4.881 5.153
a The uncertainty is f 2 in the last figure. factor.
Calcd
io*
1.998 2.288 2.579 2.869 3.160 3.450 3.741 4.031 4.322 4.612 4.903 5.193
0 * 201
b
0.252 0.298 0.352 0.395 0.440 0.479 0.521 0.560 0.602 0.641 0.680
Pitzer’s acentric
(1) J. H. Hildebrand and R. L. Scott, “The Solubility of Nonelectrolytes,” Reinhold Publishing Corp., New York, N. Y . , 1950, p 97. (2) J. H. Hildebrand and R. L. Scott, “Regular Solutions,” PrenticeHall, Inc., Englewood Cliffs, N. J., 1962, p 76. (3) H. Benninga and R. L. Scott, J . Chem. P h y s . , 23, 1911 (1956). (4) S. W. Benson, ibid., 15, 367 (1947). (6) R. L. Scott, unpublished data, cited in ref 1, p 101.
NOTES Table 11: Vapor Pressure and Molar Volume of the Liquid Substances as Functions of Temperature Antoine -B
- - - ~ V
7 eq-7 -
Substance
CC (2.5
C6 C7 C8
C9
C10
c11
C12
ClS Cl4
CIS
CClr CsClr Benzene Thiophene Pyridine
A
6.83209 6.85221 6.87776 6.90240 6.92377 6,93520 6.95367 6.97674 6.98059 6.98870 6.9957 7.0017 6.88853 7.21511 6.89745 6.95926 6.90374
946.90 1064.63 1171.530 1268.115 1355.126 1428.817 1501.268 1572.477 1625.928 1677.43 1725.46 1768.82 1217.165 1531.460 1206.350 1246.038 1293.969
0.6-0.7). Similar behavior has been observed for all the other aforementioned substances. This constant value of n, for each hydrocarbon, is plotted against the number of carbons in the molecule, nc, in Figure 2 (curve a). The average value of n,for all the hydrocarbons, is 1.42 + 0.04, which is very close to the value given by Scott.5 The small fluctuations result probably from the inaccuracy of the experimental data. Although the acentric force field changes with nc in the hydrocarbon series (as is evident from Table I, where Pitzer's acentric factors are given), the value of n is not affected by it. The values of the exponent n for carbon tetrachloride, tetrachloroethylene, benzene, thiophene, and pyridine, under the same conditions, are the following: 1.38, 1.40, 1.53, 1.63, and 1.89, respectively. As is evident from Figure 2 (curve b), the value of the constant a increases with nc. The constant a depends on temperature very strongly; nevertheless, in the limited temperature range ( T , = 0.6-0.7) the change is less than h3y0,. This is a very important fact, because as a consequence of it the radial distribution function might also be considered as temperature independent in the given temperature interval (so far considered acceptable only for a very simple potential model). Values of a and n for eq 1 were obtained by solving two simultaneous equations over a small increment of temperature. Over this temperature interval, a and n were assumed to be constant. This process was repeated throughout the entire liquid range and it was found that from T , = 0 . 6 t o 0.7, a and n were only slightly temperature dependent. Finally in Figure 3 the exponent n is plotted as a function of the dipole moment. For the substances studied, n increases with the polarity of the liquids. The rate of increase is, however, not uniform, and n seems to approach a constant value at higher dipole moments.
C
= a f
96.75 111.79 127.19 143.01 158.83 175.67 192.25 210.59 229.21 250.24 269.30 287.14 94.25 100.28 86.59 77.13 78.61
240.0 232.0 224.37 216.900 209.517 201.621 194.480 188.022 180.311 172.90 165.75 158.60 227.00 232.379 220.237 221.354 206.321
bt
+ ct------
b
a
104~
3.707 2,946 4.282 4.714 3.855 5.249 5.377 6.898 8.031 9.657 9.952 9.943 1.975 1.384 1.097
0.1696 0.1639 0.1670 0.1620 0.1721 0.1536 0.1531 0,1224 0.0954 0.0455 0.0318 0.0314 0.1084 0,0951 0.1067 0.0942 0.0904
... ...
- 4.0 n
- 3.0 - 2.0
I
I
200
,
I
r
I
t
i
i
300 Tr.O.67
17.0
1
ThO.72 400
Figure 1. (a) The cohesion energy of hexane RS a function of the temperature; ( b ) the exponent n of hexane as a function of the temperature.
The cohesion energy at pressures approaching zero was calculated from the relation
- U c = AU,,, =
+ AU*
[RT - Po(V1 - B ) ] X
where Po is the saturated vapor pressure at temperature T , V Iis the molar volume of the liquid substance, and B is the second virial coefficient. AU,,, represents the change of the internal energy associated with the vaporization of 1 mol of a liquid at a constant temVolume 79,Number I S
December 1968
NOTES
4690
perature and a pressure equal to the saturated vapor pressure at this temperature. AU* denotes the change of the internal energy associated with the change of the pressure from its saturated value to a pressure approaching zero. Pola’k,O in his basic work on cohesion energies, found that for a great number of liquids t,he value of AU* represents about 0.8-1.27, of the total value of the cohesion energy at the normal boiling point.
,766
- 70 “
”
I
0 15
Figure 2. (a) The exponent n as a function of the number of carbons, no,in the molecule; (b) the constant a as a function of the number of carbons, no,in the molecule.
The experimental data necessary to calculate the cohesion energies ( k ,saturated vapor pressures and molar volumes of the liquids as functions of temperature), except those for carbon tetrachloride, tetrachloroethylene, n-nonane, and pyridine, have been taken from the literature.’-’l All the data are summarized in Table 11. The virial coefficient was calculated from Pitzer’s equation.12
Fisher spectroanalyzed substances mere purified by the usual methods until their physical constants were in agreement with the literature values.’-1° The vapor pressure was measured by a dynamic method in which two ebulliometers were connected in parallel in the measuring systems. One of the ebulliometers contained water and the other the substance to be measured. From the boiling point of water, the corresponding vapor pressure of the substance was found. Singlestem pycnometers of about 10-ml capacity were used for density measurement. The data are reported in Table 11. As is well known, the increment of the cohesion energy per CH2 group inserted is not constant for the paraffin series at .constant temperature. Some of the conditions under which the CH2 increment might be expected to be constant are discussed by Neyer and Wagner. l 3 From the values of the cohesion energies obtained, the CH2, CH3, CH, and C-C increments of the cohesion energy were calculated at two reduced temperatures ( T , = 0.6 and 0.7). The cohesion energy, calculated from the average values of these increments, is in a very good agreement with the cohesion energy calculated from the experimental data, as is evident from Table I. The following values (Joules per mole) have been found for the different group contributions to the cohesion energy: T , = 0.6; Uc = 2(brC)CHa 4(ne - 2)(Uc)CH%= -15020 - 3439(nc - 2 ) ; CC = (nc - l)(brC)C-C (2nC 2)(cC)CH = 2353(n~- 1) - 2896(2nc 2 ) ; T , = 0.7; l i c = ~ ( U C ) C H ~ (nc - 2)(uc)CH2 = -14166 - 2905(nc - 2); UC = (2nC f 2)(UC)CH = 2 7 2 5 ( ~(nc - 1 ) ( U C ) C - C 1) - 2815(2nc 2). The observations reported in this note on cohesion energies of liquids may be helpful in the development of theories of liquids and liquid solutions (especially theories based on the radial distribution function).
+
+
Figure 3. The exponent n as a function of the dipole moment: 0 , hydrocarbons, carbon tetrachloride, tetrachloroethylene; 0, benzene; A, thiophene; 0, pyridine,
The values of the cohesion energies calculated from eq 2 are accurate enough, as has been proved by comparing the experimental (calorimetric) data on heat of vaporization with the values calculated from the modified eq 2. It was found that the difference is less than 0.15% in the normal liquid range. The vapor pressure and molar volumes of carbon tetrachloride, tetrachlorocthylene, n-nonane, and pyridine have been measured in our laboratory. The Journal of Physical Chemistry
+
+
+
+
(6) J. Pola’k, Collect. Czech. Chem. Commun., 31, 1483 (1966). (7) J. Timmermans, “Physico-Chemical Constants of Pure Organic
Compounds,” Elsevier Publishing Co., Amsterdam, The Netherlands, 1950. (8) “Selected Values of Properties of Hydrocarbons and Related Compounds,” American Petroleum Institute Research Project 44, Carnegie Press, Pittsburgh, Pa., 1953. (9) R. R. Dreisbach, “Physical Properties of Chemical Compounds,” Advances in Chemistry Series, No. 15, 22, and 29, American Chemical Society, Washington, D. c., 1955, 1959, 1961. (10) T. E. Jordan, “Vapor Pressure of Organic Compounds,” Interscience Publishers, New Tork, N. Y . , 1954. (11) G. Waddington, J. W. Knowlton, D. W.Scott, G. D. Oliver, 9. S. Todd, W. N. Hubbard, J. C. Smith, and H. M ,Huffman, J . A m e r . Chem. SOC.,71, 797 (1949). (12) K. S. Pitzer and R. F. Curl, ibid.,7 9 , 2369 (1957). (13) E. F. Meyer and R. E. Wagner, J . P h y s . Chem., 70, 3162 (1966).
