Dissociation energies of gaseous gadolinium...
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848 The second triplet state is therefore located 70.6 kcal/mol above the ground state, ;.e., 2.8 kcal/mol below SI (Figure 3). This strongly supports the participation of the Tz state in the intersystem crossing process for 1,5-dichloroanthracene and is in accord with the low fluorescence quantum yield.
Acknowledgments. We wish to thank Dr. A. Singh for the use of the flash photolysis apparatus, Miss R/I. Jonasson and Mr. F. Sopchyshyn for assistance in maintaining the equipment, and Dr. E’. J. Dyne for his comments on the manuscript.
Dissociation Energies of Gaseous Gadolinium Dicarbide and Terbium Dicarbide
by E. E. Filby and L. L. Ames* Chemistry Department, New Mexico State Uniwersity, (Received November 4, 1970)
MaG(g)
+ Mb(g)
Ma@)
nIbCz(g)
to determine mass spectrometrically the dissociation energies of GdCt and TbC2. The advantages of this method, along with the development of the formulas used, have been discussed elsewhere. 14-16 Basically, the normal K , in the equilibrium expression is replaced by a mass spectrometric K’ in which Pi,the partial pressure of a species, is replaced by I,, the measured intensity of the ith mass peak.
Experimental Section The Bendix Time-of-Flight mass spectrometer used and the rest of the experimental setup have been described previ0us1y.l~ The cerium metal was obtained from D. F. Goldsmith Chemical and Metal Corp., the gadolinium metal from the Rare-Earth Division of the American Potash and Chemical Corp., and the terbium metal and carbon from Research Organic/Inorganic Chemical Co. The metals were reported by the suppliers to be of 99.9% purity while the carbon was 99.999+% purity graphite.
Las Cruces, New Mexico 88001
Results
Publication costs assisted by the National Science Foundation
Isomolecular exchange reactions were established between cerium and gadolinium and between gadolinium and terbium. The Ce-Gd reaction consisted of four runs totaling 36 log K’ us. 1/T values, while a total of 49 points from four runs were obtained for the Gd-Tb reaction. Figure 1 shows the experimental data for the two reactions. No distinctions were made among the
Relatively few investigations have been reported on the dicarbides of the rare earth metals gadolinium and terbium although Jackson, et uZ.,I and Hoenig, Stout, and Nordine2 have published some thermodynamic data for GdC2. A mass spectrometric investigation on the Langmuir vaporization of solid terbium dicarbide by Jackson, Bedford, and Barton3 showed no gaseous T b G , whereas a later study by Haschke and Eick4 indicated that it should be a significant vapor species. They have observed that the rare earth dicarbides of those metals with generally lower vapor pressure tend to vaporize to both the metal and the gaseous h462 molecules, and terbium metal has a relatively low vapor pre~sure.~ De Rlaria and coworker^^*^ have discussed and used the hypothesis of Chupka, et ~ 1that . the ~ Cz ~ group can act as a pseudooxide l o correlate qualitatively the stabilities of various metal oxides and corresponding carbides. This correlation, coupled with the observation of gaseous TbO by Ames, Walsh, and White,g strengthened the possibility of finding a significant amount of gaseous TbC2. ‘In contrast to these dicarbides, cerium dicarbide has been studied much more e ~ t e n s i v e l y ~ oand - ~ ~ therefore Doo(Ce-C2)has been used as a reference in this investigation. I4 All the previous thermodynamic data for these systems have been obtained from mass spectrometric investigations of the various solid-vapor equilibrium reactions. The study presented here uses instead isomolecular Cz-exchange reactions of the type The Journal of Physical Chemistry, Val. 7.5, No.6 ,1971
(1) D. D. Jackson, G. W. Barton, Jr., 0. H. Krikorian, and R. S. Newbury, “Thermodynamics of Nuclear Materials,” IAEA, Vienna, 1962, p 529. (2) C. L. Hoenig, N. D. Stout, and P. C. Nordine, J. Amer. Ceram. Sac., 50, 385 (1967). (3) D. D. Jackson, R. G. Bedford, and G. W. Barton, University of California Radiation Laboratory Report, UCRL, 7362T (1963). (4) J. M. Haschke and H. A. Eick, J . Phys. Chem., 72, 1697 (1968). (5) C. E. Habermann and A. H. Daane, J. C‘hem. Phys., 41, 2818 (1964). (6) G. Balducci, A. Capalbi, G. De Maria, and M. Guido. ibi&., 48, 5275 (1968). (7) G. De Maria, G. Balducci, A. Capalbi, and M. Guido, “High Temperature Mass Spectrometric Study of Neodymium-Carbon System,” Meeting on Thermodynamics of Ceramic Systems, London, April 19, 1966. (8) W. A. Chupka, J. Berkowitz, C. F. Giese, and M. G. Inghram, J. Phys. Chem., 62, 611 (1958). (9) L. L. Ames, P. N. Walsh, and D. White, ibid., 71, 2707 (1967). (10) G. Balducci, A. Capalbi, G . DeMaria, and M. Guido, J. Chem. Phys., 43, 2136 (1965). (11) R. L. Faircloth, R. H. Flowers, and F. C. W. Pummery, J . Inorg. Nucl. Chem., 30, 499 (1968). (12) P. Wirichell and N. L. Baldwin, J. Phys. Chem., 71, 4476 (1967). (13) G. Bdducci, A. Capalbi, G. DeMaria, and M. Guido, J . Chem. Phys., 50, 1969 (1969). (14) E. E. Filby and L. L. Ames, High Temp. Sci., in press. (15) D. L. Hildenbrand and E. Murad, J. Chem. Phys., 43, 1400 (1965). (16) P. N.Walsh, D. Dever, and D. White, J. Phys. Chem., 65, 1410 (1961).
849
NOTES
I -0.20t
42
4.4
43
45
I
J/T x 10"
Figure 1. Variation of log K' with temperature for the Gd-Tb and Ce-Gd Grext:hsmge reactions.
various runs lor a given reaction because of the generally good agreement, from run to run. The second-law enthalpies, calculated by a weighted least-squares fit of the data, were reduced to 0°K using the heat contents for the gaseous metals given by Feber and Herrick" and those given in Table I for the gaseous dicarbides. These enthalpies, converted from AH"2289 = 12.5 kcal/mol for the Ce-Gd reaction and AH"2279 = 0.52 kcal/mol for the Gd-Tb reaction, are given in Table 11.
Table I : Thermal Functions of Gaseous MCZSpecies T, OR 2000 2100 2200 2300 2400
-(Cog,
- H o a ) / T , cal/deg mol
(HOT - H " Q ) koal/mole ,
CeCz
GdCz
TbCz
CeC2
GdCz
TbCz
73.91 74.54 75.13 76.71 76.26
76.24 76.85' '77.45' 78.04 78.59
76.02 76.65 77.24 77.82 78.37
25.49 26.94 28.40 29.86 31.31
25.47 26.92 28.37 29.83 31.29
25.46 26.92 28.37 29.83 31.28
Table I1 : Reaction Enthalpies and Dissociation Energies (kcal/mol)
Table XI dsc) lists the third-law enthalpies at 0°K for the reactions calciilated from the log K' values and the free energy functions given by Feber and Herrick and in Table I. The thermal functions listed in Table 1 were calculated using the usual rigid-rotor harmonic-oscillator approximation assuming nlC2 to be a linear mole-
~ u l e . ~ # ' a ,The l ~ C-C bond length (1.24 8) and the M-C bond lengths and stretching force constants were estimated by a previously used m e t h ~ d . They ' ~ ~ are 1.86 A and 5.75 mdyn/A for CeC2, 1.79 A and 5.96 mdyn/8 for GdC2, and 1.78 h; and 5.97 mdyn/8 for TbC2. The C-@ stretching force constant was taken to be 13.1 mdyn/A as has been reported for the 6-42 bond in sodium acetylide.18 The bending force constants (k,/ZIEz) were calculated using k, equal to 0.60 mdyn-8/rad.14 The calculated vibrational frequencies are 650 cm-', 458 cm-l (dad.), and 2040 cm-l for CeGz, 656 cm-l, 464 cm-l (d.d.), and 2044 cni-' for GdCs, and 655 cm-l, 465 cm-l, (d.d.), and 2044 cm-' for TbC2. The electronic multiplicities of the ground states were assumed to be equal to those for the corresponding monoxides@and no electronic excit,ations were considered.
Discussion The dissociation energies of GdCz and Tb62 were calculated from the enthalpies of the exchange reactions according to the equation D O ~ ( M ~= C ~Doo(na,c2) ) -AHO~(SLM,J starting with the value of 162 f 2 kcal/mol given by Balducci, et U Z . , * ~ for the dissociation energy for GeCz. The dissociation energies obtained are also given in Table 11. The value for GdCz can be compared to the dissociation energy which is derivable from the results obtained by Jackson, et aLJ1who measured A M " ~ I=~ ~-31.9 lccal/mol for GdC2(g)
=
Gd(g)
+ 2C(s)
Converting this enthalpy to 0°K using the heat contents from Table I, Feber and Herrick, and Stull and Sinkelg (for graphite), and then combining the result with the heat of formation at 0°K of 62(g)j20a value of 154 f 5 kcal/mol is obtained. This quantity is in good agreement with the 151 rt 3 kcal/mol measured in this investigation. There appear to be no data available for comparison with the 150 f 3 kcal/mol determined here for the dissociation energy of TbC2. It is interesting to note that the differences between the dissociation energies for the dicarbides determined here and those for the corresponding monoxides9 are 22.0 and 23.4 kcal/mol for Gd and Tb, respectively. These very similar differences are evidence in support of (17) R. C. Feber and C. C. Herrick, "Ideal Gas Thermodynamic Functions of Lanthanide and Actinide Elements," Los Aiamos Scientific Laboratory Report LA 3184 (1964). (18) J. Goubeau and 0. Beurer, Z . Anorg. AUg. Chem., 310, 110 (1961). (19) D. R. Stull and G. C. Sinke, "Thermodynamic Properties of the Elements," Advan. Chem. Ser., No. 18 (1956). (20) "JANAF Thermochemical Tables," The Dow Chemical Co., Midland, Mich., 1963.
The Journal of Physical Chemistry, Vol. 76,No. 6 , 1071
850 the pseudooxide character of the CZ group. More extensive systematic investigations of the various successful qualitative correlations are needed to determine whether or not the hypothesis might have quantitative utility.
The Journal ofPh~6isl:ctclChemistry, Vol. 76, No. 6, 1071
NOTES
Acknowledgments. The National Science Foundation is gratefully acknowledged for its support of this research. The authors also wish to thank the New Mexico State University Computer Center for gratis use of computer time.
