Dissociation Energy of the Gaseous Molecule PtTi
was partially supported by the National Science Foundation under Grant No. CHE77-03599.
References and Notes (1) A. G. Sykes, "Kinetics of Inorganic Reactions", Pergamon Press, Oxford, 1966. (2) R. C. Thompson, J . Am. Chem. Sac., 93, 7315 (1971). (3) R. M. Noyes, R. J. Field, and R. C. Thompson, J. Am. Chem. Soc., 93, 7315 (1971). (4) K. R. Sharma and R. M. Noyes, J. Am. Chem. Soc., 98,4345 (1976). (5) V. R. Mitzner, G. Fischer, and P. Leupold, Z.Phys. Chem. (Leipig), 253, 161 (1973). (6) D. A. Skoog and D. M. West, "Fundamentals of Analytical Chemistry", Holt, Rinehart and Winston, New York, 1976, p 746. (7) Reference 6, p 761. (8) R. G.Wille and M. L. Good, J . Am. Chem. Soc., 79, 1040 (1957). (9) C. Capellos and B. H. J. Bielski, "Kinetic Systems", Wiley-Interscience, New York, 1972. (10) R. J. Field, R. M. Noyes, and E. Koros, J. Am. Chem. Soc., 94, 8649 (1972).
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(1 1) H. A. Liebhafsky and L. S. Wu, J. Am. Chem. Soc., 96, 7186 (1974). (12) R. Furuchi and H. A. Liebhafsky, Bull. Chem. SOC. Jpn., 48, 745 (1975). (13) 0. Amichai and A. Treinin, J . Phys. Chem., 74, 830 (1970). (14) M. Cater and R. J. Field. unwblished results. (15j "Symposium on Reaction Mechanisms, Models and Computers", J. Phys. Chem., 81, No. 25 (1977). (16) W. J. Moore, "Physical Chemistry", Prentice-Hall, Englewood Cliffs, N.J., 1972, p 261. (1 . 7). A. C. Hindmarsh. "Gear: Ordinary Differential Equation System Solver", Technical Report No. UCID-30001, Rev". 2, Lawrence Livermore Laboratory, 1972. (18) C. W. Gear, "Numerical Initial Value Problems in Ordinary Differential Equations", Prentice-Hall, Englewood Cliffs, N.J., 1971, Chapter 11. (19) D. D. Warner, J. Phys. Chem., 81, 2329 (1977). (20) R. F. Hampson and D. Garvin, J. Phys. Chem., 81, 2317 (1977). (21) S.Barkin, M. Bixon, K. Bar Eli, and R. M. Noyes, Int. J. Chem. Kinet., 9, 841 (1977). (22) E. Abel and K. Hilferding, Z. Phys. Chem., 136, 186 (1928). (23) "Do not multiply entities beyond necessity.", quoted from P. W. Bridgman, "The Way Things Are", Harvard University Press, Cambridge, Mass., 1959, p 10.
Dissociation Energy of the Gaseous Molecule PtTi by High-Temperature Knudsen Effusion Mass Spectrometry Satlsh K. Gupta, Mario Pellno, and Karl A. Gingerich" Department of Chemistty, Texas A&M University, College Station, Texas 77843 (Received May 21, 1979)
The diatomic molecule IPtTi was observed in a mass spectrometric investigation of the vapor above the Pt-Ti-C system at high temperatures. Second- and third-law enthalpies of the gaseous equilibrium reaction PtTi(g) = Pt(g) + Ti(g) were determined in the 2476-2817 K temperature range, yielding Doo(PtTi)= 394 f 11 kJ mol-' (94.2 f 2.6 kcal mol-l), Dozgs(PtTi)= 398 f 11 k J mol-l (95.1 f 2.6 kcal/mol-l), and AHfo29s(PtTi(g)) = 637 f 11 kJ rno1-I (152.2 f 2.6 kcal mol-l). The dissociation energy of PtTi is discussed in terms of empirical models for metallic bonding in transition metals.
Introduction As part of an ongoing program concerned with the thermochemistry of gaseous homo- and heteronuclear molecular metals, we have studied the intermetallic molecule PtTi(g) by the Knudsen effusion mass spectrometric technique. The study of small-ligand free-metal clusters is of basic relevance to catalysis by dispersed metals, nucleation, crystal growth, and cluster compounds chemistry. The fundamental property of interest in these phenomena is the strength of the metal-to-metal bond as a function of the cluster size. The experimentally determined dissociation energies of the diatomic molecules provide a basis for improving and developing empirical or semiempirical models of bonding in such molecules, and hence allow one to gain an insight into their electronic and chemical properties. Once the diatomic molecules are characterized, the study of bigger clusters would be facilitated. It is now well known that the platirium group metals, which have nearly filled d orbitals, form particularly stable diatomic molecules with early transition metals, including lanthanides and actinides, which are d-electron deficient. The unusually high dissociation energies for such gaseous molecules were first suggested by Brewer1 on the basis of the extraordinary stabilities of the corresponding metal alloys predicted2 by the Engel theory of metals and later confirmed e~perimentally.~"The existence of the gaseous intermetallic compounds of high stability was first experimentally confirmed by Gingerich and Grigsbf through spark source mass spectrometric studies. Since then a large number of such molecules have been observed and their dissociation energies measured7-I2 by the technique of Knudsen effusion combined with mass spectrometry. A 0022-3654/79/2083-2335$01 .OO/O
partial list of the molecules studied so far includes RhU,7 BaPd,6 CeIr,g TiRh,l0ThPt,'l and LaFth.12 As an example of the unusually high stabilities of these molecules, the highest dissociation energy measured so far is 140 f 10 kcal mol-l for ThRu.13 Although no theoretical treatments which quantitatively account for the dissociation energy of the transition metal molecules are available at present, it is generally recognized that the bonding in these molecules involves multiple-bond formation, utilizing one or more d electrons from each atom. The extra stability of the platinum metal compounds with the early transition metals may be attributed3 to generalized Lewis acid-base interactions between the electron-rich d orbitals of the platinum metal and the electron-deficient d orbitals of the early transition metal. In recent years, several empirical models have been developed which attempt to quantitatively estimate or predict the dissociation energies of gaseous intermetallic compounds. A model based upon the valence bond approach by GingerichI4 has been particularly successful when applied to the above-mentioned group of platinum metal intermetallic compounds. The cellular model of Miedema and Gingerich15 has the potential of general applicability to gaseous intermetallic compounds. We present here the results of a Knudsen effusion mass spectrometric determination of the dissociation energy of the molecule PtTi, which had been previously observed6 through spark source mass spectrometry. These results are compared with the values estimated by the empirical models.
Experimental Section The mass spectrometer, a 90° sector and 12-in. radius 0 1979 American
Chemical Society
2336
The Journal of Physical Chemistry, Vol. 83, No. 18, 1979
TABLE I: Measured Ion Currents (Multiplier Anode Current) of 48Tit,"'Ptt, and 195Pt48Ti' as a Function of Temoerature temp, K 2476 2533 2583 2642 2706 2787 2817
I*Ti(y)
10
,A
9.45 7.1 10.7 13.8 11.9 8.44 6.91
I'PPt(i95)
lo8, A 7.20 12.6 24.2 36.0 27.2 29.0 28.1
x
S. K. Gupta, M. Pelino, and K. A. Gingerich
TABLE 11: Thermochemical Data for the Gaseous Equilibrium Reaction PtTi(g) = Pt(g) + Ti(g) - A [(GOT -
I*PtTi(z43) x
10' , A 9.30 7.10 12.2 19.0 8.20 8.40 2.42
magnetic focusing type instrument (Nuclide, 12-90-HT), and the experimental procedures have been described previo~sly.A ~ ~tantalum ~~~ effusion cell lined with a graphite liner was employed. The cell, containing a charge of about 400 mg of an Ir-Ti alloy (5% iridium), had been heated to the temperature of about 2500 K in a previous experiment. For the purpose of the present investigation, a piece of pure platinum wire was placed inside the cell, together with a small amount of gold for use in the pressure calibration of the instrument. The temperature inside the Knudsen cell was measured by sighting a Leeds and Northrup optical pyrometer a t a blackbody hole in the bottom of the cell. The energy of the ionizing electron beam was 25.6 eV, the energy scale being calibrated against AP(Au+) = 9.22 eV.I6 The ions were accelerated through a potential of 4.5 kV and detected with a 16-stage electron multiplier whose entrance shield was maintained at about -2 kV. The current gain of the electron multiplier for the various ions was measured by the use of a 50% transmission grid placed between the collector slit and the multiplier. The multiplier gain for Au+ and Ti+ were determined to be 7 A u = 6.31 X lo4 and 7Ti = 1.20 X lo5. For Pt+ and PtTi', it was assumed that ?pt = Y A and ~ ')'ptTi = (YPt + YTi)/2, respectively.
Results The ion PtTi+ was first observed a t 2476 K. Its appearance potential was determined as 10.1 f 1.0 eV by the linear extrapolation method. The ionization efficiency curve for PtTi+ showed no evidence of fragmentation in the 10-26-eV range of electron energy. The measured currents at the electron-multiplier anode due to Pt' ( m / e = 195), Ti+ ( m / e = 48), and PtTi+ ( m / e = 243) are given in Table I as a function of temperature. Four sets of Au+ and Auz+ ion currents were measured in the 1475-1745-K range for the purpose of determining the instrument sensitivity by utilizing the gaseous equilibrium Au2(g) = 2Au(g).17 From the literaturela data for the enthalpy and the free-energy function change for this reaction, the pressure constant (k = P/Z+T)for gold was determined as hAu = 0.41 f 0.07 atm A-' K-'. The pressure constants for Pt, Ti, and PtTi were calculated by using the Y ~ E Au ~is~ the ~), relation ki = ~ A ~ ( u A ~ Y A ~ E ~ / u ~where maximum ionization cross section, E is the correction factor for converting the ion current measured a t 25.6 eV to that corresponding to the maximum in the ionization efficiency curve, and n is the isotopic abundance. The atomic ionization cross sections were taken from Mann.lg The cross section for PtTi was taken to be 0.75 times the sum of Pt and Ti cross sections.20 The pressure constants thus obtained are kpt = 1.07, kTi = 0.235, and kptTi = 0.556 atm A-' K-l. The partial pressures (Pi= kil,+T) data were treated by the second- and third-law methods to determine the enthalpy of the gaseous equilibrium reaction (1) PtTi(g) = Pt(g) + Ti(g)
temp, K 2474 2533 2583 2642 2706 2787 2817
In K,, atm 8.192 X 1.235 X 2.479 X 3.124 X 4.716 X 8,076 X 1.022 X
120.0 120.1 120.3 120.5 120.7 l o F 2 121.0 lo-' 121.1 av second law
lo-' lo-' lo-' lo-'
396.0 396.9 390.1 394.5 395.4 395.6 394.7 394.7 i. 6.1a 393.0 i- 20.3&
a Standard deviation from the mean plus the error due t o free energy functions of PtTi(g), 4.0 k J mol-'. Standard deviation of the least-squares fit,
The thermodynamic functions needed in the second- and third-law calculations, HOT- HoOand (GoT - Hoo)/T,were taken from literature2' in the case of Pt(g) and Ti(g). For PtTi(g1, these were calculated from estimated parameters. The equilibrium bond distance, re(Pt-Ti), was estimated as 2.30 A on the basis of the spectroscopically determined Au-A1 bond length of 2.338 A.22 This value of re for AuAl is about 0.25 A less than the sum of the Pauling single bond radii23for Au and Ai. A corresponding "bond shortening" of 0.32 A was estimated for Pt-Ti by comparing the dissociation energy of AuAl(g), Doo = 332.2 f 6 kJ with that expected for PtTi(g), about 400 kJ mol-', from a preliminary evaluation of the present data. A vibrational frequency of we = 381.3 cm-l was estimated for PtTi(g) from the Guggenheimer relation25 for multiply bonded diatomic molecules, using ZTi = 4 and Zp, = 6. The electronic contributions to the thermodynamic functions of PtTi were computed from an estimated ground state degeneracy of gi = 3, neglecting contributions from any excited states. The calculated values of -(GoT - Hoo)/T (in J mol-' K-') and HOT - HoO(in kJ mol-l) for PtTi(g) a t 298.15, 2400, 2600, 2800, and 3000 K are 232.1, 9.540; 304.6, 87.60; 307.5, 95.08; 310.2, 102.6; and 312.7 and 110.0, respectively. The uncertainty in the free-energy functions is estimated to be f1.5 J mol-' K-l, excluding the uncertainty due to electronic contributions. The equilibrium constants and the derived thermochemical data for reaction 1 are given in Table 11. The probable error quoted with the average third law AHoo value was obtained by adding to the standard deviation from the mean an uncertainty of f4.0 kJ mol-l, corresponding to the uncertainty of f1.5 J mol-l K-' in the free-energy functions of PtTi(g). The error limits given for the second law value are the standard deviation from least-squares fitting. The second and third law enthalpies of reaction 1 a t 298.15 K are 397.5 f 20.3 and 399.3 f 6.1 kJ mol-', respectively. The entropy changes are = 130.3 f 7.7 J mol-' K-l and ASo,,, = 107.8 f 7.7 J mol-l K-l from the second law, and AS0298 = 108.4 & 1.5 J mol-l K-l by the third law method. It is seen from the results presented in Table I1 that the agreement between the second and third law determinations of the enthalpy of the dissociation of PtTi(g) is very good. By taking the mean of the two, we derive the selected values Doo = 394 f 11 kJ mol-l or 94.2 f 2.6 kcal/mol-' and DoB8= 398 f 11 kJ mol-' or 95.1 f 2.6 kcal mol-'. In addition, by combining the dissociation energy of PtTi(g) with the heats of vaporization of titanium and platinum,21the standard heat of formation of PtTi(g) is derived as AHHfo298 = 637 f 11kJ mol-' or 152.2 f 2.6 kcal mol-I.
Dissociation Energy of the Gaseous Molecule PtTi
Discussion The dissociation energy of PtTi(g) determined here is consistent with those of the other stable intermetallic compounds of platinum with early transition metals in the second and third series. Since no gaseous diatomic compound of platinum with the first transition series metals is known, the dissociation energy of PtTi(g), 394 f 11kJ molw1,may be compared with that of RhTi(g), Doo = 387.0 f 14.6 k J mol-l.lo It can readily be shown that these bond energies are much larger than what one would calculate for these molecules by using the Pauling modelz3 of polar single bonds. Thus it is clear that PtTi(g) and RhTi(g) are multiply bonded molecules as predicted by the Brewer-Engel theory. The application of the empirical valence bond method of Gingerich14yields bond energies of 360 and 427 k J mol-l, respectively, for PtTi(g) and RhTi(g). These values are based on the formation a double bond in PtTi(g), a 5d-3d and a 6s-4s bond, and a triple bond in RhTi(g) consisting of two 4d-3d bonds and one 5s-4s bond. One sees that there is a reasonable agreement between the calculated and experimental values for both molecules. In the case of RhTi(g), the experimental dissociation energy is somewhat too low and for PtTi(g) it is higher than the calculated value. This latter behavior is typical of platinum intermetallic molecules and may be qualitatively interpreted as evidence for "back-bonding", that is, the partial transfer of electrons from the filled d orbitals of platinum to the vacant d orbitals of the other transition metal atom. Alternatively, the MO theory may be invoked to account for the extra stability of the platinum intermetallic m01ecules.l~ Molecular orbital approach would yield the bond orders of 5, 5.5, 5, and 6, respectively, for PtTi (D = 394 f 11 kJ mol-'), RhTi (D = 387.0 f 14.6 kJ mol-'lO), RhV (360 f 29 kJ mol-l"), and RhY (442 f 10 kJ mol-127). Thus the dissociation energy of PtTi(g) would be expected to be similar to that of RhV(g), both of which have a bond order of 5. However, due to the greater bonding efficiency of 5d orbitals over 4d orbitals, the bond energy of PtTi(g) is significantly higher than that of RhV(g). In the same vein, the dissociation energy of the gaseous molecule IrTi which would have a bond order of 5.5 can be predicted to be about 425 k J molt1. Miedema and Gingerich15 have recently developed an empirical model for estimating the bond energies of gaseous diatomic intermetallic compounds. The PtTi(g) bond energy yielded by their method is 494 kJ
The Journal of Physical Chemistry, Vol. 83, No. 18, 1979 2337
mol-I which is much higher than the experimental value. Similar deviations occur when the model is applied to the other compounds of highly electronegative transition metals (Pd, Pt, Ni, and Au) with electropositive metals.15 Miedema and Gingerich have interpreted this behavior as the effect of a reduced charge transfer to the highly electronegative metal which has nearly filled d orbitals.
Acknowledgment. The authors appreciate the support of this work by the National Science Foundation under Grant CHE 78-08711. References and Notes L. Brewer, private communication. L. Brewer, Science, 161, 115 (1968). L. Brewer and P. R. Wengert, Metall. Trans., 4, 83 (1973). U. V. Choudary, K. A. Gingerich, and L. R. Cornwell, Metall. Trans., 8, 1487 (1977). M. Pelino, S. K. Gupta, L. R. Cornwell, and K. A. Gingerich, to be published. K. A. Gingerich and R. D. Grigsby, Metall. Trans., 2, 917 (1971). K. A. Gingerich and S.K. Gupta, J . Cbem. Pbys., 69, 505 (1978). K. A. Gingerich and U. V. Choudary, J. Chem. phys., 68,3265 (1978). K. A. Gingerich, J. Chem. Soc., Faraday Trans. 2, 70, 471 (1974). D. L. Cocke and K. A. Gingerich, J. Chem. Pbys., 60, 1958 (1974). K. A. Gingerich, Cbem. Phys. Lett., 23, 270 (1973). D. L. Cocke, K. A. Gingerich, and J. Kordis, H&h Temp. Sci., 5, 474 (1973). K. A. Gingerich, Cbem. Phys. Left., 25, 523 (1974). K. A. Gingerich, Int. J . Quant. Cbem. Quant. Chem. Symp., 12, 489 (1978). A. R. Miedema and K. A. Gingerich, to be published. C. E. Moore, Natl. Bur. Stand. Circ., No. 467, Vol. 111, 186 (1958). R. T. Grimley in "Characterization of High Temperature Vapors", J. L. Margrave, Ed., Wiley, New York, 1967, pp 195-243. J. Kordis, K. A. Gingerich, and R. J. Seyse, J. Cbem. Pbys., 61, 51 14 (1974). J. B.I Mann in "Recent Developments in Mass Spectrometry", Proceedings of the InternationalConference on Mass Spectrometry, Kyoto, Japan, K. Ogata and T. Mayakawa, Ed., University of Tokyo Press, 1970, pp 814-819. J. Drowart and P. Goldfinger, Angew Chem., 79, 589 (1967); Angew Chem., Int. Ed. fngl., 6, 581 (1967). R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, K. K. Kelley, and D. D. Wagman, "Selected Values of the Thermodynamic Properties of the Elements", American Society for Metals, Metals Park, Ohio, 1973. R. F. Barrow and D. N. Travis, Proc. R. Sac. London, Ser. A , 273, 133 (1963). L. Pauling, "The Nature of the Chemical Bond", 34d ed, Cornell University Press, Ithaca, N.Y., 1960. K. A. Gingerich, J. Crystal Growth, 9, 31 (1971). K. M. Guggenheimer, Proc. Pbys. Soc. (London), 58, 456 (1946). K. A. Gingerich and U. V. Choudary, cited in ref 14. R. Haque and K. A. Gingerich, J . Chem. Thermodynam., in press. K. A. Gingerich, J . Cbern. Pbys., 49, 14 (1968). D. L. Cocke and K. A. Gingerich, J . Phys. Chem., 75, 3264 (1971).
