980
J. DROWART AND R. E. HONIG
passivate a t low pH ~ a 1 u e s . l ~The results appear to indicate, therefore, that there is no fundamental difference between chemical or electrolytic pas-
Vol. 61
sivation, as the term is ordinarily used, and inhibition by the XO4.- inhibitors in aerated solutions.
A MASS SPECTROMETRIC METHOD FOR THE DETERMINATION OF DISSOCIATION ENERGIES OF DIATOMIC MOLECULES1 BY J. DROWART AND R. E. HONIG~ Laboratoire de Chimie Physique Moltculaire, Universitt Libre de Bruxelles, Brussels, Belgium Received March 68, 1967
By combining experimental data obtained in a mass spectrometer with thermochemical computations, dissociation energies of various diatomic molecules have been determined. This method has been applied to the Group I B and IVB dimers, and estimates have yielded values for Group I I I B and some other elements. To produce atomic and diatomic species of a given element, a milligram sample was vaporized in a mass spectrometer from a small, electrically-heated crucible. Ion intensity ratios were measured as a function of temperature, after the particles had been ionized, accelerated, mass analyzed and collected. The dissociation energies computed by the Absolute Entropy Method are based on the following quantities: ion intensity ratios; internuclear distances, estimated from known crystal spacings; electronic partition functions; and vibrational frequencies reported recently in band spectral studies. The values found agree well with those obtained by the socalled Slope Method which utilizes directly the measured heats of vaporization of monomers and dimers, and they fall within the upper limits set by band spectral data.
I. Introduction Data concerning the state, or states, of aggregation of elements in the gas phase are of considerable interest. Band spectroscopy and thermochemistry have supplied informationa concerning the diatomic molecules (dimers) of the elements in Groups IA, IIB, VB, VIB and VIIB, and recently also in Group IB,416but dissociation energies were generally not known for the remaining elements of the Periodic Table. The present study was undertaken to close, as far as possible, the existing gaps. By combining thermochemical computations with data from rate-of-vaporization experiments carried out in a mass spectrometer, dissociation energies were obtained in two independent ways. While the results obtained for the Group IB and some of the Group IIIB elements already have been briefly des~ribed,~,' the present paper will report a full account of the experimental and analytical methods employed. These methods were applied not only to the JB and IIIB elements, but also to Group IVB for which there existed experimental data obtained previously by one of the authors.s-10 Furthermore, by plotting dissociation energies against various parameters, certain trends become (1) Work supported in part b y the European Office of the Air Research and Development Command under Contract No. AF81(514)888. (2) On leave of absence from RCA Laboratories, Princeton, N. J., during 1955-1958. (3) T. L. Cottrell, "The Strength of Chemical Bonds," Butterworths Scientific Publications, London, 1954. (4) J. Ruamps, Compt. rend., 2S9, 1200 (1954). (5) (a) B. Kleman and S. Lindkvist, Arkiu Fysik, 8, 333 (1954); (b) 9, 385 (1955); (c) B. Kleman, 8. Lindkvist and L. E. Selin, ibid., 8, 505 (1954). (6) J. Drowart and R. E. Honig, J . Chem. Phys., 86, 581 (1956). (7) J. Drowart and R. E. Honig, Bull. SOC. chim. Belgei, 66, 411 (1957). (8) R. E. Honig, J . Chem. Phys., 21, 573 (1953). (9) R. E. Honig, ibid., 28, 128 (1954). (10) R. E. Honig, ibid., 22, I810 (1954). The Si vapor pressure quoted in this reference ia based on a Comparison with Ge. In the present study, Searcy and Freeman's most recent Ge values ( J . Chem. Phys., 23, 88 (1955)) have been taken into account, and Si pressures have been reduced by a factor of two.
clear which permit rough estimates to be made for some of the remaining elements. 11. Experimental The mass spectrometer used for these studies was a commercial 60" instrument11 of 20 cm. radius, originally designed for gas analysis, which was modified to permit the vaporization of solids. The milligram sample to be studied was heated in a crucible to a temperature sufficient to produce a beam of neutral particles of adequate intensity. A fraction of this beam was ionized by 30 Ma. beam of 70 e.v. electrons, was accelerated in the electrostatic field of the source region to an energy of 2000 (sometimes 1000) volts, was mass-analyzed in the magnetic field, and recorded electrically. By scanning magnetically, complete mass spectra were obtained up to mass 300 (2000 volt ions) or mass 600 (1000 volt ions) and any effects of mass discrimination were minimized. The resolving power, A M / M , of this spectrometer, i . e . , its ability to separate neighboring mass peaks sufficiently to permit quantitative measurements, was usually about 1 part in 150. Positive ion currents were recorded by a single-stage, balanced bridge amplifier,'* redesigned for a Victoreen 5800 electrometer tube, which drove directly a 0-1 mv. Philips Recorder type 110.161/00 (pen speed:l sec.). With an input resistance of 5 X 10'O ohms, currents of less than 10-15 ampere were detectable. The crucibles were supplied from a full-wave, selenium rectifier circuit which could deliver 15 amperes a t 15 volts and had a small ripple. The supply was powered from a Philips Type E 4225/05 a x . regulator with a stability of about one part in 500. In studies of this type, the choice of suitable crucible materials is of paramount importance, in order to eliminate or at least minimize chemical reactions between sample and crucible. Detailed requirements and findings have been discussed elsewhere.18 The simplest form of crucible consisted of a non-inductively wound 10 mil tungsten double helix, covered with an alumina coating to form a solid basket. Whenever alumina was not suitable as material, an inner thimble was inserted, consisting of either graphite, B e 0 or Mo . The sample surface could be viewed directly through a Pyrex window, which was of special importance whenever sample and crucible interacted.
111. Procedure After the sample of interest had been placed in the crucible and the system evacuated to a pressure of less than (11) Type CH3, Atlaswerke. Bremen, Germany. (12) L. A. DuBridge and H. B. Brown, Rev. Sci. Instr., 4 , 532 (1933). (13) J. Drowart and R. E. Honig, t o be published.
\
July, 1957
DETERMINATION O F D I S S O C I A T I O N ENERGIES OF DIATOMIC RIOLECULES
10-8 mm., a few preliminary runs were made with the sample a t room temperature, t o establish that the system was tight and the mass spectrometer properly adjusted. Next, the power input into the crucible was raised in suitable steps, and one or more runs made a t each level in the range from 25 to 250 atomic mass units (a.m.u.). To determine heats of vaporization, the peak of interest was scanned repeatedly a t each temperature level, making sure that temperature equilibrium had been established. Measurements were always made a t increasing and decreasing temperatures. A Leeds and Northru optical pyrometer was used to measure temperatures, o f t h e vaporizing surface as well as of the crucible. Whenever possible, kndwn points of fusion served to standardize the temperature scale, and emissivity corrections were applied where necessary. Occasionally, during the study of molecular species of low concentration, it was necessary to work a t temperatures where, because of the high vapor pressure of the main species, a deposit would form very quickly on the observation window during ‘the course of the experiment. In such cases, temperatures had to be estimated by extrapolation, from plots of temperaf~ versus ~ crucible heater current.
IV. Calculations The dissociation energy, DO, of a diatomic molecule can be obtained in a number of different ways.3 One of the methods is based on the thermo(dynamic cycle 2 x +2X,(g) 2LO(XI) -2x+ Xdg) X d g ) +2 X l W
-Lo(Xz) DO(X2)
(1)
where X Xdg)
= atom in liquid or solid phase = atom in gas phase (“monomer”) = diatomic molecule in gas phase
XZk)
(“dimer”) Lo(XI),LO(XZ) = heats of vaporization of atom or diatomic molecule, a t 0°K. Do(X2) = dissociation energy of dimer, a t 0°K.
From the cycle above, it follows directly that Do(&) = 2Lo(Xi)
- Lo(Xz)
(2)
- LT(X2) f Cp(X2,g) dT - 2
sor
DO(%) = zLT(X1)
981
soT
Cp(Xl,g) d T (4)
While for the diatomic species to be discussed below the exact dependence of Cp(X2,g) on temperature is not known, some first-order approximations can be made. It is found that the last two terms of eq. 4 are not likely to change the value of D oby more 2 kcal./mole. Since the experimental unthan certainties in LT(X1) and L T ( X z ) are considerably larger than & 2 kcal./mole, one may neglect the last two terms and write
*
Do(&) 2LT(X1) - LT(X2) (5) Of course, care must be taken that during the
course of an experiment the measured slopes are not modified by instrumental parameters, such as changes in the vaporizing surface, temperaturedependent electrostatic effects, changes in collection eficiency (through deformation of the source a t high temperatures), and re-evaporation a t elevated temperatures of deposits formed on the source electrodes. Therefore ion intensity ratios I + ( X 2 ) / I + ( X l )were measured, rather than the intensities I+(X,), as a function of temperature. Approximate heats of vaporization LT(X~)were obtained from the slopes of the plots log [ p ( X , ) * I+(X2)/21+(X1)] vs. 1/T, where XI) is the known vapor pressure of the monomer. It is readily shown that the quantity in the brackets represents p ( X , ) , the vapor pressure of the dimer, provided the ratio of diatomic to atomic ionization cross sections Qi(X2)/Qi(Xl)= 2. In this fashion, ,most effects due to instrumental changes were eliminated. B. Absolute Entropy Method.-The advantage of this method lies in the fact that it is very accurate and may be based on data taken a t a singIe temperature, but, on the other hand, it requires many parameters of the vaporizing species to be known. Any standard treatise on Thermodynamics and Statistical Mechanics will show that the heat of vaporization (in cal./mole) a t 0°K. of an n-atomic particle, Lo(X,), is given by
I n this equation, energies are usually given in kca1.l mole or in e.v. (electron-volts/particle). In the following, two methods will be briefly described which yield dissociation energies from data obtained in the mass spectrometer. A. Slope Method.-While this method yields results of limited accuracy14 (about f 7 kcal./ In Q ( X 4 mole or i 0.3 e.v.) and requires that the data be Lo(X,)/RT = -In p(X,) taken over a sufficient temperature range, no as( n / R T )JOT C,dT - ( n / R ) (Cp/T) d T ( 6 ) sumptions need be made concerning the vaporizing species, except that their condensation coefficient where is taken to be unity. R = gas constant = 1.98 cal./mole As previously discu~sed,~ the heat of vaporizaT = absolute temperatme, in OK. tion LT of a given species X, a t a mean temperature p(X,) = equilibrium presaure, in atm., of x, Q(X,J = partition function of X, T (in OK.) can be evaluated directly from the slope of the plot log (I+(Xn)T)vs. 1/T, where I+(X,) The last two terms of eq. 6 represent the free is the measured current of the ionic species. The energy function of the liquid or solid. Heats of Kirchhoff equation defines t h e dependence of the vaporization may be evaluated by substituting the heat of vaporization on temperature values for the partition functionI6 into. eq. 6. By applying the resulting equation to the atomic LT = Lo J T ( W g ) - Cp) d T (3) and diatomic species and combining it with eq. 2, the dissociation energy, in cal./mole, at 0°K. is obwhere tained Cp(g) = specifiq heat, a t constant pressure, of gaseous
+
+
h*
+
Cp ,
=
species specific heat, a t constant pressure, of liquid or solid species
Equations 2 and 3 are combined to yield (14) P. Goldfinger and W. Jeunehornme, Trans. Faraday Soc., 1591 (1936).
58,
+
Do(Xz)/4.576T = - log pmm(x1) log [ ~ + ( X 2 ) / ~ + ( x i ) l log [Qi(X,)/Qi(X,)l 3/2 log T 1/2 log MI 2 log Qe(X1) log Qa(X2) - 2 log r A - log Qv(X2) 2.8247 (7)
-
-
+
+
+ +
(15) G. Herzberg, “Infrared and Raman Spectra,” D. Van Nostrand Co., Inc., New York, N. y.,1945, p. 502.
982
J. DROWART AND R. E. HONIG
Vol. 61
TABLE I DATAUSED TO COMPUTE DISSOCIATION ENERGIES Element
C Si Ge Sn Pb
cu
Ag
Au Ga In
T1
Typical temp.
T (OK.)
2400 1660 1370 1200 800 1530 1285 1550 1300 1110 944
Monomer vapor pressure ~(XI)T, (mm.)
x 7x 3.5 x 3 x 4 x 7 x 7x 3 x 7x 1x 4 x 3
10-6 10-4 10-6 10-6 10-6 10-3 10-3 10-3 10-3 10-3
10-2
Ref.
j’t;gfi/T
---MonomerElectronic state Q
21 10 22 23 24 25,26 27 28 29 30 31
7-------Dimer---------We
e W )
8.85 8.02 3.83 1.48 1.oo 2.00 2.00 2.00 3.6 2.23 2
Qe(Xr)
-6 3 3 3 3 1 1 1 1 1 1
(om. -1)
1641.35 506.72 (370) (300) 256,5 266.1 192.4 190.9 (225) (135) (90)
Ref.
32,33 34
Q”(XZ)T
1.60 2.82 3.11 3.31 32 2.71 4 . 5 a 4.54 4 . 5 b 5.17 4 . 5 ~ 6.31 20 4.35 6.25 20 7.94
rA
1.31 2.25 (2.44) (2.80) (3.08) (2.34) (2.68) (2.68) (2.50) (3.0) (3.10)
.
where
obtained in an earlier study.8 Dissociation energies for the Group I B and some I I I B elements were computed from data obtained in the present study. Ql(Xz),Q,(X~) = ionization cross sections of dimer and monomer, resp. Table I lists the data employed for the Absolute M I = mass of monomer, in a.m.u. Q e ( Xz),Qe( XI) = electronic partition functions of dimer Entropy Computations. For the typical temperatures shown in column 2, there are given in columns and monomer, resp. Qv(Xz) = vibrational partition function of di- 3, 4 and 5 the corresponding vapor pressures with atomic species literature references, and ion current ratios [I+rA = interatomic distance, in 8. (XZ)/I+(X~)]T. The electronic partition function Most of the terms in eq. 7 are evaluated readily. for the monomer derived from the electronic It is assumed in this research that Qi(X2) = 2Qi- states (column 6) and known energy levels’’ is (XI). Two experimental effects may conceiv- presented in column 7 . ably modify the ion intensity ratio I+(Xz)/I+(X1) The remainder of Table I concerns the dimers. so that it would not represent accurately the di- Wherever possible, references are given for the vimer-monomer concentration ratio : mass discrim- brational constant ue. Since no band spectroination, and the production of some ionized atomic scopic information was available for Gez and Sn2, fragments from the dimer. Even if these effects rough estimates were obtained by interpolation were to change the ratio by a factor of two, the re- from a graph of We us. 2, plotted for all known symsulting error would not exceed =t0.1 e.v., which is metric diatomic molecules. The vibrational frethe maximum uncertainty quoted below in Table quencies for Gaz, Inz, Tlz were estimatedzOfrom the 11. The ion intensities are measured directly, a t Debye temperature of the corresponding solid a given temperature which is read on the pyrom- metal. The vibrational partition functions based eter. The vapor pressure of the atom is ob- on these frequencies are believed to be accurate to tained from the literature. The electronic parti- some f 20oJ,, but the error in the dissociation ention function of the atomic species is calculated ergy due to this cause is less than 1%. Exact interfrom the known atomic energy states.17 While nuclear distances ?‘A are known only for Cza2and such information is usually not availahle for the Siz.34 For the other molecules, estimates had to be dimer, assumptions can be made on a theoretical made which are probably accurate to about =I= basis. l8 The internuclear spacings are usually not 10%. The double bond distances suggested by known for the diatomic molecules studied, but can (20) E. C. Baughan, Trans. Faraday Soc., 48, 121 (1952). be obtained from known crystal spacinglg to an (21) L. Brewer, P. Gilles and F. A. Jenkins, J. Chem. Phys., 18, estimated accuracy of about 10%. The vibra- 797 (1948). (22) A. W. Searcy and R. D. Freeman, ibid., 23, 88 (1955). tional frequencies are known in some cases, but (23) A. W. Searcy and R . D. Freeman, J. A m . Chem. SOC.,7 6 , 5229 have to be estimated in others. These details are (1954). discussed for each individual case in the next sec(24) 0.Kubaschewski and E . L. Evans, “Metallurgical Thermochemistry,” 2nd Ed., Pergamon Press Ltd., London, 1956. tion. (25) H. N. Hersh, J. A m . Ckem. SOC.,75, 1529 (1953). V. Results (26) J. W. Edwards, H. L. Johnston and W. E. Ditmars, ibid., 75, (1953). The computational methods outlined in Section 2467 (27) C. L. McCabe and C. E. Birchenall, J. Metals, 5 , 707 (1953). 1V were first applied t o CZ,Siz, and Gez, whose dis(28) L. D.Hall, J. A m . Ckem. Soc., 73, 757 (1951). sociation energies had p r e v i o ~ s l y been ~ ~ ~ ~deter(29) R. Speiser and H. L. Johnston, ibid., 75, 1469 (1953). (30) T. S. Anderson, J. Ckem. Soc., 141 (1943). mined by the slope method. The computations (31) R. C. Miller and P. Kush, Phya. Rev., 99, 1314 (1955). carried out for Snz and Pbz used data that had been (32) G. Herzberg, ”Spectra of Diatomic Molecules,“ D. Van NosPmm(Xi)
= vapor pressure of atomic species, in mm.
(16) J. W.Otvos and D. P. Stevenaon, J. A m . Chem. Boc., 7 8 , 546 (1956). (17) R. F. Bacher and S. Goudsmit, “Atomic Energy States,” McGraw-Hill Book Co., Inc., New York, N. Y., 1932. (18) G. Herzberg, “Spectra of Diatomic Molecules,” D. Van Nostrand Co., Inc., New York, N. y., 1950,p. 315. (19) W. Hume-Rothery, “The Struoture of Metals and Alloys,” The Inatitute of Metala, Londoh, 1950,
trand Co., Inc., New York, N. Y.,1950, Table 39. (33) A. R. Gordon, J. Chem. Phys., 5 , 350 (1937). (34) A. E. Douglas, Can. J . Phys., 33, 801 (1955). (35) L. Pauling, “Nature of the Chemical Bond,” 2nd Ed., Oxford University Press, London, 1950, p. 164. (36) H. W. Leverens, “Periodic Chart of the Elements,” RCA Laboratories, 1953. (37) R. M. Badger, J. Chem. Phys.. 2, 128 (1934); 3, 710 (1935).
t
DETERMINATION OF DISSOCIATION ENERGIES OF DIATOMIC MOLECULES
July, 1957
983
P a ~ l i n were g ~ ~ used for the remainder of the Group IVB elements. For Cu2, Ag2 and Auz the single bond values listed by lever en^^^ were employed, which checked with those from Badger's The electronic states of the dimers appear to be known only for C232and Si2.34 While it was suggested recently38 that the ground state of C2 had not been identified correctly, a direct determination of the heat of formation of the 3rIustate of C2 from graphite39 yields, when combined with AHoo(C1) = 170 kcal./mole, a dissociation energy D0(C2).= 150 kcal./mole or 6.5 e.v., in fair agreement with the values presented below. The remaining Group IVB dimers are assumed to have a ground state like Si2, and in all cases Q e ( X 2 ) = 3 was used. It seems reasonable to postulate40that the group JB dimers are in a ' 2 state, from which follows that Qe(X2) = 1. For both groups of elements the assumption was made that low-lying excited states do not contribute significantly to the electronic partition function. For the group I I I B elements, Q e ( X 2 ) = 1 was used, which yields a maximum value for the dissociation energy. Table I1 presents the dissociation energies of the Group IVB and I B diatomic molecules, as well as estimates for Ga2and T12,computed by the methods outlined in Section IV. It will be noted that the slope values which were computed by the least squares method are quoted at T'K. (see Table I for representative temperatures). But since the difference between Do and DT amounts to less than the experimental errors involved in the slope method (see Section IVA), it is quite legitimate to compare Do computed by the Absolute Entropy Method with the slope value DT.
quoted band spectral values, wherever available, obtained mostly by linear Birge-Sponer extrapolations. The agreement is seen to be reasonably satisfactory, falling within the expected accuracy of the extrapolation. For Gaz, an upper limit of the dissociation energy could be established based on the fact that I+(Ga2)/l+(Gal) was found to be < 1/10,000. Such an estimate was not possible for In2 because of its unfavorable isotopic di~tribution.~The upper limit of the dissociation energy of Tl2 is based on the estimate I+(Tl2)/I+(Tl1)< obtained from velocity distribution measurements in a T1 molecular beam.31 VI. Discussion The dissociation energies computed for Cu2, Ag2 and Au2 by the absolute entropy method were each based on the average of about 10 independent determinations and showed an internal consistency of f 0.03 e.v. The errors quoted in Table 11 take into account the uncertainty in ?A, an estimated instrumental discrimination, and possible doubts concerning the relative ionization cross sections of monomer and dimer. Schissel is reported43to have evaporated, in a parallel study, Cu, Ag and Au from a graphite Knudsen cell in a mass spectrometer and t o have obtained similar values which, however, all lay about 0.15 e.v. higher. It is interesting that the present rate-ofvaporization values appear to agree well with Schissel's equilibrium values. Agreement with the band spectral values is satisfactory in view of the fact that they were obtained from linear BirgeSponer extrapolations which may lead to values that are as much as 30% too high.44 The values presented would be lowered by an amount RT In TABLEI1 COMPARISON OF DISSOCIATION ENERGIES (IN E.v.) OB- Q e ( X 2 ) if Q(X2) fi 1, Le., if low lying states contribute significantly and if the ground state is TAINED BY ABSOLUTE ENTROPY AND SLOPE METHODS WITH BANDSPECTRAL VALUES Molecule
Cz
St
Absolute entro y DO %ef.
6 . 2 f0.2
Slope
DT
Ref.
Band spectra DO Ref.
9 5.6 f 0 . 4 9 4.9 f 0 . 3 6 . 8 f . 5 42 7 . 2 " 10 3 . 2 f . 5 10 4.0" 8 3 . 2 f . 2 10 8 8 0 . 6 f0.2 1.9 f .3 2.1 1.8 .3 1.8 2.0 f .3 2.7
41 32 34
TABLEI11 PREFERRED VALUES OF DISSOCIATION ENERGIES O F DIMERS This Dimer study
3.2 f .2 Gee 2 . 8 f . 2 Snz 2 . 0 f . 2 Pbz 1 . 0 f . 2 41 cuz 2.02 f . 1 5a Agz 1.6s f . I 5b ALIZ 2.1s f . l 50 Ga?
