2231
NOTES
Vaporization, Thermodynamics, and Dissociation Energy of Lanthanum Monosulfide.
11’
by E. David Cater and Ronald P. Steiger Department of Chemistry, University of Iowa, Iowa City, Iowa 68840 (Received October 18, 1967)
Mass spectrometric and vacuum balance studies of the sublimation of lanthanum monosulfide, LaS, were reported in paper I by Cater, Lee, Johnson, Rauh, and Eick.2 They obtained an equation for the vapor pressure of LaS, calculated as though the sublimation occurs only to molecules LaS. Taking the heat of sublimation of La to be 100.0 kcal/mole a t 298°K and estimating the heat of formation of LaS(s) to be AHf”298 = - 113 f 5 kcal/mole, they obtained a dissociation energy of 137 f 6 kcal/mole or 5.9 0.2 eV. The ion LaS+ dominated the mass spectrum. The ions La+ and S+ were also observed, but because 30-70 eV ionizing energy was used and the slopes of log I + T vs. 1/T were nearly equal for all species, it could not be determined whether the La+ ions observed were the result of primary ionization of La(g) or of fragmentation of LaS(g). However, calculations indicated that 7-10% of the S atoms. vapor was La I n this note we present a dissociation energy of LaS determined from a mass spectrometric study of the isomolecular gaseous equilibrium
+
US
+ La
=
LaS
+U
(1)
and the value Do(US) = 5.38 f 0.10 eV or 124.0 f 2.3 kcal/mole as determined by Cater, et aL3 We then correct two errors in paper I and discuss the thermodynamics of LaS(s) and LaS(g). Experiments Equilibrium 1 was studied by mixing equimolar amounts of finely ground lanthanum and uranium monosulfides, placing the mixture in an effusion”cel1of single-crystal tungsten, and heating to 2207-2493°K in a Bendix Model 12-101 time-of-flight mass spectrometer. The samples had been prepared at the time of earlier studies on LaS2 and US.394 Since that time they had become slightly oxidized by exposure to air. No analysis was performed on the samples, but in the mass spectrometer the oxide peaks UO+ and L a 0 +,while very intense at the start of the experiments, were barely detectable a t the end. The mass spectrometer was operated in the continuous ionization mode6 and had
been fitted with a 2 m long flight tube for improved resolution. Electrons of 12-eV energy were used to ionize the effusing molecules. This energy is too low to cause appreciable fragmentation of LaS and US molecules, while at the same time lying in the region in which the ion current ratio U+/US+ is constant3over a range of several volts in the sublimation of pure US. Since similar results have also been obtained for Pr+/ PrS+ 8 and Y+/YS+ 7 in the sublimation of pure PrS and YS, this should be an appropriate voltage for use with LaS as well. The techniques used were essentially those described earlier.2*3 Experimental Results Ion current equilibrium constants for reaction 1, K = I + L , s l + ~ / I + L a Iuncorrected +~~, for different sensitivities of the instrument to the several species, are plotted in Figure 1 as log K vs. 104/T. The line shown there was drawn by least-squares analysis, and its equation with standard deviations is log K = [(0.315 f 0.063)104/T] (0.615 f 0.267) (2) The slope corresponds at the mean temperature 2350°K to a heat for reaction 1 of AH02360 = -14.4 f 2.9 kcal/mole. The intercept, again neglecting relative sensitivities, corresponds to AX”2360 = -2.81 f 1.22 eu. No appreciable error should be introduced by neglecting the relative sensitivities (ionization cross sections) since the form of the equilibrium constant will cause these to tend to cancel one another. Reducing the heat to 0°K by means of the estimated thermal functions of , ~ US(g), paper I for LaS(g), those of Cater, et ~ l . for and the tabulated values for La(g)6 and U(g)g gives
(1)
Based on work supported by the U. S. Atomic Energy Commission under Contract AT(l1-1)-1182 with the University of Iowa. (2) Paper I : E. D. Cater, T. E. Lee, E. W. Johnson, E. G. Rauh, and H. A. Eick, J . Phys. Chem., 69,2684 (1965). (3) E. D. Cater, E. G. Rauh, and R. J. Thorn, J. Chem. Phys., 44, 3106 (1966). Note that Do(US) and Do(USz) are incorrect as calculated in the reference from the data there. They should be DO(US) = 124.0 i 2.3 kcal/mole or 5.38 f 0.10 eV and Do(USz) = 247 f 4 kcal/mole or 10.7 f 0.2 eV. (4) E. D. Cater, P. W. Gilles, and R. J. Thorn, J . Chem. Phys., 35, 608 (1961). (5) Modifications were made in the ion source similar to those described by M. H. Studier, Rev. Sci. Instr., 34, 1367 (1963). (6) B. A. Holler, M.S. Thesis, University of Iowa, 1967. (7) R. A. Steiger, Ph.D. Thesis, University of Iowa, 1967. (8) D. R. Stull and G. C. Sinke, “Thermodynamics Properties of the Elements,” American Chemical Society, Washington, D. C., 1956. (9) R. C. Feber and C. C. Herrick, “Ideal Gas Thermodynamic Functions of Lanthanide and Actinide Elements,” Los Alamos Scientific Laboratory Report LA-3184, 1965. Volume 73, Number 6 June 1968
2232
NOTES
,
2400 1 1
1.0t
L
23?0
,
US+LaoLaS+U
-
O
0.4
The estimate of paper I, that 7-10% of the vapor over LaS(s) in this temperature range consists of La and S atoms, is confirmed by calculations from this dissociation energy.
I
I
Corrections to Paper I The effusion orifice of paper I had a nominal depth of 0.254 cm rather than the reported value, 0.125 cm. The resulting Clausing factor, KO = 0.36,” gives the following corrected equation for the vapor pressure of LaS(s), replacing eq 3 and 5 of paper I
0
1
t t
4D
1
4.1
I
I
42
4.5
Figure 1. Temperature dependence of the equilibrium constant of the reaction US(g) La(g) = LaS(g) U(g).
+
moo= -13.5 f 3.2 kcal/mole where additional uncertainty includes those in the estimated functions. Combined with Do(US) = 124.0 f 2.3, this value gives Do(LaS) = 137.5 f 5.2 kcal/mole or 5.96 f 0.22 eV. Note that the value of &(US) is a second-law value and does not depend on assumptions regarding the ground state of US(g) ,which is unknown. Using the tabulated and estimated quantities from the same sources as before and a 22ground state for LaS(g) as discussed below, one calculates an electronic entropy of 3.2 f 1.5 eu a t 2350°K, which corresponds to a ground-state degeneracy of 5 . The uncertainty, which includes the and estileast-squares standard deviation in AS02850 mated uncertainties in the other quantities, allows a ground-state degeneracy of US(g) between 2 and 13. Third-law calculations based on the 29 individual values of K and free energy functions obtained from the above sources gave for reaction 1the average value with standard deviation A H O o = -9.11 f 0.50 kcal/ mole, with a maximum scatter of k l . 0 kcal/mole and no systematic variation with the experimental temperature. However, the estimated standard deviations in the free energy functions increase this uncertainty by 3-4 kcal/mole. We have taken the ground-state degeneracy of US(g) to be 8 in this calculation and have neglected contributions from possible excited states. The average third-law heat thus gives Do(LaS) = 133.1 f 4 kcal/mole or 5.77 =k 0.17 eV. It is seen that the second- and third-law dissociation energies agree within their standard deviations. Coppens and DrowartlO have obtained Do(LaS) = 137.5 f 2.5 kcal/mole or 5.96 f 0.1 eV from mass spectrometric data for the isomolecular exchange reactions of LaS(g) with SiS(g) and CeS(g). This value is in excellent agreement with the present determination. For further calculations we have taken as the “best” 0.1 value Do(LaS) = 136 f 3 kcal/mole or 5.9
*
eV. The JOUTTXZ~ of Physical Chemistry
+
(7.719
9
I
4A
; ; ,4 0 1
+
log PE(atm) = - [(28,730 f 210)/T
f
0.094)
(3)
The uncertainties are standard deviations from the least-squares treatment of the data. Here we have used the symbol PEfor the “effective” vapor pressure, calculated as though the vapor were totally LaS molecules. Equation 3 gives pressures higher by a factor 2.26 than eq 5 of paper I, or values of log PEhigher by 0.354. For the reaction LaS(s) = LaS(g) (4) the second-law entropy of sublimation is thus increased by 1.62 eu to A.S02240= 35.1 f 0.6 eu. Studies12I1*published since paper I have shown that the ground state for Lao, and therefore presumably also LaS, is 22rather than 42as used in paper I (see ref 14). Applying the corresponding correction to the estimated entropy and free energy function of LaS(g), one obtains the values given in Table I for equilibrium
4. The second- and third-law values agree within their assigned uncertainties, although the agreement is marginal. The third-law values depend strongly on the
Table I: Corrected Thermochemical Results for the Reaction LaS(s) = LaS( g)”
AH02240,kcal/mole
ASOZZ~O, eu AHOo, kcal/mole
2nd-law valuea
3rd-law values
131 5 I 1 . 0 35.1 f 0.6 141.8 i= 2 . 0
124.9 f 6 32.4 f 2.4 135.1 =k 6
I
Uncertainties are standard deviations for second-law values
at 2240°K and are estimated limits for other values.
(10) P.Coppens, 8. Smaes, and J. Drowart, Trans. Faraday Soc., 63, 2140 (1967). (11) S. Dushman and J. M. Lafferty, “Scientific Foundations of Vacuum Technique,” 2nd ed, John Wiley and Sons, Inc., New York, N. Y.,1962,pp 94,95. (12) K. D. Carlson, E. Ludeiia, and C. Moser, J. Chem. Phye., 43, 2408 (1965). (13) W.Weltner, S. McLeod, Jr., and P. H. Kasai, ibid., 46, 3172 (1967). (14) L. Akerlind, Arkiv Fysik, 22, 66 (1962); U. Uhler and L. A. Akerlind, ibid., 19, 1 (1961).
NOTES
2233
estimated average heat capacity of solid LaS between 298 and 2240°K, 13.9 cal/deg mole. An average heat capacity of 12.55 cal/deg mole would give excellent agreement and change AHOo in Table I to 139 f 2 kcal/mole.
-3.OC
Heat of Formation of LaS -3s The heat of formation of LaS(s) can be calculated from the above values for the dissociation energy and heat of sublimation of LaS, the heat of formation of S(g), AH0298 = 66.7 i 0.5 k ~ a l / m o l e ,and ~ ~ the heat -4.OC I I I +XI03 of sublimation of La, = 103 f 1 k ~ a l / m o l e . ~ ~ J ~ ) 3.5 4.0 4.5 5.0 The result is AHfo298[LaS(s)] = - 108 f 4 kcal/mole, Figure 1. based on the second-law value for the heat of sublimation of LaS. values for the dielectric constants and density reported (15) “JANAF Thermochemical Tables,” Addendum, U. S. Governin the literature5 and the viscosity data determined by ment Clearinghouse for Federal Scientific and Technical Information, Publication No. P B 168370-1,Washington, D. C., 1966. C. Sutphen, the latter being listed in Table I. The (16) R.J. Ackermann and E. G. Rauh, J . Chem. Phys., 36,448 (1962). derived values of BO and K d i s s are listed in Table 11. (17) C. E. Habermann and A. H. Daane, ibid., 41,2818 (1964). Plots of log K d i s e vs, 1/T are shown in Figure 1, and the respective heats and entropies of dissociation were calculated to be -0.8 f 0.3 kcal/mol and -17 eu for the hexachloroantimonate and -0.5 i 0.3 kcal/mol The Heat and Entropy of Dissociation and - 20 eu for the hydroxychloroantimonate. of Carbonium Ion Pairs
by E.Kalfoglou and M. Szwarc
Table I : Viscosity of Methylene Chloride” Temp,
Department of Chemistry, State University College of Forestry at Syracuse University, Syracuse, New York 13810 (Received November 1 , 1967)
Present interest in the role of free ions and ion pairs in ionic polymerization induced us to investigate the dissociation of some salts of carbonium ions in methylene chloride. We have chosen for our studies trityl hexachloroantimonate and trityl hydroxypentachloroantimonate. The salts were prepared as described in the literature’ and were purified by repeated crystallization followed by high-vacuum drying. The solvent was fractionated and carefully dried over calcium hydride. The conductance was determined in an apparatus described elsewhere2 using the procedure outlined in ref 3. The concentration of the salt was determined 413 or 435 mp; the spectrophotometrically a t A,, decimal extinction coefficients were determined to be 3.35 X lo4and 3.30 X lo4,respectively. (The two close peaks observed in the spectrum of trityl salts (see, e.g., ref 4) either do not represent two types of ion pairs or the heat of conversion of one into the other is approximately 0. Their relative heights are not affected by temperature variation (-70 to + 2 5 O ) or by dilution.) The conductance was determined within a temperature interval of -75 to +25O, at concentrations ranging from about low4to M . The final results were calculated by using the Fuoss method, taking the
O C
25 15 5
-5
- 15 a
Log q = -3.435
Temp,
n, mP
OC
4.58 4.99 5.42 6.07 6.76
-25
-35
-45 - 55 -65
t),
mP
7.59 8.61 9.88 11.5 13.6
+ (326/T).
However, when the ionization results from the reaction Ph3CC1
+ niLleC1, I_ Ph3C+, (MeCI,+J-, (MeCl,).-l
the relative optical densities of these two peaks seem to be affected by the nature of the MeCI, (compare, e.g., the spectra given in ref 4b and 4c). It should be mentioned that the studies of Evans were criticized by Price and Lichtin.O Their combined (1)W. M. Pasika, J . Polym. Sci., Part A-3, 4287 (1965); Tetrahedron, 22, 557 (1966). (2) D. N. Bhattacharyya, C. L. Lee, J. Smid, and M. Szwaro, J . Phys. Chem., 69, 612 (1965). (3) P. Chang, R. V. Slates, and M. Szwarc, ibid., 70, 3180 (1966). (4) (a) A. G. Evans, I. H. McEwan, A. Price, and J. H. Thomas, J . Chem. Soc., 3098 (1955); (b) J. L. Cotter and A. G. Evans, ibid., 2988 (1959); (c) J. W.Bayles, A. G. Evans, and J. R. Jones, ibid., 206 (1955). (5) 8. 0.Morgan and H. H. Lowry, J . Phys. Chem., 34,2386 (1930). (6) E. Price and N. N. Lichtin, Tetrahedron Lett., 18, 10 (1960). Volume 78, Number 6 June 1968
