J . Phys. Chem. 1991, 95, 4242-4245
4242
Ultraviolet-Vklble Absorption Spectra of Equllibrlum Sulfur Vapor: Molar Absorptlvlty Spectra of Ss and S, Richard I. Billmers Naval Air Development Center, Code 501 2, Warminster, Pennsylvania 18974
and Alan L. Smith* Chemistry Department, Drexel University, Philadelphia, Pennsylvania 191 04 (Received: June 18, 1990; In Final Form: December 3, 1990)
Ultraviolet-visible absorption spectra of equilibrium sulfur vapor were measured at various allotropic concentrations. This was achieved by using a two-temperaturecell having sulfur liquid in equilibrium with sulfur vapor. Independent variation of either temperature changes the vapor composition and, therefore, the absorption spectrum. Factor analysis techniques were applied to these vapor-phase mixtures to determine the identity and spectrum of each allotropic component. Our results show S3and S4 to be two of the components which absorb in the spectral region between 350 and 600 nm. Quantitative, pure-component spectra of S3and S4 were determined and used to calculate the partial pressures present in each mixture. AHo,, and ASo,, for the reaction 3S4* 4S3 were determined to be 77.65 kJ/mol and 28.1 J/(mol K),respectively, at 810 K.
Introduction Elemental sulfur in the vapor phase exists in many allotropic forms, as has been reviewed by Meyer.' In 1972, Meyer and co-workers reported that the spectrum of sulfur vapor changes with temperature and pressure? They studied and characterized the visible absorption spectra of S3 and S4 by photolyzing the chlorosulfanes S3Cl2 and S4C12trapped in a low-temperature krypton m a t r i ~ . Strong ~ absorption peaks at 400 and 530 nm were attributed to S3 and S4, respectively. More recently, Krasnopolsky' attempted to use these data as well as those of Braune and SteinbacherJ to astimate the absorption cross sections of S3and S4. Steudel and co-workers6 recently measured the optical absorption spectra of S, (n = 6-10, 12, 15, and 20) in solution and estimated the extinction coeficients for each allotrope. The molecular composition of equilibrium sulfur vapor has been studied by vapor density measurements and by mass spectrometry. Meyer has reviewed all of the early work in ref 1. Rau7 has developed a thermodynamic model which predicts the composition of equilibrium sulfur vapor as a function of pressure and temperature. The model is based upon the equilibria s, =. (n/2)Sz (1) and assumes that all allotropic forms from S2 to S8are present at temperatures up to the critical point. Equilibrium constants are computed from the standard entropy, heat of formation, and Gibbs free energy of formation of each of the allotropes, using S2as a reference. The partial pressure of each allotrope and the density of the vapor are then calculated from the total pressure and temperature. Chaos has reviewed the thermodynamics of gaseous sulfur allotropes, concluding that only the thermodynamic parameters for S2,s6, and S8are reliably determined. Thus, the parameters Rau used for S3,S4, S5, and S7 are somewhat uncertain. More recently, Lenain et al? measured the Raman spectra of sulfur vapor over a wide range of temperature and pressure, (1) Meyer. B. Chem. Rev. 1976. 76. 367.
(2) Meyer. B.; Gouterman. M.; Jensen. D.; Oomen, T. V.; Spitzer, K.; Stroyer-Hansen. T. Adu. Chem. Ser. 1972, 53, No. 110, 53. (3) Meyer, B.; Stroyer-Hansen,T.; Oomen, T. V. J. Mol. Specrrosc. 1972, 42, 335. (4) Krasnoplsky, V. A. Ado. Spuce Res. 1987, 7, 25. (5) Braune, H.; Steinbacher, E. Z . Naturforsch. 1952, 70, 486. (6) Steudel, R.; Jensen. D.; Gobel, P. Ber. Bunren-Ges Phys. Chem. 1988, 92, 118. (7) Rau, H.; Kutty, T. R. N.; Guedcs De Carvalho, J. R. F. J . Chem. Thermodyn. 1973, 5, 833-844. ( 8 ) Chao, J. Hydrocarbon Process. 1980, 11, 217. (9) Lenain, P.; Piquenard, E.; Corset, J.; Jcnsen, D.; Steudel, R. E . Bunsen-Ges Phys. Chem. 1988, 92, 859.
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determining mole fractions of S2, s6, S7, and S8. Their results indicate that Rau's model underestimates the heat of formation of S7and possibly overestimates the standard entropy of Sa.There is clearly a need for more precise thermodynamic data for the sulfur allotropes. In this work, sulfur vapor at temperature TI in equilibrium with liquid sulfur at temperature Tz (
