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Thermodynamics of Some Simple Sulfur-Containing Molecules William H

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Thermodynamics of Some Simple Sulfur-Containing Molecules William H Journal of Research of the National Bureau of Standards Vol. 49, No. 3, September 1952 Research Paper 2350 Thermodynamics of Some Simple Sulfur-Containing Molecules William H. Evans and Donald D. Wagman The t hermodynamic functions ( F o- f1 ~) / T, ( HO - H~) / T, So ( Ho- Tl~) , and C; are calculated to high temperatures for gaseous sulfur (monatomic and di atomic), sulfur monoxide, sulfur dioxide, sulfur trioxide, and hydrogen sulfide from molecular and spectro­ scopic data. Values of the heats of formation of the various atomic and molecuiar species are selected from published experimental data, and certain industrially importantequilibria are calculated. 1. Introduction For monatomic sulfur gas the only other contri­ bution is from the electronic excitation. The The calculation of the thermodynamic properties electronic functions were calculated by direct of a number of simple gaseous sulfur-containing summation of the energy levels, using term values molecules has been carried out as a part of the and multiplicities (table 1) from Moore [4) and Bureau's program on the compilation of tables of the conversion factor 1 em- I = 2. 5 51 cal/mole. Selected Values of Chemical Thermodynamic Prop­ Only the five lowest levels arc significant below erties. The data on a large number of inorganic 5,000°K. sulfur compounds had been critically evaluated by K . K. Kelley in 1936 [1].1 Since that date, sufficient TA B LE 1. Spectroscopic energy levels for (g) new information has been reported in the literature to warrant a reevaluation and recalculation of the Term deSignation Energy Multi- properties of gaseous monatomic and diatomic plicity sulfur, sulfur monoxide, sulfur dioxide, sulfur tri­ 2 rm-1 oxide, and hydrogen sulfide. 'p, 0. 0 5 The calculations are divided into two part : 'P, 396.8 3 'Po 573. 6 1 (a) Calculation of the thermodynamic functions, ID, 9239. 0 5 ( FO- Fl ~)/ T, (HO- Fl ~)/ T, S o, ( HO- Fl ~) , and 0 : , for ISO 22181. 4 1 the various molecules in the ideal gaseous state; and (b) selection of "best" values for the heats of For diatomic sulfm gas the rotational and vibra­ formation of the various compounds. tional constants selected by Herzberg [5) for the isotopic S~2 molecule wore corrected to the liaturally 2 . Units occurring i otopic mixtme, using the relation given. by H erzberg [6] : The calorie used in these calculations is the thermo­ chemical calorie, defined as 4.1840 abs j . The _J1. = p=_Wei and gas constant R is taken as l.9S719 cal/mole OK . J1. i We The atomic weights used are H , 1.00 0; 0 , 16.0000; S, 32.066 [2]. The standard tates choscn for the where W e is the fundamental equilibrium vibrational frequency, Xe the anharmonicity constant, and J1. the elements are O2 (g), H2 (g), both in the ideal gas state at l-atm pressure, and S (c, rhombic). As is reduced mass. These corrected values, we= 724.62 customary, nuclear spin and isotopic mL'{ing con­ cm- I and xewe=2.S44 cm- I , were used to calculate tributions to the entropy and free-energy functions approximate thermodynamic function , assuming a have been omitted. rigid rotator of symmetry number 2 and an inde­ pendent harmonic oscillator of frequency we-2xewe. 3 . Calculation of the Thermodynamic Func­ In the rigid rotator calculation the equation given by Wagman et al. r3] were used. The harmonic tions oscillator calculations were carried out, using the tables of the Planck-Einstein functions calculated by The translational con tributioos to the free-energy Johnston, Savedoff, and Belzer r7]. The triplet function, (FO -H~ ) / T; the heat-content function, electronic ground state required the addition of (}fD -H~)/ T ; entropy, So; and heat capacity, 0 : , R In 3 to the entropy and - R In 3 to the free-energy were calculated for all the molecules, using the function. equations given by Wagman et al. [3]. Correction for rotational stretchiIlg, vibrational I FigW'es in brackets indicate the literatW'e references given at the end of this anharmonicity, and rotational-vibrational interaction. paper. , The higher polymeriC forms of sulfur, S4, S6, and S8, arc not included in this were calculated by using the second-order expansions report. The necessary molecular data on S. and S6 are not available; indeed the existence of S" which has been assumed in the irrterprctation of the most recent given by Mayer and Mayer [S] at 300, 500, 1,000, gas density measurements [53], is still unproved. Dr. George Guthrie of tbe 1,500, and 2,000oK; values at intermediate tempera­ U. S. Bureau of Milles. Bartlesville, Okla., bas recently completed calculations of the tbermodynamic functions of gaseous S, [54]. tures were obtained by graphical intcrpolation. At 141 1,500 0 K these corrections amounted to - 0.03 From this the correction to the free-energy function cal/mole oK fo r the free-energy function, 0.04 for the is given by - Fc/ T = R In Qc. Differentiation with re­ heat-content function, and 0.09 for the heat capacity. spect to T gives the corrections to the heat-content For sulfur monoxide gas the rotational and vibra­ function, Hc/T= RT(dlnQc/dT), and the heat capac­ tional constants taken from Herzberg [5] were ity, Cc= Rd(T?dlnQc/dT)/dT. In this way correc­ corrected for isotopic composition to give the con­ tions to the free energy function, heat content func­ stants We= 1123.09 cm- I and Xe We= 6.109 em- I, which tion, and heat capacity (amounting to - 0.05, 0.10, were used in the rigid rotator-harmonic oscillator and 0.23 cal/mole OK at 1,500 0 K, respectively,) were calculation. The triplet ground state required the calculated at 300°, 500°, 1,000°, and 1,500°I{ ; inter­ addition of R In 3 to the entropy and - R In 3 to mediate values were interpolated graphically. the free-energy function. Anharmonicity and The value 59.29 cal/mole OK for the entropy at stretching corrections were evaluated as for diatomic 298.16 OK may be compared with 59.24 ± 0.10 [14} sulfur gas. At 1,500° K these corrections were obtained from the low-temperature calorimetric - 0.02, 0.02, and 0.05 cal/mole oK for the free-energy data of Giauque and Stephenson [15}. function, heat-content function, and heat capacity, In the case of sulfur trioxide gas, the recent calcu­ respec tively. lations of Stockmayer, Kavanagh, and Mickley [13} For sulfur dioxide gas, the product of the moments were checked and converted to tbe values of the of inertia was taken as the average of the microwave fundamental constants used in this paper. measurements of Dailey, G olden, and liVilson [9], For hydrogen sulfide gas, the rigid rotator-har­ who obtained 106.403 X 10- 117 g3cm6, Sirvetz [10], monic oscillator calculations and corrections, made 107.007 X 10- 117 g3cm6 , and Crable and Smith [11], in the same way as for sulfur dioxide, were based 106.996 X 10- 117 g3cm6. This product of the moments upon the recent complete vibrational analysis of of inertia, 106.80 X lO - 117 g3cm6, and the vibrational Allen, Cross, and King [16] , which gives the anhar­ frequencies given by Herzberg [12] were used in a monicity terms. l\i[oments of inertia 'were taken rigid rotator-harmonic oscillator calculation. As from the work: of Allen, Cross, and Wilson [17], the available data do not permit the calculation of Grady, Cross, and King [1 8], and Hainer and King the anharmonicities, these were estimated from the [19] and corrected to approximate eq uilibrium relation, based on the data for sulfur monoxide, values by com.parison with water vapor. These X ij= 0.003 (Vi+Vj), where X ij is the anhannonicity gave a product Ix/vIz equal to 49.25 X 10 - 120 g3 cm6 • arising from the interaction of the two fundamental A stretching correction, insignificant in the case of frequencies Vi and Vj [13] . These were used to the other polyatomic molecules, was applied by correct the rigid rotator-harmonic oscillator calcula­ using the method of Wilson [20]. The corrections tion by the method developed by Stockmayer, Kav­ to the rigid rotator-harmonic oscillator at 1,500 OK anagh, and Mickley [13]. In this treatment the were - 0.06 , 0.08, and 0.22 cal/mole OK for the vibrational levels of a molecule with nondegenerate free-energy function, heat-content function, and fundamental frequencies are taken as heat capacity. The calculated value 01 the entropy at 298.16 OK , E.-Eo 49.17 cal/mole OK, may be compared with the value he [14] 49.11 ± 0.10 obtained from the low- temper­ ature calorimetric data of Clusius and Frank [21 1 where Vi are the observed fundamentals, in cm- 1,vi are and Giauque and Blue [22[. quantum numbers, and X ii are the anharmonicities, To correct values of t,HjD and t,Ff' between 0 OK in cm- I , as calculated above. If the anharmonicities and 298.16 OK, it was necessary to know the ther­ are considered to be small, their contribution to the modynamic functions at t he latter temperature for boltzmann factor can be expanded and the vibra­ crystalline rhombic sulfur. These were obtained by tional partition function Q. readily summed: graphical integration of the heat.. capacity data of Eastman and McGavock [23] as follows: T A BLE 2. Thermodynamic functions for S (c, rhombic) where 1 298. 160 K 300 0 K u i=hev ;/kT cal/mole cal/mole OK OK Ui } ii=2Xiihc[kT(e - l )2]- 1 ( FO- H ~)/ T__ _____ - 4.
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