The thermodynamic properties of dibenzothiophene

J. 677em. Thermodynamics 1991, 23, 431-450

The thermodynamic properties of dibenzothiophene a, b

R. D. C H I R I C O , c S. E. K N I P M E Y E R , A. N G U Y E N , and W. V. S T E E L E

HT Research Institute, National Institute for Petroleum and Energy Research, P.O. Box 2128, Bartlesville, Oklahoma 74005-2128, U.S.A.

(Received 15 August 1990)

Measurements leading to the calculation of the ideal-gas thermodynamic properties for dibenzothiophene are reported. Thermochemical and thermophysical properties were determined by adiabatic heat-capacity calorimetry, differential-scanning calorimetry (d.s.c.), comparative ebulliometry, and inclined-piston manometry. A literature value for the energy of combustion was selected and combined with the results to calculate standard entropies, standard enthalpies, and standard Gibbs energies of formation for the ideal-gas at selected temperatures from 298.15 K to 800K. The critical temperature and critical density were measured with the d.s.c., and a value for the critical pressure was derived. Sublimation pressures from 298.15 K to the triple-point temperature (371.8 K) were derived. All measured and derived properties were compared with literature values.

1. Introduction

This research was completed as part of a program, funded by the U.S. Department of Energy (DOE) Office of Fossil Energy, Advanced Research Section of Coal Liquefaction (ARL) research program, in which thermochemical and thermophysical properties are determined for "key" organic compounds present in alternative crudes

a Contribution number 323 from the Thermodynamics Research Laboratory at the National Institute for Petroleum and Energy Research. This paper is published in honor of the retirement of Professor Edgar F. Westrum, Jr. from The University of Michigan, Ann Arbor, MI.

b By acceptance of this article for publication, the publisher recognizes the Government's (license) rights in any copyright and the Government and its authorized representatives have unrestricted right to reproduce in whole or in part said article under any copyright secured by the publisher.

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency, thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, cqmpleteness, or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. References herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

c To whom correspondence should be addressed.

432 R. D. CHIRICO E T AL.

(i.e. shale oil, tar sands, heavy petroleum, and particularly liquids derived from coal). Upgrading of these heavy fossil fuels is effected normally by hydrotreating in the presence of catalysts, such as sulfided CoO-MoO3/7-AlzO3, at 5 MPa to 25 MPa pressure of hydrogen and at a temperature of 573 K to 723 K. ~1) Important reactions include hydrogenation of aromatics, hydrodesulfurization (HDS), hydrodenitro- genation (HDN), and hydrodeoxygenation (HDO). When these reactions are applied to polycyclic aromatic moloecules, over-saturation of rings often results. Therefore, to reduce consumption of expensive hydrogen, the reaction pathway that involves the most efficient use of hydrogen is sought. The problem of oversaturation is exacerbated as the number of rings increases.

Dibenzothiophene is widely used as a model compound in catalyst-comparison studies and kinetics studies of the HDS mechanism. An overview of the literature prior to 1982 was given by Zdra2il. (2) Although thermodynamic limitations to the HDS of dibenzothiophene similar to those observed for quinoline (a) are not expected, ~2) the thermodynamic information necessary for the analysis of possible reaction pathways and stable intermediates is not available. Present thermodynamic analyses are based on crude extrapolations from the properties of thiophene.

Because of the enormous number of individual compounds present in fossil materials, group-contribution and corresponding-states methods are employed to estimate thermodynamic properties in the absence of measured values. Much of the empirical information necessary to extend the existing group-contribution parameterization ~4,s) to include polycyclic aromatic sulfur-containing species does not exist. The studies reported here begin to provide this information. The critical properties reported here are the first reported for a polycyclic sulfur-containing compound.

The thermodynamic properties of dibenzothiophene were measured by means of adiabatic heat-capacity calorimetry, comparative ebulliometry, inclined-piston gauge manometry, and differential-scanning calorimetry. An energy of combustion value was selected from the literature, and standard Gibbs energies of formation for the ideal-gas state were derived. Standard ideal-gas entropies are compared with values derived from spectroscopic analyses reported in the literature. All heat capacities, vapor pressures, and critical properties measured or derived in this research are compared with literature values.

2. Experimental

The sample of dibenzothiophene was purified by zone refining as part of American Petroleum Institute Project 48 (API-48). The mole-fraction impurity was ~stimated by g.l.c, to be 0.0005 within API-48. The high purity of the sample was corroborated in the ebulliometric vapor-pressure studies by the small observed differences between the boiling and condensation temperatures of the sample. The fractional-melting study results reported later do not afford a reliable indication of the sample purity because the sample was zone refined.

Molar values are reported in terms of M = 184.256 g. mol-1, based on the relative atomic masses of 1981, ~6) and the gas constant R = 8.31451 J . K 1 .mol 1 adopted

PROPERTIES OF DIBENZOTHIOPHENE 433

by CODATA. C7) The platinum resistance thermometers used in these measurements were calibrated by comparison with standard thermometers whose constants were determined at the National Institute of Standards and Technology (NIST), formerly the National Bureau of Standards (NBS). All temperatures reported are in terms of the IPTS-68. ~8) The platinum resistance thermometer used in the adiabatic heat- capacity studies was calibrated below 13.81 K with the method of McCrackin and Chang. w) Measurements of mass, time, electrical resistance, and potential difference were made in terms of standards traceable to calibrations at NIST.

The essential features of the ebulliometric equipment and procedures for vapor- pressure measurements are described in the literature. (1° 12) The ebulliometers were used to reflux the substance under study with a standard of known vapor pressure under a common helium atmosphere. The boiling and condensation temperatures of the two substances were determined, and the vapor pressure was derived from the condensation temperature of the standard. ~12)

The uncertainties in the temperature measurements for the ebulliometric vapor- pressure studies were 0.001 K. Uncertainties in the vapor pressures or(p) of the sample were described adequately by the expression:

r~(p) = (0.001 K)" {(dpref/dT) 2 + (dpx/dT) 2} 1/2, (l)

where Pref is tile vapor pressure of the reference substance, and Px is the vapor pressure of the sample under study. Values of dpref/dT for the reference substances were calculated from fits of the Antoine equation ~13) to vapour pressures of the reference materials (decane and water) reported in reference 12.

The equipment for vapor-pressure measprements with an inclined-piston gauge was described by Douslin and McCullough (14) and Douslin and Osborn. (is) Revisions to the equipment and procedures were reported by Steele et alJ 16) Uncertainties in the pressures determined with the inclined-piston apparatus, on the basis of estimated precision of measuring the mass, area, and angle of inclination of the piston, were adequately described by the expression:

~(p)/Pa = 1.5" 10 4. (p/Pa) + 0.200. (2)

The uncertainties in the temperatures were 0.001 K. Adiabatic heat-capacity and enthalpy measurements were made with a

calorimetric system similar to that described by Huffman et al. (17-19) The four gold-plated copper adiabatic shields were controlled to within 1 mK by electronic controllers with proportional, derivative, and integral actions responding to imbalance signals from (copper-to-constantan) difference thermocouples. The platinum calorimetric vessel ~17) and the loading and sealing procedures ~16) have been described. The calorimeter characteristics and sealing conditions are given in table 1.

Thermometer resistances were measured with self-balancing a.c. resistance bridges (H. Tinsley & Co. Ltd.; Models 5840C and 5840D). Energy-measurement procedures were the same as those described for studies on quinoline. 116) Energies were measured to a precision of 0.01 per cent, and temperatures were measured to a precision of 0.0001 K. The energy increments to the filled calorimeter were corrected for enthalpy changes in the empty calorimeter, for the helium exchange gas, and for

434 R.D. CHIRICO ET AL.

TABLE 1. Calorimeter and sample characteristics: m is the sample mass; Vii is the internal volume of the calorimeter; Tc.~ is the temperature of the calorimeter when sealed; PCa~ is the pressure of the helium and sample when sealed; r is the ratio of the heat capacity of the full calorimeter to that of the empty; Tm. x is

the highest temperature of the measurements; and ~C/C is the vaporization correction

m/g Vi(298.15 K)/cm 3 T~a,/K P~l/kPa r(Tmax) /'rain 10 2. (~C/C)max

Dibenzothiophene

55.960 61.78 297.2 3.20 3.3 1.7 0.016

vaporization of the sample. The correction to the measured energy for the helium exchange gas was approximately 0.2 per cent near 5 K, and was less than 0.01 per cent for all temperatures above 15 K. The sizes of the other two corrections are indicated in table 1.

D.s.c. measurements were made with a Perkin-Elmer DSC II which was fitted with a glove box to exclude air from the head. The calorimeter head was flushed with dry nitrogen. A Perkin-Elmer Intercooler II "Freon" refrigeration unit was used to remove energy from the calorimetric head. High temperature liquid-phase heat- capacity and critical-property measurement procedures with the d.s.c, have been described.(2o, 21)

3. Results

Measured vapor pressures are listed in table 2. Following previous practice, ~11) the ebulliometric results were adjusted to common pressures. The common pressures, the condensation temperatures, and the difference between the boiling and condensation temperatures for the sample are reported in table 2.

Previous studies ~22) have shown that the Cox equation ~23) can adequately represent measured vapor pressures from the triple-point pressure to 0.3 MPa, and can be used for extrapolation with good precision over a 50 K temperature range. The Cox equation in the form:

ln(p/pref) = {1 - (T~ef/T)} • exp{A + B(T/K) + C(T/K)2}, (3)

was fitted to the experimental vapor pressures. T~ef and pr~f were chosen to be the critical temperature and critical pressure determined in this research. These quantities were not allowed to vary in the fit. The fitting procedure has been described/12,16) Parameters derived from the fit are given in table 3. Details of the Cox equation fit are given in table 2.

PROPERTIES OF D I B E N Z O T H I O P H E N E 4 3 5

TABLE 2. Summary of vapor-pressure results: IP refers to measurements performed with the inclined- piston gauge; water or decane refers to which material was used as the standard in the reference ebulliometer; T is the temperature of the experimental inclined-piston pressure gauge measurements or, for ebulliometric measurements , of the condensation temperature of the sample; the pressure p for ebulliometric measurements was calculated from the condensation temperature of the reference substance; Ap is the difference of the calculated value of pressure from the observed value of pressure; cy(p) is the propagated error calculated from equations (1) and (2); AT is the difference between the boiling and

condensat ion temperatures (Tboil-- T~o,d) for the sample in the ebulliometer

T p Ap cy(p) AT Method

K kPa kPa kPa K

IP 375,000 0.0413 -0 .0002 0.0002 IP 384.998 0.0736 - 0.0002 0.0002 IP 395.002 0.1270 -0 .0001 0.0002 IP 404.998 0.2119 0.0000 0.0002 IP 415.000 0.3434 0.0001 0.0003 1P 425.003 0.5417 0.0002 0.0003 IP 435,000 0.8329 0.0001 0.0003 IP 445.000 1.2521 0.0003 0.0004 1P 455.006 1.8424 0.0001 0.0005 decane 457,203 2.0000 0.0000 0.0001 0.108 IP 460.001 2.2176 0.0002 0.0005 IP 465.001 2.6573 0.0006 0.0006 decane 465.103 2.6660 - 0.0003 0.0002 0.079 IP 470.004 3.1689 0.0002 0.0007 decane 476.820 3.9999 0.0000 0.0002 0.035 decane 485.573 5.3330 - 0.0001 0.0003 0.033 decane 498.590 7.9989 0.0004 0.0004 0.019 decane 508.358 10.6661 0.0000 0.0005 0.010 decane 516.254 13.3320 0.0006 0.0006 0.008 decane 524.457 16.6650 0.0002 0.0007 0.005 decane 531.270 19.9330 0,0006 0.0009 0.003 decane 540.237 25,023 0.001 0.001 0.002 water 540.236 a 25.023 0.002 0.001 0.002 water 549.264 31.177 0.001 0,002 0.000 water 558.347 38.565 -0 .001 0.002 0.000 water 567.486 47.375 - 0.002 0.002 - 0.001 water 576.682 57.817 - 0.003 0.003 - 0.001 water 585.936 70.120 -0 .006 0.003 -0 .002 water 595.245 84.533 - 0.005 0.003 - 0.003 water 604.609 101.325 -0 .004 0.004 -0 .004 water 614.030 120.790 - 0,004 0.005 - 0.004 water 623.507 143.25 0.00 0.01 - 0.003 water 633.032 169.02 0.01 0.01 - 0.002 water 642.616 198.49 0.03 0.01 0.001 water 652.265 232.02 -0 .01 0.01 -0 .006 water 661.951 270.02 -0 .01 0.01 0.002

The value at this temperature was not included in the fit.

E n t h a l p i e s o f v a p o r i z a t i o n A g H m w e r e d e r i v e d f r o m t h e C o x e q u a t i o n f i t s b y

m e a n s o f t h e C l a p e y r o n e q u a t i o n :

dp/dT = A~Hm/(T" A~Vm), (4)

w h e r e A [ V ~ is t h e i n c r e a s e i n m o l a r v o l u m e f r o m t h e l i q u i d t o t h e r e a l v a p o r .


TABLE 3. Cox-equation coefficients for dibenzothiophene

T~ef/K 897 pree/kPa 3857 A 2.48680 103. B 1.40484 106• C 1.04187 T/K a 375 to 662

Temperature range of the vapor pressures used in the fit.

Est imates of second virial coefficients were made with the ex tended co r re spond ing- states equa t ion of Pi tzer and Curl. m4) L iqu id -phase densities were es t imated with the cor re la t ion of Riedel. t25) Thi rd virial coefficients were es t imated with the cor responding-s ta tes me thod of O r b e y and VeraJ TM This fo rmula t ion for th i rd virial coefficients was app l ied successfully in analyses of the t h e r m o d y n a m i c p roper t i e s of benzene, toluene, and decane, t27) Thi rd virial coefficients are requi red for accura te ca lcula t ion of the gas vo lume for pressures greater than 0.1 MPa . Der ived enthalpies of vapor i za t ion and ent ropies of compress ion are repor ted in table 4.

F o r the ad iaba t i c hea t -capac i ty and en tha lpy studies, c rys ta l l iza t ion of the sample was in i t ia ted by slowly cool ing the l iquid sample (2 m K . s 1). The d ibenzo th iophene supercooled app rox ima te ly 7 K p r io r to nucleat ion. Comple te c rys ta l l iza t ion was ensured by ma in ta in ing the sample under ad iaba t i c condi t ions in the par t i a l ly mel ted state (10 per cent to 20 per cent l iquid) for app rox ima te ly 8 h. N o spon t aneous warming, which would indicate incomple te crystal l izat ion, was observed in this t ime period. The sample was cooled at an effective rate of 2 m K - s 1 to crystal l ize the remain ing liquid. Final ly , the sample was the rmal ly cycled from < 100 K to within 2 K of the t r ip le -poin t t empera ture , where it was held for at least 6 h to p rov ide further tempering. All of the so l id-phase measurements were pe r fo rmed u p o n crystals p re - t rea ted in this manner .

TABLE 4. Enthalpies of vaporization and entropies of compression for dibenzothiophene obtained from the Cox and Clapeyron equations °

T AgHm AScomp, m T AIgHm AScomp, m

K R.K R K R.K R

298• 15 o 8996 _+ 9 - 13.787 + 0.001 600.00 6665 _+ 26 -- 0.08~ _+ 0.000 300.006 8981 _+ 9 - 13.601 + 0.001 650.00 6233 _+ 46 0.792 + 0.000 350.00 b 8573_+4 -9.417_+0.000 700•00 b 5 7 4 5 _ + 7 2 1.531_+0.000 400.00 8180_+2 -6.422_+0.000 750.00 b 5175_+106 2.163_+0.000 450.00 7802_+2 -4.198_+0.000 800.00 b 4479_+147 2.716_+0.000 500.00 7434+5 -2.497+0.000 850.00 b 3559__ 199 3.212-+0.000 550.00 7061 -+ 13 - 1.161 + 0.000

a ASeomp, m R = ln(p/pO) where pO = 101.325 kPa and R = 8.31451 J. K 1. mol 1. b Values at this temperature were calculated with extrapolated vapor pressures determined from the

fitted Cox coefficients.

PROPERTIES OF D I B E N Z O T H I O P H E N E 437

TABLE 5. Melting-study summary for dibenzothiophene: F is the fraction melted at observed temperature T(F); Ttp is the triple-point temperature; x is the apparent mole-fraction impurity; and Ka is the

distribution coefficient for the impurity as defined in reference 28

F T(F)/K F T(F~K F T(F)/K F T(FffK F T(F)/K

0.181 371.7978 0.360 371.8075 0.599 371.8124 0.779 371.8143 0.958 371.8157

~p = 371.821K x - 0.00014

K~ = 0.07

The triple-point temperature Tip was determined from the measurement of the equilibrium melting temperature T(F) as a function of fraction F of the sample in the liquid sate. Equilibrium melting temperatures were determined by measuring temperatures at approximately 300 s intervals for 0.75 h to 1 h after an energy input and extrapolating to infinite time by assuming an exponential decay towards the equilibrium value. The observed temperatures at 0.75 h to 1 h after an energy input were invariably within 3 mK of the calculated equilibrium temperatures for F values listed in table 5.

The results indicated the presence of solid-soluble impurities, and published procedures (28) were used to derive the apparent mole fraction of impurities, triple- point temperature, and effective distribution coefficient for the impurities between the two phases. The derived mole fraction of impurities is not a reliable

TABLE 6. Experimental molar enthalpy measurements for dibenzothiophene (R = 8.31451 J. K 1. mol 1)

N a hb r i r f r tr s Atot H m e AtrsHm d K K K R . K R . K

Single-phasemeasurements in cr

6 1 73.341 170.355 6 1 170.354 253.805 6 1 253.787 306.251 7 1 297.008 366.964

cr to liquid

1 3 366.473 376.916 371.821 2 6 364.930 384.716 7 2 367.041 375.651

1004.43 0.05 1418.20 -0 .08 1175.41 0.00 1859.40 0.65

2943.34 2610.93 3257.61 2610.82 2883.16 2610.76

Average: 2610.83

Single-phasemeasurements in liquid

9 1 374.994 459.475 3071.18 -0 .48 9 1 459.401 500.348 1614.69 - 0 . 1 9

° Adiabatic series number. b Number of heating increments. c Atot/_/l n is the molar energy input from the initial temperature T~ to the final temperature T~.. d At~Hm is the net molar enthalpy of transition at the transition temperature Ttr s or the excess enthalpy

relative to the heat-capacity curve described in the text for single-phase measurements.


representation of the sample purity because the sample was zone refined. The results are summarized in table 5.

Experimental molar enthalpy results are summarized in table 6. The table includes both enthalpies of fusion and single-phase measurements, which serve as checks on the integration of the heat-capacity results. Corrections for pre-melting caused by impurities were not necessary. Results with the same series number in tables 6 and 7 were taken without interruption of adiabatic conditions.

The experimental molar heat capacities Csat , m under vapor saturation pressure determined by adiabatic calorimetry are listed in table 7. Values in table 7 were corrected for effects of sample vaporization into the gas space of the calorimeter. The temperature increments were small enough to obviate the need for corrections for non-linear variation of Csat, m with temperature. The precision of the heat-capacity measurements ranged from approximately 5 per cent at 5 K, to 1 per cent at 10 K, 0.2 per cent near 20 K, and improved gradually to less than 0.1 per cent above 100 K, except in the solid phase near the triple-point temperature where equilibration times were long. Extrapolation of the heat-capacity results to T ~ 0 was made by linear extrapolation of a plot of C s , t / T against T 2 for results below 9 K.

For heat-capacity measurements in the liquid phase, equilibrium was reached in less than 1 h. Equilibration times for the crystal phase were all less than 1 h for temperatures more than 40 K below the triple-point temperature. As the triple-point temperature was approached, the equilibration times increased gradually to a greatest value of approximately 10 h near 365 K.

The theoretical background for the determination of heat capacities Csat,m at vapor-saturation pressure with results obtained with a d.s.c, has been described/2°'21) Table 8 lists the experimental two-phase heat capacities n Cx, m for dibenzothiophene obtained for three cell fillings. Heat-capacities were determined at 20 K intervals with a heating rate of 0.083 K. s -1 and a 120 s equilibration period between heatings. Sample decomposition precluded heat-capacity measurements above 850 K.

By employing a single continuous heating at a rate of 0.333 K . s 1, sample decomposition was greatly reduced, and the conversion from the two-phase to one- phase region was observed. Temperatures at which conversion to a single phase occurred were measured in this way for eight cell fillings. Table 9 reports the density, obtained from the mass of sample and the cell volume calculated with equation (6) of reference 21, and the measured temperatures at which conversion to a single phase was observed. A critical temperature of (897_+ 2)K and a corresponding critical density of (360_+ 10)kg .m -3 were derived graphically for dibenzothiophene with these results, as seen in figure 1. Results of measurements on benzene an~l decane performed as "proof-of-concept" measurements for these procedures have been reported, t2°) At temperatures above 890 K sample decomposition was rapid even at a heating rate of 0.333 K.s -1 . Three additional attempts to determine temperatures on the two-phase boundary near the critical density were unsuccessful due to extensive sample decomposition.

In this research, the critical pressure was not measured directly, but was estimated by means of simultaneous non-linear least-squares fits of the vapor pressures listed in table 2 and the n Cx, m values given in table 8. Experimental n Cx,m were converted to


TABLE 7. Experimental molar heat capacities at vapor-saturation pressure for dibenzothiophene (R=8 .31451J .K 1.mol 1)

N" ( T ) AT Csat.m b N a ( T) __AT C s,t,m b K K R K K R

er

5 5.075 1.1138 0.041 3 113.887 9.8721 9.786 5 6.009 0.9384 0.066 3 123.815 9.9672 10.457 5 6.938 0.9886 0.102 3 133,846 10.0944 11.155 5 7.938 1.0383 0.152 3 143.880 9.9748 11.861 5 8.943 1.0331 0.223 3 153.808 9.8851 12.572 5 9.986 1.0515 0.314 3 163.786 10.0740 13.301 5 11.083 1.1496 0.423 3 173.889 10.1392 14.048 5 12.278 1.2354 0.557 3 184.061 10.2140 14.804 5 13.578 1.3664 0.718 3 194.193 10.1701 15.590 5 15.024 1.5258 0,918 3 204.302 10.1359 16.369 5 16.635 1.7129 1.142 3 214.375 10.1125 17.154 5 18.463 1.9325 1.408 3 224.425 10.0944 17.946 5 20.483 2.1006 1.697 4 232.238 15.2062 18.572 5 22.689 2.3122 2.013 3 244.452 10.0814 19.540 5 25.105 2.5241 2.349 4 247.524 15.3660 19.792 5 27.756 2.7809 2,700 3 254.527 10.0783 20.361 5 30.693 3.0901 3.073 4 262.971 15.5320 21.030 5 33.930 3.3826 3.465 3 264.593 10.0872 21.158 5 37.525 3.8062 3.872 3 274.520 10.0946 21.975 5 41.555 4.2504 4.296 4 278.578 15.7014 22.293 5 46,080 4.8011 4.739 3 284.613 10.1102 22.785 5 51.157 5.3516 5.223 4 294.330 15.8863 23.558 5 56.808 5.9509 5.715 1 303.224 10.1901 24.248 3 57.920 4.9720 5.802 4 310.125 15.7376 24.840 5 63.027 6.4862 6.218 1 313.430 10.2109 25.081 3 63.598 6.3781 6.263 1 323.656 10.2375 25.899 3 70.257 6.9340 6.773 1 333,908 10.2654 26.725 3 77.478 7.5035 7.295 1 344.185 10.2983 27.544 3 85.416 8.3684 7.850 1 354.471 10.3313 28.370 3 94.365 9.5275 8.464 2 354.547 20.6596 28.379 3 104.040 9.8202 9.119 ! 363.070 6.9769 29.095

liquid

8 377.242 7.8753 34.319 8 421.833 14.8324 36.605 7 380.033 8.7554 34.465 8 436,947 15.5641 37.359 1 381.009 8.2021 34.518 8 452.396 15.3630 38.121 8 385.540 8.7128 34.749 8 468.121 16.1107 38.880 2 389.142 8.8696 34.934 8 484.126 15.9309 39.635 1 389.416 8.6832 34.947 8 500.390 16.6249 40.421 8 394.661 9.4842 35.219 9 510.258 19.9097 40.846 8 406.911 15.0179 35.847 8 515.746 14.1718 41.111

Adiabatic series number. b Average heat capacity for a temperature increment of AT with a mean temperature (T) .

C~, m v a l u e s w i t h e q u a t i o n (6) o f r e f e r e n c e 21 fo r t h e cel l e x p a n s i o n a n d t h e n v a p o r - p r e s s u r e fit d e s c r i b e d b e l o w f o r (Op/OT)sat. T h e v a l u e s o f Cv, m w e r e u s e d t o

d e r i v e f u n c t i o n s f o r (O2p/OT2)sat a n d (~2#/~TZ)sat . T h e C o x e q u a t i o n ~23) w a s u s e d to

r e p r e s e n t t h e v a p o r p r e s s u r e s in t h e f o r m :

ln(p/p~) = (1 - - 1/T~)" e x p ( A + BT~ + CT~2), (5)

440 R . D . C H I R I C O ET AL.

TABLE 8. Experimental Clxlm/R values for masses m of dibenzothiophene (R = 8.31451 J. K - 1 . mol-1)

m/g 0.014826 0.009879 0.026495 V(cell)/cm 3a 0.05387 0.0552 0.05409

T/K C I /R C II /R C II /R x , m t x , m t x , m /

395.0 35.22 35.17 35.35 415.0 36.61 36.07 36.27 435.0 37.71 36.88 37.20 455.0 38.28 38.45 38.23 475.0 39.59 38.97 39.26 495.0 40.47 40.60 40.00 515.0 41.89 41.80 41.27 535.0 41.96 42.32 42.18 555.0 43.74 43.49 42.90 575.0 44.46 45.58 44.21 595.0 45.57 46.14 45.03 615.0 46.42 49.13 45.95 635.0 46.98 47.04 46.46 655.0 48.19 48.55 47.51 675.0 49.67 50.29 48.52 695.0 50.14 52.09 49.71 715.0 51.60 53.97 50.20 735.0 52.94 57.55 51.11 755.0 54.01 57.30 51.87 775.0 55.71 58.33 52.94 795.0 55.93 58.47 53.86 815.0 57.28 59.61 53.93 b 835.0 59.10 61.92 41.85 b 855.0 51.08 b 53.76 b

a Volume of the d.s.c, cell measured at 298.15 K. b The sample decomposed at this temperature.

with T~ = T/T~, where T~ and Pc are the critical temperature and critical pressure. The critical pressure was included as a variable in the non-linear least-squares analysis. The functional form chosen for variation of the second derivative of the chemical potential with temperature was:

(O2#/OT2)s.t = ~ b~(1- T/Tff. (6) i o

{For compounds where sufficient in format ion was available to evaluate reliable (82#/ST2)sa t (e.g. benzene(29)), four terms (i.e. expansion to n = 3) were required to

TABLE 9. Densities and temperatures for the conversion from two phases to a single phase for dibenzothiophene

T/K p/ (kg .m 3) T/K p / (kg .m 3) T/K p/ (kg .m -3) T/K p/ (kg-m -3)

859.8 118.7 883.9 210.0 889.5 491.4 865.3 600.2 867.9 131.8 884.4 236.5 882.0 551.7 858.0 606.7 880.6 171.8 895.0 360.0 882.3 551.7

900 I I I [ I

890

880

870

860

850


i I i I I i I I

100 200 300 400 500 600

p/(kg-m -3)

F I G U R E 1. (Vapor+liquid) coexistence region for dibenzothiophene: p denotes density. The crosses indicate the range of uncertainty for values of this research; - - , drawn to be consistent with these experimental values.

represent the function. Thus, four terms were used in this research.} In these fits the sum of the weighted squares in the following function was minimized:

A C n / R - s Vm(1)T/nR}(~Zp/~T2)sat + (T/R)(Oz#/~TZ)sat. (7) V, m~ t

For the vapor-pressure fits, the functional forms of the weighting factors used have been reported. (~6) Within the heat-capacity results the weighting factors were proportional to the square of the mass of sample used in the measurements. A weighting factor of 20 was used to increase the relative weights of the vapor-pressure measurements in the fit. The weighting factor reflects the higher precision of the vapor-pressure values relative to the experimental heat capacities. Table 10 lists the coefficients determined in the non-linear least-squares fit.

Values of Cs, t m were derived from n , C v , m(,° = P s a t ) using results of the fit and

TABLE 10. Parameters for equations (5) and (6), critical constants, and acentric factor m for dibenzothiophene

A 2.48714 b o -0 .41297 B --1.26117 bl -0 .92358 C 0.83906 b 2 1.42173

b 3 - 1.46759

T ~ - 8 9 7 K p ¢ = 3 . 8 6 M P a p ~ - 3 6 0 k g . m 3 co=0.397

442 R.D. CHIRICO E T AL.

TABLE 11. Values of C~,m( p = Psat)/R and Csat,m/R for dibenzothiophene (R = 8.31451 J. K 1. mol 1)

T 11 11 CV,m(P ~ Psat) C . . . . . T Cv, m(, 0 ~ Psat) C . . . . . K R R K R R

300.0 29.9 29.9 580.0 44.0 44.0 320.0 31.1 31.1 600.0 44.9 44.9 340.0 32.3 32.3 620.0 45.7 45.8 360.0 33.4 33.4 640.0 46.6 46.6 370.0 33.9 33.9 660.0 47.4 47.4 380.0 34.5 34.5 680.0 48.1 48.2 400.0 35.5 35.5 700.0 48.9 49.0 420.0 36.5 36.5 720.0 49.5 49.7 440.0 37.5 37.5 740.0 50.2 50.4 460.0 38.5 38.5 760.0 50.8 51.1 480.0 39.4 39.4 780.0 51.3 51.8 500.0 40.4 40.4 800.0 51.7 52.5 520.0 41.3 41.3 820.0 52.1 53.3 540.0 42.2 42.2 840.0 52.5 54.3 560.0 43.1 43.1 860.0 52.9 56.0

TABLE 12. Molar thermodynamic functions at vapor-saturation pressure for dibenzothiophene (R = 8.31451 J. K - 1 . mol - 1)

T C . . . . . ATSm A T H m T C . . . . . ATSm A T H m

R R R T K R R R T

cr

5.000 0.038 0.013 0,010 140.000 11.587 11.84 6.27 10.000 0.315 0.103 0.077 160.000 13.023 13.48 7.02 20.000 1,628 0.697 0.505 180.000 14.50 15.10 7.77 30.000 2.986 1.621 1.112 200.000 16.04 16.70 8.52 40,000 4,136 2.643 1.729 250.000 19.99 20.70 10.42 50.000 5.115 3.673 2.310 298.150 23.85 24.56 12.28 60.000 5.977 4.683 2.851 300.000 23.99 24.70 12.35 80.000 7.473 6.613 3.824 350.000 28.01 28.71 14.30

100.000 8.846 8.429 4.692 371.821" 29.83 30.45 15.16 120.000 10.20 10.16 5.50

liquid

298.150" 30.11 30.41 19.73 450.000 38.00 44.34 24.59 300.000" 30.21 30.59 19.79 500.000 40.40 48.47 26.05 320.000" 31.29 32.58 20.48 550.0 42.69 52.43 27.46 340.000" 32.36 34.51 21.15 600.0 44.91 56.24 28.82 360.000" 33.42 36.39 21.80 650.0 47.03 59.92 30.14 381.821" 34.04 37.47 22.18 700.0 49.00 63.47 31.42 380.000 34.46 38.22 22.44 750.0 50.79 66.92 32.65 400.000 35.49 40.01 23.06 800.0 52.49 70.25 33.84

" Values at this temperature were calculated with graphically extrapolated heat capacities.


equation (8) of reference 21. Required densities were obtained from the corresponding-states equation in the form: (25)

(P/Pc) = 1.0 + 0.85(1.0 - T/T•) + (1.692 + 0.986~)(1.0 - T/T~) a/3, (8)

with Pc = 360 kg- m 3 Tc = 897 K, Pc = 3857 kPa, and the acentric factor co = 0.397. The acentric factor is defined as {- lg(p/pc)-1.0}, where p is the vapor pressure at T~ = 0.7. The Cox equation coefficients given in table 10 were used to calculate p. The results for " Cv, m( p =Psat)/R and Csat.m/R are reported in table 11. The estimated uncertainty in these values is 1 per cent.

Condensed-phase entropies and enthalpies relative to those of the crystals at T ~ 0 for the solid and liquid phases under vapor-saturation pressure are listed in table 12. These were derived by integration of the smoothed heat capacities corrected for premelting, together with the entropies and enthalpies of fusion as described previously. (a6,2t~ Premelting corrections were made by means of standard methods for a solid-insoluble impurity and the mole-fraction impurity value shown in table 1.

Enthalpies and entropies at selected temperatures for the ideal gas were calculated with values in tables 4 and 12, and are listed in columns 2 and 4 of table 13. The derived molar ideal-gas enthalpies and molar standard entropies were combined with an enthalpy of formation (55.755 + 1.40) kJ- tool a for the reaction:

12C(cr, graphite) + 4H2(g ) + 0.5S2(g) = Ca 2HsS(cr), (9)

to calculate the standard molar enthalpies, entropies, and Gibbs energies of formation listed in columns 6, 7, and 8, respectively, of table 13. The enthalpy of formation is based on an energy of combusl;ion for the crystalline phase determined by Good (3°~ and the enthalpies of formation for COe(g), H20(1), and H2SO 4. 115H20 selected by CODATA. {31) Enthalpies and entropies for equilibrium

TABLE 13. Thermodynamic properties of dibenzothiophene in the ideal-gas state" (R = 8.31451 J . K -1 -mol -a and p° - 101.325 kPa)

T AorH~ AimpH~ b AoTS~n Ai,np S~n c AfH,°n AfS~n ArG,~ RT RT R R RT R RT

298.15 a'e 49.90+0.04 0.00 46.79_+0.04 0.00 60.12+0.28 300.00 d'e 49.73+0.04 0.00 46.93+0.04 0.00 59.71__+0.28 400.00 43.52-+0.02 0.00 54.04-+0.04 0.00 43.31___0.21 500.00 40.95 _+ 0.03 0.03 60.86 + 0.05 0.02 33.73 _+ O. 17 600.00 40.07-t-0.08 0.15 67.36_+0.09 0.11 27.56___0.16 700.00 d 40.05_+0.16 0.43 73.53-+0.18 0.32 23.34__+0.20 800.00 d 40.39 -+ 0.27 0.95 79.28 -+ 0.29 0.71 20.25 __+ 0.29

38.02_+0.04 98.14-t-0.28 -38.06_+0.04 97.77_+0.28 -39.76_+0.04 83.07+0.21 -40.80_+0.05 74.52_+0.18 - 4 1 . 4 0 + 0 . 0 9 68.95+0.17 -41.68_+0.18 65.03_+0.22 -41.83_+0.29 62.07_+0.29

~' The reference state chosen for elemental sulfur was S2(g ) in the ideal-gas state. ~' Gas-imperfection correction to the ideal-gas enthalpy. c Gas-imperfection correction to the ideal-gas entropy. a Values at this temperature were calculated with extrapolated vapor preessures calculated from the

fitted Cox coefficients. e Values at this temperature were calculated with graphically extrapolated values of the liquid-phase

heat capacities.


hydrogen and S2(g) were determined from JANAF tables. ~32) Values for graphite were determined with the polynomial ~33) used to calculate the values from 298.15 K to 6000 K listed in the JANAF tables. All uncertainties in table 13 represent one standard deviation, and do not include uncertainties in the properties of the elements.

The "third-law" method ~21) was employed to calculate sublimation pressures for dibenzothiophene from 298.15 K to the triple-point temperature. The "third-law" values were calculated from the tabulated thermodynamic functions of the ideal gas (table 13) and the liquid (table 12). The sublimation pressures were represented by the equation:

ln(p/Pa) = 32.09- 1.0202.104 - (T/K)- 1 _ 1.543.105 • (T/K) 2, (10)

in the temperature region 298.15 K to 371.8 K.

4. D i s c u s s i o n

Vapor-pressure measurements on dibenzothiophene have been reported in the literature for both the liquid ~34 36~ and solid (35'37) phases. Figure 2 shows the deviations of the results of Aubry et al/34) (471K to 573 K), Edwards and

10

o r j

= &

-lO

A ,

A

A 0 u •

OOOof s ¢ A A A •

o o o •

• Q • • i i A A

430 ~4~ 550 T/K

-20 ' 370 610

A

FIGURE 2. Deviation plot for dibenzothiophene vapor pressures, p(Cox) was calculated with the Cox-equation coefficients in table 3. ©, Edwards and Prausnitz; ~3s) A, Aubry eta/.; ~34) O, Sivaraman and Kobayashi. (36)


Prausnitz ~351 (374 K to 405 K), and Sivaraman and Kobayashi (36) (425 K to 608 K) from those of this research.

The results of Edwards and Prausnitz ~35) were obtained with a gas-saturation apparatus, and are approximately 3 per cent lower than ours on average with a 14 per cent range. The magnitude of the differences are in accord with the accuracy claimed by the authors. It is possible that complete saturation was not achieved. In addition, the sample used was a commercial sample with a purity of "98 per cent" claimed by the manufacturer. Edwards and Prausnitz found "no evidence of any impurities" by g.l.c, analysis, but did not report a sensitivity for their chromatograph.

The results of Aubry e t al. ~34) are generally within 6 per cent of the present results. The values plotted in figure 2 are based on an equation provided by the authors. The method employed by Aubry e t al. ~34) involved comparisons of g.l.c, retention times.

Sivaraman and Kobayashi ~36) used a static method and claimed a pressure- measurement accuracy of 0.0! per cent. They used a zone-refined sample, and checked its purity with a "freezing-point" method. Such techniques are not valid for zone-refined samples because eutectic formation cannot be detected. The deviations of their vapor-pressure results from ours are shown in figure 2, and range to 20 per cent near 500 K. We have observed similar large deviations between our results and those of Sivaraman and co-workers for acridine,(3s) biphenyl,(21) and

7750 • , i , , i • ,

A A

7250

E

6750

z

6250 I 425 500 575 650

~K

FIGURE 3. Enthalpies ofvaporization ~r dibenzothiophene. A, Sivaraman and Kobayashi; c36~ G, Mrawand Keweshan;~4°)--,Thisresearch. Theerrorbarsarethoseofthisresearch.


dibenzofuran. ~39) The deviations show no apparent trend from compound to compound.

Mraw and Keweshan ~4°) derived the enthalpy of vaporization near the normal- boiling temperature for dibenzothiophene by "ballistic Calvet calorimetry". The measured enthalpy increment was that between the real gas near the normal-boiling temperature (590 K to 630 K) and the crystal near room temperature (298.15 K). The enthalpy of vaporization was derived by subtraction of the enthalpy difference between the liquid at the vaporization temperature of interest and the crystal at 298.15 K from the measured increment. Condensed-phase heat capacities and an enthalpy of fusion measured with a d.s.c. (41) were used in the original calculations. ~4°) The enthalpies of vaporization were recalculated here with enthalpy increments from table 12 based primarily on adiabatic calorimetry.

Figure 3 shows enthalpies of vaporization derived from the results of Mraw and Keweshan, (4m calculated from the vapor-pressure measurements of Sivaraman and Kobayashi, ~36) and obtained in this research (table 4). The results of Mraw and Keweshan are in excellent agreement with ours, while those of Sivaraman and Kobayashi deviate widely. Indeed, the enthalpies of vaporization derived from the results of Mraw and Keweshan combined with our more precise enthalpies fo r the crystal and liquid phases all lie within the error range (one standard deviation) of the values based on our vapor-pressure measurements. Mraw and Keweshan estimated the uncertainty in their derived enthalpies of vaporization to be 3.1 kJ .mo1-1. In view of the present results, the estimated uncertainties appear to be too pessimistic.

-5

-10

~-~ -15

-20

011

0

0 ooo

%o

0

O 0

0 O 0

0 o 0

O

O

-25 , ' , ' ' , 300 320 340 360

T/K

FIGURE 4. Deviation plot for dibenzothiophene sublimation pressures; P~,~c was calculated with equation (10) of this research. O, Hansen and Eckert; (37) ©, Edwards and PrausnitzJ 35)


Figure 4 shows a comparison of the sublimation pressures for dibenzothiophene reported in the literature {3s'37~ with those calculated in this research, equation (10); Hansen and Eckert (303 K to 348 K); (37) and Edwards and Prausnitz (336 K to 366 K), (35) used gas-saturation methods. Their values are 10 per cent lower than ours on average. Because the pressures involved are small (0.1 Pa to 30 Pa), the accord is considered fair. The accuracy of our results depends primarily on the accuracy of the extrapolated liquid-phase vapor pressures derived with the Cox coefficients of table 3. This is difficult to assess; however, Scott and Osborn (22) have shown that the Cox equation can be used with confidence for extrapolations of 50 K.

Molar enthalpies of sublimation at 298.15 K were derived from the sublimation pressures in the literature. Derived values were: Edwards and Prausnitz, {35) 91.9 kJ ' mol 1; Hansen and Eckert, (37) 91.2 kJ. mo1-1. The ideal-gas (table 13) and crystal-phase (table 12) molar enthalpies of this research yielded a derived value of 93.3 kJ. mol-1, in good accord with the sublimation-pressure results. There is serious disagreement between these values and that reported by Sabbah and Antipine (4z~ (85.09_+ 0.35)k J -mol 1. The source of the discrepancy is not known.

O'Rourke and Mraw (41~ measured heat capacities (220 K to 560 K) and an enthalpy of fusion for dibenzothiophene by d.s.c, with the intermittent-heating method they had described previously. (43) Linear equations were provided to represent the heat capacities. Their heat-capacity values for the solid phase range from 2.8 per cent low near 220K to 1.5 per cent low near the triple-point temperature (372 K) relative to the results of our research. The values for the liquid phase range from 0.9 per cent low at 380 K to 0.3 per cent high at 560 K. The accuracy claimed was 1.5 per cent. The poorer agreement for the results for the solid phase could have arisen from poorer contact between the sample and its container relative to that for the liquid. The molar enthalpy of fusion reported by O'Rourke and Mraw: ~41) (21.6-t-0.2)kJ. mol-1 is in excellent accord with that determined here (21.71_+0.02) kJ-mol 1.

The experimental critical-property values reported here are the first for dibenzothiophene. Table 14 shows a comparison of the experimental results with values estimated by the group-contribution methods of Lydersen, (44) Somayajulu, (45~ and Joback. (46) The Lydersen parameters were published in 1955. (44) Joback 146~ and Somayajulu (45) made use of the modern critical-property database to modify the Lydersen equations and expand the applicability of the approach. For the critical

TABLE 14. Comparison of experimental and estimated critical properties for dibenzothiophene

This research Lydersen (44) Joback ~ ' .6) Somayajulu 145)

Tc/K 897__+2 880 878 901 " pd(kg • m - 3) 360 + 7 351 360 361 /rc/MPa 3.86+0.08 b 3.17 3.76 3.67

° This value was calculated with equation 12 of reference 45. An alternative formulation, equation 11 of reference 45, yielded T c - 868 K.

b This value was derived using the fitting procedure described in the text. Tc and Pc were obtained graphically with figure 1.

448 R. D. C H I R I C O E T AL.

pressure, the revised precedures provide an improved estimate. The parameters of Somayajulu ~45) provide an improved estimate of the critical temperature.

Sabbah and Antipine (42) reported results of combusion calorimetric measurements on dibenzothiophene in which the sample size was approximately 5 mg. Their value for the molar energy of combustion is 16 kJ .mol 1 more negative than that of Good. (3°) To resolve the discrepancy, combustion studies on dibenzothiophene were made in this research. The value obtained for the molar energy of combustion was exactly the same as that reported by Good, ~3°) with a slightly smaller uncertainty interval (1.4 kJ .mol 1).

Bree and Zwarich (47) reported a complete vibrational assignment for a single crystal of dibenzothiophene. They listed experimental wavenumbers for 52 of the 57 vibrational modes and a complete set of 57 calculated values. The 52 experimental values were supplemented here with the appropriate calculated values provided by Bree and Zwarich for the five missing wavenumbers, and ideal-gas entropies were calculated. The moment-of-inertia product (1.4112. l0 132. kg3 .m 6) was calculated with the crystal structure reported by Schaffrin and Trotter. ~48) Differences between these calculated ideal-gas entropies and those derived calorimetrically in this research are shown in figure 5. Near 300 K the agreement is fair; however, the

1.5

1.0

&

.~ 0.5 i

<1 0.0

- 0 . 5 i i J I 300 400 500 600 700 800

~ K

F I G U R E 5. Deviation of ideal-gas molar entropies calculated from spectroscopically determined vibrational frequencies and statistical mechanics (spect) from the calorimetricaUy (cal) derived values of this research. The curved lines represent the uncertainty limits of the calorimetric results (one s tandard deviation). O, Derived from the experimental wavenumbers of Bree and Zwarich (47~ supplemented with five calculated values; A , derived with all wavenumbers below 500 cm-1 reduced by 20 cm-1. See text.


spec t roscopica l ly der ived values deviate low with increasing temperature , and are well outs ide the bounds of uncer ta in ty for the ca lo r imet r i c values.

The obse rved differences are due in par t to the use of crysta l ra ther than gas-phase spectra for the fundamen ta l wavenumber de te rmina t ions . Crys t a l - to -vapor shifts of 20cm -1 for the low-ly ing modes are expected. ~49'5°) The ideal-gas en t ropy was recalcula ted with each wavenumber below 500 cm 1 decreased by 20 cm ~. The agreement was improved , bu t the t rend with t empera tu re r emained unchanged, as shown in figure 5. I t is fruitless to speculate on the source of the discrepancy wi thou t

exper imenta l gas -phase spectra.

The au thors acknowledge the f inancial suppor t of the U.S. D e p a r t m e n t of Energy. This research was funded by the U.S. D e p a r t m e n t of Energy Office of Fossi l Energy within the A d v a n c e d Research Section of Coa l Liquefac t ion (ARL) p rog ra m as par t of the coopera t ive agreement DE-FC22-83FE60149 . The au thors grateful ly acknowledge N . K . Smith for combus t ion ca lor imet r ic measurements , and I . A . Hossen lopp for v a p o r t ransfer of samples for measurements .

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450 R. D. CHIRICO ET AL.

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JANAF Thermochemical Tables. 3rd edition. Supplement No. 1 to J. Phys. Chem. Ref Data 1985, 14.

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equations and parameters are listed in reference 5. 47. Bree, A.; Zwarich, R. Speetrochim. Acta 1971, 27A, 599. 48. Schaffrin, R. M.; Trotter, J. J. Chem. Soc. (A) 1970, 1561. 49. Crowder, G. A.; Scott, D. W. J. Mol. Spect. 1965, 16, 122. 50. Scott, D. W. J. Chem. Thermodynamics 1971, 3,649.

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The thermodynamic properties of dibenzothiophene