Ind. Eng. Chem. Res. 1994,33, 157-167
157
Reconciliation of Calorimetrically and Spectroscopically Derived Thermodynamic Properties at Pressures Greater Than 0.1 MPa for Benzene and Methylbenzene: The Importance of the Third Virial Coefficient Robert D. Chirico’ and William V. Steele’ IZT Research Institute, National Institute for Petroleum and Energy Research, P.O. Box 2128, Bartlesville, Oklahoma 74005-2128
Heat capacities for the liquid phase (to within 25 K of T,)and the critical temperature for benzene and methylbenzene were determined by differential-scanning calorimetry (dsc). The critical pressures were derived by a fitting procedure involving measured vapor pressures, densities, and the dsc results. The critical densities were estimated with a corresponding states correlation. Good agreement with reliable critical properties from the literature is shown. New measurements of vapor pressures for methylbenzene (305-422 K; 5.3-270.0 kPa) by comparative ebulliometry are reported. New density measurements for benzene (310-523 K) and methylbenzene (303-428K) are reported also. The results were combined with literature entropies for the liquid t o calculate ideal-gas entropies to near the respective critical temperatures. Validation of the results was accomplished by comparison with reliable ideal-gas entropies based on molecular spectroscopy and statistical mechanics. The significance of the third virial coefficient in the calorimetric calculations is demonstrated. 1. Introduction
Recent research at the National Institute for Petroleum and Energy Research (NIPER) has provided the means to determine by calorimetric methods ideal-gas thermodynamic properties from near the triple-point temperature to within 50 K of T, for polycyclic molecules such as biphenyl (Chirico et al., 1989a), dibenzofuran (Chirico et al., 1990), benzo[blthiophene (Chirico et al., 1991a), dibenzothiophene (Chirico et al., 1991b), and 2-aminobiphenyl (Steele et al., 1991). In that research the critical temperature and critical density were determined experimentally and the critical pressure was derived by a fitting procedure involving measured vapor pressures, densities, and two-phase (liquid + vapor) heat capacities determined with a differential-scanning calorimeter (dsc). Excellent accord with reliable literature values of the critical temperature and critical density for biphenyl were reported (Chirico et al., 1989a). Details of “proof-of-concept” determinations of the critical properties of benzene and methylbenzene are reported here together with results for ideal-gas thermodynamic properties to within 25 K of T,. Validation of the results is accomplished by comparison of the calorimetric results with reliable ideal-gas entropies based on molecular spectroscopy and statistical mechanics. The significance of the third virial coefficient in the calorimetric calculations is demonstrated. There are two independent routes to the determination of ideal-gas entropies: calorimetry and spectroscopy. The spectroscopic method involves the assignment of vibrational wavenumbers observed in gas-phase infrared and Raman spectra to the fundamental vibrational modes of a molecule. Significant liquid-to-vapor wavenumber shifts for low-frequencyvibrations preclude the use of condensedphase spectra for accurate statistical calculations (Kagarise, 1963). The moment-of-inertia product and symmetry number are determined from the molecular
* T o whom correspondence should be addressed. t Contribution No. 341 from the Thermodynamics Research Laboratory at the National Institute for Petroleum and Energy Research.
structure, and standard methods of statistical mechanics are employed to calculate the ideal-gasentropy. Typically, the harmonic-oscillator and rigid-rotor approximations are used. Due to the low vapor pressures involved, application of the spectroscopic method to polycyclic molecules is hampered by experimental difficulties in the determination of gas-phase spectra. Furthermore, the lowest-lying vibrations are often not harmonic (Smithson et al., 1984). Consequently, the spectroscopic method is most reliable for relatively small rigid molecules such as benzene and methylbenzene. The rotation of the methyl group in methylbenzene is well understood and can be accounted for accurately in the statistical calculations. Ideal-gas entropies are determined calorimetrically by the summation of terms derived from the results of several measurement techniques. The summation can be written
where bTSL(l) is the entropy of the condensed phase a t temperature T relative to 0 K (in this research, the condensed phase is the liquid), AfS, is the entropy of vaporization, and AScomp,m is the entropy of compression to a standard pressure. In this research the selected standard pressure is 101.325 kPa. Entropies of the liquid are derived by appropriate integration of the heat-capacity-against-temperaturecurve. Entropies of vaporization AfS, may be determined directly by vaporization calorimetry, however, they are more often determined with accurate vapor pressures through application of the Clapeyron equation: dpldT = ~ f s , f ~ f V ,
(2)
An equation of state is required in the calculation of the molar volume of the vapor. In early research a t Bartlesville (Waddington et al., 1947)the Berthelot equation was used. In recent years the virial equation of state has become the preferred choice. The expression for the entropy of compression A S c o m p p , truncated after the third virial
oaas-5aa519412633-oi57$04.5~10 0 1994 American Chemical Society
158 Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994
coefficient, is Ascomp,m
= R ln(p/po) + (dB/dTlp + (dC’/dT)p2 (3)
where p is the saturation pressure, B is the second virial coefficient, and C’ = (C- B2)/RT,where C is the third virial coefficient. It will be shown that second virial coefficients are required for calculations above T/Tc= 0.5 (Le., p = 1kPa) and third virial coefficients are required for calculations above T/Tc = 0.65 (Le., p = 100 kPa). Experimental information on third virial coefficients is rare, and discrepancies between results for the same compound are common. Except for measurements on n-octane, all experimental third virial coefficients are for hydrocarbons with less than seven carbons, C02, or diatomic and monatomic gases (Orbey and Vera, 1983).In this research, the correlation developed by Orbey and Vera (1983) was employed because of its ready applicability to polycyclic molecules. The correlation parameters are T,, p mand the acentric factor w , which are all determined as part of the research at NIPER. It will be shown that use of this correlation for the third virial coefficients in combination with calorimetric results for benzene and methylbenzene yields results in excellent accord with reliable spectroscopically-derived properties. In this research high-temperature heat capacities (to within 25 K of T,)and the critical temperature for benzene and methylbenzene were determined by differentialscanning calorimetry (dsc). The critical pressure p c was derived for each compound by a fitting procedure, which fits simultaneously vapor pressures and two-phase (liquid + vapor) heat-capacity results from the dsc. It will be shown that accurate vapor pressures for relatively low pressures (p < 300 kPa) are sufficient for reliable evaluation ofp,. The critical densities were estimated with measured densities and a corresponding-states correlation. Saturation heat capacities were derived. The results were combined with literature entropies for the liquid to calculate ideal-gas entropies to near the respective critical temperatures. The calorimetric results are compared in this paper with reliable ideal-gas entropies calculated via assigned vibrational spectra and application of statistical methods. These latter values are referred to as “spectroscopic” entropies, while those derived from the calorimetric and vapor-pressure studies are termed “calorimetric” entropies. As part of these studies, new density measurements are reported for benzene and new density and vapor-pressure measurements are reported for methylbenzene. 2. Experimental Section
Materials. The samples of benzene and methylbenzene used in this research were HPLC grade (>99.9% pure) chemicals purchased from Aldrich Chemical Company, Inc. Traces of water were removed by vapor transfer through a molecular sieve. All sample handling was completed in a nitrogen atmosphere. Physical Constants and Standards. Molar values are reported in terms of the relative atomic masses: benzene, 78.114 pmol-l; methylbenzene, 92.141 pmol-1 and the gas constant R = 8.31451 J-K-l-mol-l, adopted by CODATA (Cohen and Taylor, 1988). All temperatures reported were converted to ITS-90 (Goldberg and Weir, 1990). Measurements of mass, time, electric resistance, and potential difference were made in terms of standards traceable to calibrations at NIST. Differential-Scanning Calorimetric (dsc) Measurements. The dsc measurements were made with a
Table 1. Experimental Crf, Values for Benzene (R = 8.31451 J.K-l.mol-l) 0.012 903 0.015498 0.021 186 mass/g: 0.007 941 0.052 72 0.053 39 0.052 72 0.053 39 vcell/cmB:a T/K C;-/R C&/R C&,/R C;!/R 17.48 16.67 16.77 315.0 16.71 18.26 18.05 335.0 17.61 17.29 19.35 18.57 18.55 355.0 18.33 20.49 19.54 19.47 18.99 375.0 21.70 20.44 395.0 20.24 19.82 23.10 21.63 21.32 20.62 415.0 24.64 22.95 435.0 22.36 21.49 455.0 26.24 24.18 23.28 22.11 28.04 23.93 23.17 24.65 475.0 30.02 26.73 25.19 24.17 495.0 515.0 32.57 28.22 26.79 25.34 35.40 30.33 28.47 26.55 535.0 4
VC.uis the volume of the cell measured at 298.15 K.
Perkin-Elmer DSC 11. Experimental methods were described previously (Knipmeyer et al., 1989; Chirico et al., 1989a). Precision of the measured two-phase (liquid + vapor) heat capacities is approximately 1%. Densities. Densities for the liquid phase of benzene and methylbenzene were measured with a vibrating-tube densitometer. The experimental methods were reported previously (Chirico et al., 1993a). The precision was demonstrated to be 0.05% with an accuracy estimated to be within 0.1% (Chirico et al., 1993a). Vapor Pressures. The essential features of the ebulliometric equipment and procedures used for vaporpressure measurements for methylbenzene are described in the literature (Swietoslawski,1945;Osborn and Douslin, 1966). The ebulliometers were used to reflux the sample of methylbenzene with a reference substance (n-decane or water) of known vapor pressure under a common helium atmosphere. The boiling and condensation temperatures of the two substances were determined, and the vapor pressure of the methylbenzene was derived using the condensation temperature of the reference (Chirico et al., 1989b). Purification of the water and n-decane reference materials has been described (Chirico, 1991a). The precision in the temperature measurements for the ebulliometric vapor-pressure studies was 0.001 K. Uncertainties (one standard deviation) in the pressures, as calculated by standard error propagation methods, are described by a@) = (0.001 K)((dprefldTl2 + (dp,/dT‘)21’/2 (4) where prefis the vapor pressure of the reference substance and p x 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 to vapor pressures of the reference materials (n-decane and water) listed by Chirico et al. (1989b).
3. Measurement Results
The theoretical background for the determination of heat capacities for the liquid phase at vapor-saturation pressure Csat,mwith results obtained with a dsc has been described (Knipmeyer et al., 1989; Chirico et al., 1989a). Measured two-phase (liquid + vapor) heat capacities for a minimum of two fillings, vapor pressures, and reliable liquid-density values are required. Tables 1 and 2 list the experimental two-phase heat capacities C;Im for benzene and methylbenzene obtained for four cell fillings for each compound. Two-phase heat capacities were determined at 20 K intervals with a heating rate of 0.083 K d and a 120-9equilibration period between
Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 159 Table 2. Experimental C&, Valuesa for Methylbenzene (R= 8.31481 J.K-l.rno1-l) mass/g: 0.019 717 0.009 206 0.010 144 0.021 780 V&cms:b 0.054 80 0.054 80 0.052 92 0.052 92 T/K CftmIR C;JR T/K C,qm/R C$/R 310.0 19.40 19.54 315.0 19.73 19.59 335.0 20.67 20.42 19.81 20.00 320.0 21.71 21.25 355.0 20.15 20.49 330.0 22.84 22.20 375.0 20.62 21.00 340.0 24.06 23.11 21.54 395.0 350.0 21.02 22.11 25.37 24.07 415.0 360.0 21.61 435.0 22.70 26.76 25.07 370.0 21.94 28.23 26.17 23.32 455.0 380.0 22.29 23.97 29.71 27.10 475.0 390.0 22.92 31.43 28.12 400.0 23.50 24.65 495.0 25.35 515.0 33.22 29.21 410.0 23.95 535.0 35.21 30.17 24.63 26.07 420.0 37.46 31.15 555.0 430.0 24.92 26.76 25.56 27.47 440.0 450.0 26.08 28.38 26.52 29.23 460.0 30.01 470.0 26.91 480.0 27.38 30.92 500.0 28.44 32.78 510.0 29.20 33.78 520.0 29.73 34.83 35.95 530.0 30.49 37.16 540.0 31.22 550.0 31.72 38.44 39.85 560.0 32.37 41.44 570.0 33.05 ~~~
a Heat-capacity values are listed here and in Table 1 with one more digit than is fullyjustifiedto avoid round-off errore in subsequent calculations. V-u is the volume of the cell measured at 298.15 K.
.
*
35
I
30
-
tD
A A *
p / (kg.m-3) Figure 2. (Vapor + liquid) coexistenceregion, for benzene: p denotes density, the crosses denote the range of uncertainty for the values of this research, and 0 denotes T, and p, selected by Tsonopoulos and Ambrose (1993). The curve represents values selected in the review by Goodwin (1988). Table 3. Densities and Temperatures for the Conversion from Two Phases to a Single Phase benzene methylbenzene
138 149 192 239 259 290 329 392
547.5 550.7 557.7 560.6 561.5 561.3 560.7 557.4
pl(kp.m-9 166 183 249 276 355 423
the sample and cell volume calculated with eq 5, and the measured conversion temperatures. In this research the thermal expansion of the cells was expressed as Vx(T)/Vx(298.15K) = 1+ ay
280
340
400
460
520
T/K Figure 1. Two-phase (liquid + vapor) heat capacities for benzene: sample mass = 7.94 mg, H; 12.90 mg, A; 15.50 mg, 0;21.19 mg, 0. Saturation heat capacities,+, (Oliveret al., 1948). The arrow indicates the temperature range of the truncated vapor-pressure data set (Le., Scott and Osborn, 1979). See text.
heats. (Intervals of 10 K were used for two of the methylbenzene fillings.) Figure 1 shows the Cz:, values values for benzene for the four cell fillings and C,t, determined by adiabatic calorimetry (Oliver et al., 1948). The effect of vaporization of the sample into the free space of the cell as the temperature is increased is observed readily in the figure. In separate experiments the temperature at which conversion to a single phase occurred was measured for four additional fillings for benzene and two additional fillings for methylbenzene. The conversion temperature is indicated by an abrupt decrease in the observed heat capacity as the two-phase to one-phase boundary is crossed. Table 3 reports the densities, obtained from the mass of
T/K 587.2 589.1 592.0 592.5 590.0 582.8
+ by2
(5) where, y = (T- 298.15) K, a = 3.216 X 106 K-l, and b = 5.4 X 10-8 K-2. The volume of the cell at 298.15 K, Vx(298.15K), was determined from the mass of the cell filled completely with water. Small volume differences between sealingswere determined by measuring the height of the cell. Critical temperatures were determined graphically as shown in Figures 2 and 3. The critical temperatures were (561.8 f 1.0) K for benzene and (592.5 f 1.0) K for methylbenzene. Several precise vapor-pressure studies have been reported for methylbenzene; however, these are not consistent, as will be shown. Vapor pressures for methylbenzene measured in this research are reported in Table 4. The pressures, the condensation temperatures, and the difference between condensation and boiling temperatures for the sample are reported. The small differences between the boiling and condensation temperatures indicated correct operation of the twin ebulliometers and the high purity of the sample. Several precise and consistent determinations of benzene vapor pressures exist in the literature (Scott and Osborn, 1979; Forziati et al., 1949; Ambrose et al., 1981, “1968/2”; Ambrose et al., 1990, “metal”;Bender et al.,1952;Ambrose, 1987;Connolly and Kandalic, 19621, so no vapor pressures were measured in this research. Detailed comparisons between the literature values are described later. Densities for the liquid phase of benzene and methylbenzene measured in this research are listed in Table 5.
160 Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 593
I
.
Y
I-
150
250
350
450
p / (kg.m-3) Figure 3. (Vapor + liquid) coexistence region, for methylbenzene: p denotes density, the crosses denote the range of uncertainty for the values of this research, and 0 denotes T, and p, selected by Tsonopoulos and Ambrose (1993). The curve represents values selected in the review by Goodwin (1989) scaled to T,= 592.5 K. Table 4. Summary of Vapor-Pressure Results for Met hvlbenzene. methvlbenzene standard T/K dkPa Ap/kPa u;/kPa 0.0004 5.3330 0.0002 decane 304.889 0.0005 7.9989 0.0000 decane 313.438 0.0006 10.6661 -0.0004 decane 319.865 0.0008 13.332 -0.0004 decane 325.069 O.Oo0 0.001 16.665 decane 330.481 0.001 19.933 O.Oo0 decane 334.982 0.001 25.023 0.000 decane 340.915 25.023 0.001 0.002 waterb 340.914 0.001 0.002 346.894 31.177 water 0.002 38.565 0.001 water 352.920 0.001 0.003 358.992 47.375 water 0.003 57.817 0.001 water 365.110 0.003 70.120 0.000 water 371.276 0.004 84.533 0.000 water 377.488 0.005 101.325 -0.002 water 383.747 -0.002 0.005 390.052 120.79 water 0.006 -0,004 396.406 143.25 water 0.00 0.01 169.02 water 402.801 0.01 198.49 0.00 water 409.247 0.00 0.01 415.737 232.02 water 270.02 0.00 0.01 water 422.272
ATIK 0.007 0.005 0.005 0.005 0.004 0.005 0.005 0.005 0.005 0.004 0.005 0.005 0.005 0.005 0.005 0.006 0.006 0.007 0.007 0.007 0.007
a Water or n-decane refers to which material was used as the standard in the reference ebulliometer; T is the condensation temperature of the sample; the pressure p was calculated from the condensation temperature of the reference substrince; A p is the difference of the calculated value of pressure from the observed value of pressure; ui is the propagated error calculated from eq 4; AT is the difference between the boiling and condensation temperatures (Thil - Tmnd) for the sample in the ebulliometer. *The value at this temperature was given zero weight in the fits.
Table 5. Measured Densities at Saturation Pressure benzene methylbenzene TIK Pl(kgm-9 T/K pl(kg.m-9 310.05 361.23 423.14 498.15 523.15
860.7 804.6 729.5 613.0 558.3
302.83 337.40 352.72 372.64 400.86 427.89
857.5 824.6 809.9 790.1 762.3 731.0
4. Data Analysis and Derived Results
In this research the critical pressure was not measured directly, but was estimated by a simultaneous nonlinear least-squares fit of the vapor pressures and the C,: values
given in Table 1. Differences between the observed twophase heat capacities for the various filling levels are directly related to the magnitude of the enthalpy of vaporization (through the slope of the vapor-pressure curve, i.e., the Clapeyron equation) at a given temperature. Accurate vapor-pressure measurements (i.e., temperatures within 0.01 K and pressures within 0.1%) rarely exceed 0.1 MPa. By including the heat capacities in the fit, the extrapolation of the vapor pressures to T, is constrained. The derived pc and measured T, are then used as fixed parameters in a fit of the Wagner equation to the vapor pressures alone, and enthalpies of vaporization are derived. Finally, the parameters derived from the Wagner-equation fit and the critical constants are fixed, and saturation heat capacities are derived. A more detailed description of the procedure follows. The compounds studied in the present research are unusual in that high-quality vapor-pressure measurements are available from near the normal-boiling temperature to near T,. The critical constants are well-known also and have been reviewed recently (Tsonopoulos and Ambrose, 1993). It will be shown that critical constants and vapor pressures in good accord with the accepted values can be derived with the dsc measurements and the vapor pressures to near 0.1 MPa only. The Wagner equation, as formulated by Ambrose et al. (1990), was used to represent the vapor pressures: ln@/p,) = (l/T,)[A(l - T,)
+ B(1- Tr)'.5+ C(1- Tr)2.5 + D(l - TJ5] (6)
where T, = T/T,. The vapor-pressure fitting procedure resembled that used previously, when the Cox vaporpressure equation was used (Steele et al., 1988; Chirico et al., 1989b). In fits using the Wagner equation, the sums of the weighted squares in the following expression were minimized (replacing eq 1 2 of Steele et al., 1988): A = [ln@/pJ/(l/T,)] - A ( 1 - T,) - B(1- T,)'.' -
C(l - T,)2.5- D(1- T J 5 (7) The weighting factors were derived with eq 13 of Steele et al., 1988. If two phases are present and the liquid is a pure substance, then the vapor pressure p and the chemical potential p are independent of the amount of substance n and the cell volume V, and are equal to psatand psat.The two-phase heat capacities at cell volume V,, Cyw, can be expressed in terms of the temperature derivatives of these quantities: C,:
= -T(a2p/aP),,,
+ v,(7'/n)(a2p/~P),,,+ (T/n)(a VJBT), (ap/dT),
(8)
The third term on the right-hand side of eq 8 includes the thermal expansion of the cell. Experimental Cy:, values were converted to CF, by means of eq 5 and the vaporpressure fit for (ap/a!n),,.
c;,m= qrn - c~/n,~cav,/aT),(aP/eI?,,)
(9)
The fitting procedure involved iterations in which the Wagner equation was fit to the vapor pressures, (a2p/arZ)BBt values were calculated, and the values of CF,mwere used to derive functions of (a2p/aTz)8at. The functional form chosen for variation of the second derivative of the chemical potential with temperature was
Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 161 Table 6. Parameters for Eqs 6 and 10. Benzene A -7.026 13 bo -0.301 33 B 1.571 56 bl -0.380 82 C -1.874 97 bz 0.550 20 D -3.690 60 b3 -0.922 61 Tc (561.8 f 1.0) Kb p c (4884 50) kPac pc (303.8 f 3.0) kern3
*
A
B C
D
*
Tc (592.5 1)Kb
Methylbenzene -7.402 24 bo 1.823 31 bl -2.189 76 b2 -3.376 53 bs p c (4162 f 50) kPac
-0.353 51 -0.605 77 0.134 92 -0.167 34 pc (291.0 f 3.0) kgm4 d
The units of the bi coefficients are J.K-2.mol-1. b Measured in this research by differential-scanning calorimetry. Derived in this research through a simultaneous fit of two-phase heat capacities and vapor pressures. See section 4 of text. The value of p c is closely correlated to the value of T,. See Discussion section 5a of the text. Estimated with eq 13 and measured densities. See text. n
Four terms were used in this research (i-e., expansion to n = 3). In these fits the sum of the weighted squares in the following function was minimized:
Iterations continued until the weighted deviations as calculated with eqs 7 and 11were minimized. 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 obtained by dsc. Heat capacities measured to near the normal-boiling temperature by high-precision adiabatic calorimetry were included in the fit and were weighted equally with the vapor pressures. These effectively “anchored” the low-temperature end of the heat-capacity curve. (See Figure 1.)In this initial fit, the critical pressure was included as a variable, and its value was derived. The Wagner-equation fit was repeated with Tc (measured by dsc in this research) and pc (derived in the heatcapacitylvapor-pressure fit described above) fixed, and the two-phase heat capacities were not considered. For benzene and methylbenzene the result of this fit was only slightly different from that involving the two-phase heat capacities. Significant differences were observed only for extrapolated values below the range of the vapor-pressure measurements. These are caused by small inconsistencies between the vapor-pressure and heat-capacity values. This problem could possibly be eliminated by careful adjustment of weighting factors, however, the more expedient solution was chosen. The derived Wagner-equation parameters are listed in Table 6. All fitting procedures were completed with two vaporpressure data sets for each compound. The first set included measured vapor pressures from near 300 K to near T, (“complete set”), and the second included only values belowp = 0.3 MPa (“truncated set”). For benzene, vapor pressures measured by Scott and Osborn (1979) (308-389 K; 20-270 kPa) were used alone and in conjunction with values measured by Ambrose (1987) (404-
Table 7. Entropies of Vaporization, Compression, the Liquid, and Ideal Gas (R= 8.31451 J-K-l-rno1-l and p o = 101.325 kPa)
250.0 260.0 280.0 298.15 300.0 320.0 340.0 360.0 380.0 400.0 420.0 440.0 460.0 480.0 500.0 520.0 540.0
17.65 16.68 14.98 13.65 13.52 12.25 11.13 10.13 9.21 8.36 7.56 6.81 6.08 5.37 4.67 3.97 3.22
250.0 260.0 280.0 298.15 300.0 320.0 340.0 360.0 380.0 400.0 420.0 440.0 460.0 480.0 500.0 520.0 540.0 560.0 570.0
19.68 18.64 16.80 15.36 15.22 13.85 12.65 11.57 10.60 9.71 8.87 8.09 7.34 6.61 5.90 5.20 4.50 3.76 3.37
Benzene -4.83 -4.15 -2.97 -2.06 -1.97 -1.11 -0.37 0.30 0.90 1.45 1.95 2.42 2.88 3.30 3.72 4.13 4.54
18.07 18.67 19.83 20.84 20.94 22.02 23.06 24.08 25.08 26.06 27.02 27.97 28.92 29.86 30.80 31.76 32.76
30.89 31.20 31.84 32.43 32.50 33.16 33.84 34.51 35.19 35.86 36.53 37.20 37.87 38.53 39.20 39.86 40.53
Methylbenzene -6.36 23.38 -5.61 24.07 -4.29 25.40 -3.27 26.57 -3.18 26.69 -2.22 27.94 -1.39 29.15 -0.67 30.34 -0.01 31.51 0.57 32.66 1.12 33.80 1.62 34.93 2.09 36.05 2.54 37.16 2.96 38.27 3.39 39.38 3.80 40.49 4.22 41.62 4.43 42.21
36.70 37.10 37.91 38.66 38.74 39.57 40.41 41.25 42.10 42.94 43.79 44.63 45.47 46.31 47.14 47.97 48.79 49.60 50.01
562 K; 386-4898 kPa) and Bender et al. (1952) (373-562 K; 180-4898 kPa). For methylbenzene, the available vapor pressures below 0.3 MPa were found to be inconsistent with the results of the high-temperature study by Ambrose (1987). New vapor-pressure measurements for methylbenzene (305-422 K; 9-270 kPa) were completed as part of this research and are listed in Table 4. These new values were used alone in the fitting procedures and in conjunction with the high-temperature results reported by Ambrose (1987) (398-592 K; 305-4109 kPa). Differences between properties derived with each fit were small. All tabulated values were derived with the truncated vapor-pressure sets. Differences from results obtained with the complete vapor pressure sets are shown graphically or described in the table footnotes and text. Entropies of vaporization AfS, were derived with the Clapeyron equation (eq 2) and the Wagner-equation parameters listed in Table 6. Second and third virial coefficients were estimated by the corresponding-states methods of Pitzer and Curl (1957) and Orbey and Vera (19831, respectively. Wormald (1975) showed that the experimental second virial coefficients for benzene and those estimated by the method of Pitzer and Curl are in excellent agreement. Entropies of compression AScomp,m and the acentric factor w were derived with pressures calculated also with the fitted Wagner-equation parameters. The acentric factor is defined as {-log@/p,) - 11, where p is the vapor pressure at T,= 0.7 and pc is the critical pressure. The A f S m and ASc0mp.m values are included in Table 7.
162 Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 Table 8. CI.Values Determined by Differential-Scanning Calorimetry and the Fitting Procedures Described in This Research
T/K 300.0 320.0 340.0 360.0 380.0 400.0 420.0 440.0 460.0 480.0 500.0 520.0 540.0 560.0 570.0
benzene 16.41 16.96 17.53 18.12 18.75 19.4 20.1 20.8 21.7 22.6 23.7 25.3 28.5
CwtdR methvlbenzene 18.98 19.68 20.42 21.20 22.03 22.89 23.8 24.7 25.7 26.6 27.7 28.8 30.2 32.3 34.4
Saturation heat capacities Cmt were derived with the following equation: = Vm(1)T(d2P/dP),,,- T(d2N/dP),,,+ T@p/dr),,{dV,(l)/dT) (12) Temperature derivatives of the pressure were calculated with the Wagner-equation parameters listed in Table 6. Molar volumes of the liquid V,(l) were calculated with densities obtained with the corresponding-states equation of Riedel (1954) as formulated by Hales and Townsend (1972): (pip,) = 1.0 + 0.85{1.0- (T/T,)} + (T/T,) + (1.6916 + 0.9846~)(1.0 - (T/T,)}1’3(13)
Values of (d2p/dF),,t were determined by refitting the two-phase heat capacities with the Wagner-equation parameters fixed at the values listed in Table 6. The derived coefficients for eq 10 are listed in Table 6 also. The derived Cmt,m values are reported in Table 8. The estimated uncertainty in these values is 1% . Condensed-phase heat capacities and fusion enthalpies were determined previously by adiabatic calorimetry for benzene (10-340 K) (Oliver et al., 1948)and methylbenzene (10-320 K) (Scott et al., 1962). The curves of heat capacity versus temperature were integrated, and entropies of the liquid were calculated to the highest temperatures studied. The Csat,m values listed in Table 8 were combined with these results, and entropies of the liquid were calculated to within 25 K of T,for each molecule. These are listed in column 4 of Table 7. Entropies at selected temperatures for the ideal gas were calculated with eq 1 and are listed in column 5 of Table 7. The individual contributions shown in eq 1 are listed explicitly. Ideal-gas entropies for benzene and methylbenzene were calculated with published vibrational assignments and molecular structures. The rigid-rotor and harmonicoscillator approximations were used in the calculations. For benzene, the wavenumber values listed by Brodersen and Langseth (1956)and the structure reported by Cabana et al. (1974)were used. For methylbenzene, the vibrational assignments and moment of inertia product reported by Draeger (1985a,b)were employed. An alternative assignment has been proposed by Sverdlov (1970)and was chosen by Chao et al. (1984) for the calculation of methylbenzene ideal-gas thermodynamic functions. Differences between the derived thermodynamic functions for eachvibrational assignment are small but significant, as will be shown.
-
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,
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,
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,
,
,
,
,
,
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400
,
450
,
,
,
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,
,; 550
T/K Figure 4. Deviation of literature vapor presures p(1it) for benzene from the Wagner-equation fit ~(calc).0, Forziati et al. (1949); +, Ambrose et al. (1981; “1968/2”); 0,Ambrose et al. (1990; ‘metal”); A,Bender et al. (1952);0 ,Ambrose (1987);0, Connolly and Kandalic (1962). The arrow indicates the temperature range of the truncated vapor-pressure data set (i.e., Scott and Osborn, 1979). The curved line indicates deviations of values selected by Goodwin (1988). See text.
Until a definitive assignment of methylbenzene is determined, some ambiguity will remain. The small barrier to rotation of the methyl group in methylbenzene (Kreiner et al., 1973) was included in all calculations.
5. Discussion 5a. Physical Property Measurements: Critical Properties. Critical properties for benzene and methylbenzene were reviewed most recently by Tsonopoulos and Ambrose (1993). Recommended values for benzene were T, = (562.05 f 0.06) K, pc = (4.895 f 0.004) MPa, and values for methylbenzene were p c = (305 f 4) T,= (591.75f 0.15) K,pc = (4.108 f 0.010) MPa,pc = (291 f 5) kgm-3. Values determined in the present research for the critical temperatures and critical densities (listed in Table 6) are in excellent accord with these values. The derived critical pressures are correlated closely to the selected critical temperatures. If the T,values selected by Tsonopoulos and Ambrose (1993)are used in the fitting procedure with the truncated vapor-pressure sets, the derived critical pressures are very near the selected values: benzene, pc= 4.89 MPa; methylbenzene, pc= 4.13 MPa. The uncertainty in the critical pressures derived in this research is approximately 0.05 MPa for a given T,. Vapor Pressures. Numerous studies of the vapor pressure of benzene have been reported. The literature was reviewed recently by Goodwin (19881, and highprecision studies only are considered here. These can be split roughly into two groups: “high-pressure” studies above 0.1 MPa (Bender et al., 1952; Ambrose, 1987; Connolly and Kandalic, 1962) and “low-pressure” studies (Forziati et al., 1949;Ambrose et al. 1990,“metal”;Ambrose et al. 1981, “set 1968/2”) below 0.1 MPa. Figure 4 shows the deviations of literature vapor pressures from values calculated with the Wagner-equation parameters listed in Table 6. All data were converted to ITS-90. In the lowpressure region below 400 K, agreement between the data sets is excellent. Only the values reported by Forziati et
Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 163 n
-m
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0
0.2
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400
500
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T/K Figure 6. Deviation of literature vapor pressures p(lit) for methylbenzene from the Wagner-equation fit p(calc). +, Zmaczynski (1930); m, Pitzer and Scott (1943); 0 , Willingham et al. (1945); 0, Forziati et al. (1949); A, Besley and Bottomley (1974); A, Akhundov and Abdullaev (1969); X, Munday et al. (1980); 0,Ambrose (1987). The arrow indicates the temperature range of the truncated vaporpressure data set (i.e.,values of this research listed in Table 4). The curved line indicates deviations of values selectedby Goodwin (1989). See text.
al. (1949) deviate slightly from the fit, particularly at the lowest pressures. At high pressures, all of the published studies show small deviations from the fit with no apparent trend. Deviations of vapor-pressure values calculated with eq 2 of Goodwin (1988) are shown also in Figure 4. Differences are primarily related to differences in temperature scale. Goodwin fitted vapor pressures published on the 1948 and 1968 temperature scales without conversion. Vaporpressure shifts on the order of 0.15% arise from temperature scale changes. The extensive literature on the vapor pressure of methylbenzene was reviewed also by Goodwin (1989). Figure 5 shows the deviations of literature vapor pressures from values calculated with the Wagner-equation parameters listed in Table 6. High-precision studies only were considered. Inconsistencies between results above and below the normal-boiling temperature (near 384 K) are apparent. These inconsistencies prompted the measurement in this research of the methylbenzene vapor pressures used in the Wagner-equation fit. The small deviations from the fit of values reported by Forziati et al. (1949) and Ambrose et al. (1987), which are common to benzene and methylbenzene, are very similar in magnitude and sign for both compounds. Deviations of vapor-pressure values calculated with eq 2 of Goodwin (1989)are shown also in Figure 5. Differences are primarily related to differences in temperature scale, for the reasons noted above for benzene. The large deviations below 300 K reflect the high weighting by Goodwin of the Besley and Bottomley (1974) results between 273 and 298 K. Values listed by Besley and Bottomley (1974) are approximately a constant (6 f 2) P a higher than those calculated in the present research. Densities. Figure 6 shows differences between the measured liquid-phase densities for benzene and those calculated with eq 13 for temperatures to within 10 K of T,. For temperatures below the normal-boiling temperature (353 K), agreement between the various studies is
.
290
370
450
530
T/K Figure 6. Deviationof experimental densities perpt for benzene from values calculated with eq 13, pa. +, Valuesof this research; X, Young (1910);D, Connolly and Kandalic (1962); A,Campbell and Chatterjee (1967); Shraiber and Pechenyuk (1965); 0 ,Hales and Townsend (1972); V,Kuss (1976); 0 ,Teichmann (1978); m, Hales and Gundry (1983); 0,Straty et al. (1987); A, Beg et al. (1993). Values reported by Smyth and Stoops (1929) are not shown but are nearly identical to those reported by Shraiber and Pechenyuk (1965).
+,
excellent. A t higher temperatures, significant differences are apparent. Values reported by Hales and Townsend (1972),Connolly and Kandalic (1962),Teichmann (1978), Hales and Gundry (1983), Kuss (1976), and this research group all lie well within f0.2 % of the calculated values. Densities measured by Young (19101, Campbell and Chatterjee (1967), Stratyetal. (1987),andBegetal. (1993) deviate high by approximately 0.6% near 500 K. The source of the differences is not known. Figure 7 shows differences between the measured liquidphase densities for methylbenzene and those calculated with eq 13. The measured values, including those of this research, are in excellent agreement, except for those reported by Rudenko et al. (1981). The deviations show a smooth variation with temperature from 0.25 5% low near 300 K to 0.25% high near 550 K. The deviations are sufficiently small to allow use of eq 13 in the calculations of this research without introduction of significant error. The variation of the deviations with temperature is nearly identical to that observed previously for naphthalene (Chiricoet al., 1993b). It may have been possible to remove the linear variation with temperature, if a modification of the corresponding-states equation had been used, as has been proposed (Joffe and Zudkevitch, 1974). 5b. Comparisons of Ideal-Gas Entropies and Effects of Virial Coefficients. Figure 8 shows the differences between the calorimetric and spectroscopicallyderived ideal-gasentropies for benzene. Results are shown for fits involving the truncated and complete vaporpressure sets. The differences are not significant, as would be expected based on Figure 4. High-temperature vapor pressures reported by Bender et al. (1952) and Ambrose et al. (1987) used in the complete fit are almost evenly distributed to the high and low sides of the truncated fit. The error bands in Figures 8 and 9 represent one standard deviation for the calorimetric entropies. The error bands represented by solid curves do not include contributions
164 Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 0.4,
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T/K Figure 7. Deviation of experimental densitiespwtfor methylbenzene from values calculated with eq 13, pa. D, Values of this research; A, Shraiber and Pechenyuk (1965);+, Akhundov and Abdullaev (1970); 0,Hales and Townsend (1972);0 ,Akhundov and Abdullaev (1977); 0 , Rudenko et al. (1981); 0 , Albert et al. (1985); Dymond et al. (1988).
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/
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Figure 9. Ideal-gas entropy differences for methylbenzene between calorimetric L$SL(cal) and spectroscopic L$S;(spect) values. 0 , Calorimetric values based on the truncated vapor-pressure data set and spectroscopic values calculated with the assignment of Draeger (198Sa,b);0 ,calorimetricvalues based on the completevapor-pressure data set and spectroscopic values calculated with the assignment of Draeger (1985a,b); A, calorimetric values based on the truncated vapor-pressure data set and spectroscopic values based on the assignment of Sverdlov (1970). The curved lines represent the uncertainty (one standard deviation) in the calorimetric values without consideration of uncertainties in virial coefficients. The dashed lines include 5 % uncertainty in the virial coefficients. See text.
entropies of vaporization are very sensitive to small differences in the extrapolated vapor pressures in this region. The differencesare a result of small inconsistencies between the high-pressure values by Ambrose (1987) and the low-pressure values of this research. Results for pressures above 0.3 MPa for both benzene and methylbenzene indicate that the high-temperature results of Ambrose and co-workers (1987) are slightly low systematically. Chao et al. (1984)reviewed the ideal-gasthermodynamic properties of methylbenzene and selected the vibrational assignment published by Sverdlov (1970) rather than that of Draeger (1985a,b). This selection was based primarily upon an improved agreement between calorimetric and spectroscopically-derivedideal-gasproperties. Differences between ideal-gas entropies based on the Sverdlov assignment and the calorimetric values of this research derived with the truncated vapor-pressure set are shown in Figure 9 also. Agreement is near perfect except for temperatures below the range of the vapor-pressure measurements, where small errors in extrapolation can cause significant systematic errors. Differences between the ideal-gas entropies derived with the assignments of Draeger and Sverdlov are too small for the calorimetric results to provide an unequivocal determination of which is more correct. Figure 10 shows differences between the spectroscopic and calorimetric ideal-gas entropies for benzene for three different calculations of the calorimetric values: (1) without consideration of gas imperfection (Le., all virial coefficients are ignored), (2) with the second virial coefficient alone, and (3) with the second and third virial coefficients included in the calculations. All calculations were done with the truncated vapor-pressure set. Several generalizations can be drawn from the figure. Failure to include the effects of gas imperfections leads to significant
---y 300
380
T/K
460
540
Figure 8. Ideal-gas entropy differences for benzene between calorimetric L$Sa(cal) and spectroscopic L$Sa(spect) values. 0 , Calorimetric values calculated with the truncated vapor-pressure data set; 0 , calorimetric values calculated with the complete vaporpressure data set. The curved lines represent the uncertainty (one standard deviation) in the calorimetric values without consideration of uncertainties in virial Coefficients. The dashed lines include 5 % uncertainty in the virial coefficients. See text.
from uncertainties in virialcoefficients. The dashed curves include a 5 % uncertainty in the virial coefficients. Figure 9 shows the differences between the calorimetric and spectroscopically-derived ideal-gas entropies for methylbenzene. Values derived with the truncated and complete vapor-pressure sets are shown relative to the spectroscopic values based on the assignment published by Draeger (1985a,b). Differences between the truncated and complete results are significant only below the temperature range of the vapor pressures. Derived
540
T/K
Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 165 1.01
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T I Tc Figure 10. Ideal-gas entropy differences for benzene between calorimetric @L(cal) and spectroscopic A$L(spect) values plotted against reducedtemperature. Calorimetricvalueswere calculated with the truncated vapor-pressure data set, and spectroscopic values were calculated with the assignment of Brodersen and Langseth (1966). 0 , Second and third virial coefficients were included in calculation of the calorimetric values; A, second virial coefficients only were included; X, gas imperfections were ignored. The curved lines represent the uncertainty (one standard deviation) in the calorimetric values without consideration of uncertainties in virial coefficients. See text.
errors at reduced temperatures above approximately TITc = 0.5. Inclusion of the second virial coefficient is sufficient for calculations to TIT, = 0.65, while excellent accord between the spectroscopic and calorimetric ideal-gas entropies is achieved to above TIT, = 0.8, if the third virial coefficient estimates are included. Higher virial coefficients are expected to become important near TIT, = 0.9. The good agreement in this temperature region in the present analysis is probably fortuitous. The graph and conclusions would be completely analogous, if the methylbenzene results were used. The virial coefficients impact two terms in the summation used to calculate the calorimetric ideal-gas entropy (eq 1); the entropy of vaporization and the entropy of compression. Figure 11showshow these terms are affected by the inclusion of the second and third virial coefficients in the calculations for benzene. Positive deviations result for the entropies of vaporization, and negative deviations result for the entropies of compression. The analogous figure for methylbenzene is nearly identical. The effects are opposite in sign, but because the corrections to the entropy of vaporization are larger, there is a net reduction in the calculated ideal-gas entropy when the virial coefficients are included. Figure 12 shows the percent change in the entropy of vaporization for benzene and methylbenzene calculated with the Clapeyron equation if (1)the vapor is assumed to be ideal and (2) if the second virial coefficient alone is used in the calculation of the molar volume of the vapor. Changes are plotted relative to values calculated with both the second and third virial coefficients. The figure shows that inclusion of the third virial coefficients has a significant impact on the calculated entropies of vaporization for pressures as low as 0.1 MPa.
Acknowledgment The authors gratefully acknowledge the contributions of their colleagues at NIPER Stephen E. Knipmeyer for the dsc measurements, An Nguyen for the density and
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TIT, Figure 11. Entropies of vaporization and entropies of compression all relative to values calculatedwithsecond and third virialcoefficients included. Entropies of compression calculated without third virial coefficients, e, and without third and second virial coefficients, Entropies of vaporization calculated without third virial coefficients, 0 ,and without third and second virial coefficients, X. 0,The sum of the deviations for the entropies of vaporization and entropies of compression (Le., the net deviation) calculated without third virial coefficients.
+.
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0.6
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TIT, Figure 12. Percent errors in entropies of vaporization calculated with the Clapeyron equation against reduced temperature. Deviatiom are calculated relative to values calculated with second and third virial Coefficients. T h e lower curve waa calculated with second , benzene; 0,methylbenzene. The upper virial coefficients only: . curve waa calculated without virial coefficients (Le., the ideal-gaa approximation): ,benzene; A,methylbenzene. T h e vertical lines indicate the approximate reduced temperature for p = 0.1 and 1.0 ma.
vapor pressure measurements, Norris K. Smith for preliminary dsc measurements on benzene, and I. Alex Hossenlopp and Aaron P. Rau for in uucuo sample handling. The authors acknowledge financial support from the following: Wright-Patterson Air Force Base, Dayton, OH, and the Naval Air Propulsion Center, Trenton, NJ, for the differential-scanning calorimetric measurements on methylbenzene; the Office of Fossil Energy of the U.S. Department of Energy within the Advanced Research and Technology Development program for the differential-scanning calorimetric measurements on benzene; and the Offic e of Energy Research/ Chemical Sciences Division within Grant DE-FGO5-
166 Ind. Eng. Chem. Res., Voi. 33, No. 1, 1994 Draeger, J. A. The methylbenzenes. 11. Fundamental vibrational shifts, statistical thermodynamic functions, and properties of formation. J. Chem. Thermodyn. 1985b, 17, 263. Dymond, J. H.; Malhotra, R.; Isdale, J. D.; Glen, N. F. (p, p, T) of n-heptane, toluene, and oct-1-ene in the range 298 to 373 K and Literature Cited 0.1 to 400 MPa and representation by the Tait equation. J.Chem. Thermodyn. 1988,20, 603. Akhundov,T. S.; Abdullaev,F. G. Saturatedvapor pressure of toluene. Forziati, A. F.; Norris, W. R.; Rossini, F. D. Vapor pressures and Izv. Vyssh. Uchebn. Zaved., Neft Gaz 1969,12,44. FromGcmdwin, boiling points of sixty API-NBS hydrocarbons. J.Res. Nat. Bur. 1989. Stand. 1949, 43, 555. Akhundov, T. S.; Abdullaev, F. G. Experimental study of specific Goldberg, R. N.; Weir, R. D. Conversion of temperatures and volumes of toluene. Izv. Vyssh. Uchebn. Zaved., Neft Gaz 1970, thermodynamic properties to the basis of the International 13, 67. From Goodwin, 1989. Temperature Scale of 1990. Pure Appl. Chem. 1990, 64, 1545. Akhundov, T. S.; Abdullaev, F. G. Thermal properties of benzene Goodwin, R. D. Benzene thermophysical properties from 279 to 900 and toluene in a state of saturation. Izv. Vyssh. Uchebn. Zaved., K at pressures to lo00 bar. J. Phys. Chem. Ref. Data 1988,17, Neft Gaz 1977,20,64. From Goodwin, 1989. 1541. Albert, H. J.; Gates, J. A.; Wood, R. H.; Grolier, J.-P. E. Densities of toluene, of butanol and of their binary mixtures from 298 K to Goodwin, R. D. Toluene thermophysical properties from 178to 800 400 K, and from 0.5 to 20.0 MPa. Fluid Phase Equilib. 1985,20, K at pressures to lo00 bar. J. Phys. Chem. Ref. Data 1989, 18, 321. 1565. Ambrose, D. Reference values of vapour pressure. The vapour Hales, J. L.; Townsend, R. Liquid densities from 293 to 490 K of nine pressures of benzene and hexafluorobenzene. J. Chem. Theraromatic hydrocarbons. J. Chem. Thermodyn. 1972,4,763. modyn. 1981,13, 1161. Hales, J. L.; Gundry, H. A. An apparatus for accurate measurement Ambroee, D. Vapour pressures of some aromatic hydrocarbons. J. of liquid and vapour densities on the saturation line, up to the Chem. Thermodyn. 1987,19, 1007. critical temperature. J. Phys. E 1983, 16, 91. Ambrose, D.; Ewing, M. B.; Ghiassee, N. B.; Sanchez Ochoa, J. C. Joffe, J.; Zudkevitch, D. Correlation of liquid densities of polar and The ebulliometric method of vapour-pressure measurement: nonpolar compounds. In AlChE Symposium Series,Number 140; vapourpressurea of benzene, hexafluorobenzene,and naphthalene. Zudkevitch, D., Zarember, I., a s . ; AlChE: New York, 1974. J. Chem. Thermodyn. 1990,22,589. Kagarise, R. E. Vapour-liquid frequency shifts in some substituted Beg, S. A.; Tukur, N. M.; Al-Harbi, D. K.; Hamad, E. Z. Saturated methanes. Spectrochim. Acta 1963,19,1979. liquid densities of benzene, cyclohexane,and hexane from 298.15 Knipmeyer, S. E.; Archer, D. G.; Chirico, R. D.; Gammon, B. E.; to 473.15 K. J. Chem. Eng. Data 1993,38, 461. Hossenlopp, I. A.; Nguyen, A.; Smith, N. K.; Steele, W. V.; Strube, Bender, P.; Furukawa, G. T.; Hyndman, J. R. Vapor pressure of M. M. High-temperature enthalpy and critical property meabenzene above 100 OC. Ind. Eng. Chem. 1952,44, 387. surements using a differential scanning calorimeter. Fluid Phase Besley, L. M.; Bottomley, G. A. Vapour pressure of toluene from Equilib. 1989, 52, 185. 273.15 to 298.15 K. J. Chem. Thermodyn. 1974,6, 577. Kreiner, W. A.; Rudolph, H. D.; Tan, B. T. Microwave spectra of Brodersen, S.; Langseth, A. The infrared spectra of benzene, symseveral molecular isotopes of toluene. J.Mol. Spectrosc. 1973,48, benzene-d3, and benzene-d6. K. Dan. Vidensk. Selsk., Mat.-Fys. 86. Skr. 1956, 1, 1. Cabana, A.; Bachand, J.; Giguere, J. The v4 vibration-rotation bands Kuss, E. PVT Data at High Pressures. Ber.-Dtsch. Ges. Mineralof C a e a n d C&3: The analysis of the bands and the determination oelwiss. Kohlechem. 1976, 4510. From Goodwin, 1988. of bond lengths. Can. J. Phys. 1974,52,1949. Munday, E. B.; Mullins, J. C.; Edie, D. D. Vapor pressure data for Campbell, A. N.; Chatterjee, R. M. Orthobaric data of certain pure toluene, 1-pentanol, 1-butanol,water, and 1-propanol and for the liquids in the neighborhood of the critical point. Can. J. Chem. water and 1-propanol system from 273.15 to 323.15 K. J. Chem. 1967, 46, 575. Eng. Data 1980,25, 191. Chao, J.; Hall, K. R. Chemical thermodynamic properties of toluene, Oliver, G. D.; Eaton, M.; Huffman, H. M. The heat capacity, heat 0 - , m-, and p-xylenes. Thermochim. Acta 1984, 72, 323. of fusion, and entropy of benzene. J. Am. Chem. SOC. 1948, 70, Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A.; Steele, W. V. The 1502. thermodynamic properties of biphenyl. J. Chem. Thermodyn. Orbey, H.; Vera, J. H. 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Chem. 1979,83, 2714. thermodynamic properties to 700 K of naphthalene and 2,7Scott, D. W.; Guthrie, G. B.; Messerly, J. F.; Todd, S. S.; Berg, W. dimethylnaphthalene. J. Chem. Thermodyn. 199313, in press. T.; Hossenlopp,I. A.; McCullough,J. P. Toluene: Thermodynamic Cohen, E. R.; Taylor, B. N. The 1986CODATA recommended values properties, molecular vibrations, and internal rotation. J. Phys. of the fundamental physical constants. J.Phys. Chem. Ref. Data Chem. 1962,66, 911. 1988, 17, 1795. Shraiber, L. S.; Pechenyuk, N. G. Technique for precision measureConnolly, J. F.; Kandalic, G. A. Saturation properties and liquid ment of liquid density over a wide temperature range. Russ. J. compressibilities for benzene and n-octane. J.Chem. Eng. Data Phys. Chem. 1965,39,219. 1962, 7, 137. Draeger, J. A. The methylbenzenes. I. Vapor-phase vibrational Smithson, T. L.; Duckett, J. A.; Wieser, H. 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87ER13758 for the data analysis. This research was completed as part of the Cooperative Agreement DE-FC2283FE60149.
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