2487
Ind. Eng. Chem. Res. 1991, 30, 2487-2492 in urethane coatings, even in the absence of detailed composition information. Conclusion The chemistry and kinetics of photooxidation have been determined for a series of acrylic and polyester urethanes under near-ambient exposure conditions. Results have been compared to recent measurements of free radical formation rates and concentrations of hydroperoxides in these coatings. The major photooxidation processes in these coatings are carbonyl formation and urethane cross-link scission. The rates of carbonyl growth and cross-link scission correlate well with measured hydroperoxide concentrations. The kinetic behavior observed under near-ambient conditions is qualitatively different from that observed previously for harsh, short wavelength UV light exposures typical of many accelerated testa. In addition, harsh exposure has been found to distort the balance between carbonyl formation and cross-link scission in HALS-stabilized acrylic urethanes. These results point out some of the pitfalls in using harsh exposure conditions to predict service life. Registry No. T I N 770, 52829-07-9; T I N 079L, 128088-48-2;
(BMA) (HEA)(AA) (N3200) (copolymer), 135929-15-6; (BMA)(HEA)(AA)(N3300)(copolymer), 135929-16-7.
Literature Cited Bauer, D. R.; Dickie, R. A.; Koenig, J. L. Cure and Photodegradation of Two-Package Acrylic/Urethane Coatings. Ind. Eng. Chem. Prod. Res. Deo. 1986,25, 289-296. Bauer, D. R.; Gerlock, J. L.; Dickie, R. A. Rapid, Reliable Tests of Clearcoat Weatherability: A Proposed Protocol. Prog. Org. Chem. 1987, 25, 209-221. Bauer, D. R.; Dean, M. J.; Gerlock, J. L. Comparison of Photostabilization in Acrylic/Urethane and Acrylic/Melamine Coatings.
Ind. Eng. Chem. Prod. Res. Dev. 1988,27,65-70. Bauer, D. R.; Gerlock, J. L.; Mielewski, D. F.; Paputa Peck, M. C.; Carter, R. O., 111. Photostabilization and Photodegradation in Organic Coatings Containing a Hindered Amine Light Stabilizer. Part IV. Photoinitiation Rates and Photooxidation Rates in Unstabilized Coatings. Polym. Degrad. Stab. 1990a, 27,271-284. Bauer, D. R.; Gerlock, J. L.; Mielewski, D. F. Photostabilization and Photodegradation in Organic Coatings Containing a Hindered Amine Light Stabilizer. Part VI. ESR Measurements of Nitroxide Kinetics and Mechanism of Stabilization. Polym. Degrad. Stab. 1990b, 28, 115-129. Bauer, D. R.; Mielewski, D. F.; Gerlock, J. L. Photooxidation Kinetics in Crosslinked Polymer Coatings. 1991, manuscript in preparation. Carduner, K. R.; Carter, R. O., 111; Zinbo, M.; Gerlock, J. L.; Bauer, D. R. End Groups in Acrylic Copolymers. Part 1. Identification of End Groups by Carbon-13 NMR. Macromolecules 1988, 21, 1598-1603. Gerlock, J. L.; Bauer, D. R.; Briggs, L. M.; Hudgens, J. K. Photostability of Acrylic/Melamine Enamels: Effect of Polymer Composition and Polymerization Conditions on Photoinitiation Ratee. Prog. Org. Coat. 1987,15, 197-208. Gerlock, J. L.; Mielewski, D. F.; Bauer, D. R. Nitroxide Decay Assay Measurements of Free Radical Photoinitiation Rates in Polyester Urethane Coatings. Polym. Degrad. Stab. 1989, 26, 241-254. Mielewski, D. F.; Bauer, D. R.; Gerlock, J. L. The Role of Hydroperoxides in the Photooxidation of Crosslinked Polymer Coatings. Polym. Prep. 1989, 30 (2), 144-145. Mielewski, D. F.; Bauer, D. R.; Gerlock, J. L. Determination of Hydroperoxide Concentrations in Crosslinked Polymer Coatings Containing Hindered Amine Light Stabilizer. Polym. Mat. Sci. Eng. 1990,63,642-646. Mielewski, D. F.; Bauer, D. R.; Gerlock, J. L. The Role of Hydroperoxides in the Photooxidation of Crosslinked Polymer Coatings. Polym. Degrad. Stab. 1991 33, 93-104. Potter, T. A,; Schmelzer, H. G.; Baker, R. 0. High Solids Coatings Based on Polyurethane Chemistry. Prog. Org. Coat. 1984, 12, 321-338. Received for reuiew April 15, 1991 Accepted July 8, 1991
The Riedel Equation Alessandro Vetere SnamprogettilResearch Laboratories, 20097 Via Maritano, 26, Sun Donato Milanese, Italy
A comparison is given between the Riedel equation and some literature relations for calculating the vapor pressure of pure compounds. It is shown that the Riedel equation represents a simple and reliable predicting model in the whole subcritical range. The peculiar features of the Riedel equation are also discussed. Some possible improvements of the Riedel model are examinated, and a simple modification which greatly improves the accuracy of the Riedel equation is proposed. This modification is particularly suitable in the case of some strongly associated compounds, such as alcohols, and polyfunctional molecules, such as glycols. The superiority of the Riedel model is discussed on the basis of the results obtained by predicting the vapor pressure curve of several nonpolar and polar compounds in a wide experimental range. The performances of the Thodos and Riedel equations in the region of very low vapor pressures are emphasized. Introduction In 1954 Riedel published a semina] paper on vapor pressure prediction whose importance was readily recognized (Riedel, 1954; Reid and Sherwood, 1977). In fact, after nearly four decades, the Riedel equation In
PR
=A
- - + C In TR + DTR6
(l)
TR must be considered as the first remarkable advancement over the 19th century relationships.
0888-5885/91/2630-2487$02.50/0
However, the novelty of the Riedel equation goes far beyond form. Ridel developed accurate method for calculating the four empirical constants of relation 1 which is routed in a subtle analysis of the fluid behavior at the critical point. As will be shown later, the reliability of the Riedel equation rests entirely on the thermodynamic constraints which link together the A, B, and C constants through the Riedel factor, ac. As with all fundamental works, the Riedel equation stimulated further research efforts aimed at improving the Riedel equation performances through some empirical 0 1991 American Chemical Society
2488 Ind. Eng. Chem. Res., Vol. 30, No. 11,1991 Table I. ComDarieon between the Riedel and the Gomez-Thodos Eauations n-decanea absolute 7'0 error T/K Plbar Riedel Gomez-Thodos T/K 240.2 O.ooOo13 7.38 28.56 344.3 17.31 347.9 253.8 O.ooOo53 3.49 9.32 350.8 0.01 263.9 0.00013 3.67 355.8 286.4 O.OOO8 5.43 7.82 358.0 303.8 0.0027 6.10 8.86 360.0 318.6 0.0067 5.53 8.11 361.9 326.8 0.0107 4.35 5.50 365.8 1.59 352.8 0.0400 4.22 369.4 0.76 368.7 0.080 2.76 412.7 0.32 392.9 0.200 418.7 1.60 414.0 0.400 0.17 0.38 422.6 438.2 0.800 0.03 427.7 0.02 446.2 0.987 0.05 0.10 428.3 1.04 0.07 448.3 0.55 433.3 458.4 1.33 0.15 1.38 437.8 0.29 483.2 2.33 445.6 2.06 513.2 4.20 0.50 3.83 2.26 518.2 4.68 4.61 533.2 6.12 3.01 5.69 4.29 563.2 10.0 6.20 593.2 15.6 5.39 a Wilhoit
2-methylpropionic acidb absolute '70 error Plbar Riedel Gomez-Thodoe 0.0343 6.00 25.08 0.0413 5.90 23.47 0.0480 5.40 21.73 0.0615 5.09 19.53 0.0685 4.84 18.47 0.0755 17.51 4.58 0.0826 4.39 16.68 0.0989 4.19 15.25 0.1164 3.84 13.82 0.6269 2.32 0.82 0.7632 1.53 0.70 0.8655 0.45 0.90 1.018 0.08 0.09 1.036 0.10 0.04 1.207 0.83 0.39 1.377 1.30 0.56 1.721 2.17 1.00
and Zwolinski (1971). *Ambrose and Ghiassee (1987a).
modifications of the Riedel procedure for calculating the relation 1 constants. To this class belong also two papers by Vetere (1986, 1988). A noticeable exception is the Gomez-Thodos equation
which has gained a wide acceptance (Reid et al., 1987). The Riedel equation describes the vapor pressure of fluids with two critical constants, T, and P,, and two universal constants only. The other literature equations, such as the Vetere and Gomez-Thodos equations, often require ad hoc empirical parameters for different classes of compounds. However, the superiority of some recent relationships over eq 1 is doubtful. As an example, we report, in Table I, the results obtained by predicting the vapor pressure data of n-decane and 2-methylpropionic acid through the Riedel and the Gomez-Thodos equations. It shows that the Gomez-Thodos equation is excellent in a moderate range of pressures but its reliability decreases markedly when very low vapor pressure values are considered, especially in the case of very high molecular compounds. A comparison given in Table 111confirms that the Riedel equation is not inferior to some recent literature relations which predict the vapor pressures of pure compounds from the normal boiling temperature and the critical constants only. However, Riedel worked out his equation in the precomputer age so that a more reliable calculation of the empirical constants in relation 1 now appears feasible.
Analysis of the Riedel Equation Since the Riedel equation is both simple and accurate in predicting the vapor pressure curve, its derivation deserves a careful examination. The starting point to derive a universal relation valid for all the compounds is the Clausius-Clapeyron equation, written as follows in the reduced form: (3)
For integration of eq 3, no simple relation is known that
links A2 to the reduced temperature. Fortunately, the variation of the ratio AH/U with T i s well described by the relation
M / A Z = RT,(a - bTR + cTR")
(4)
where the exponent term, n, takes into account the inflection point of the vapor pressure curve in the highpressure region. Experimentally, it was found that n can assume a value between 6 and 8. Riedel chooses the mean value n = 7. Accordingly, from eqs 3 and 4 with n = 7 the Riedel equation expressed by relation 1 is easily derived. The most interesting side of the Riedel work is the analysis of the empirical parameter behavior. By an accurate inspection of the vapor pressure data near the critical point, Riedel derived the following rule
which imposes thermodynamic constraints between the four constants of eq 4, namely, a = (n - l)c (6) b = nc - a, (7) a, being the so called Riedel parameter, expressed by re-
lation 3, calculated at the critical point. Contrary to modern theory, the d 2 P / d F value calculated through relation 5 is not indeterminate, but it was stressed by Ambrose (1985) that "as far as correlation is concerned, whether or not an equation is analytic at the critical point is of no importance". Thanks to relations 6 and 7, the independent constants of the Riedel equation are only a and a,. Riedel was able to derive a third empirical constraint that links a to acby plotting the a(TR)function for several compounds at some fixed TRvalues. As indicated in Figure 1, an important characteristicof the Riedel equation is the focal point along the X = Y line of the Cartesian axis. Further, a simple analysis of the Riedel equation shows that the focal point in Figure 1at the X = Y coordinate is a direct consequence of the independence of the a constant from temperature and that the value 3.758 of the crossing point coordinates depends only on the choice of an exponential term equal
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2489
12
-
sequence of the Riedel restriction. The choice of n = 7 made by Riedel was fortunate, so that the 3.758 value can also be retained. On the contrary, the K value 0.0838 is the only weak point of the Riedel work, since the search of a more proper value was evidently prevented by practical difficulties found in the precomputer era. Therefore, the only modification of the Riedel equation proposed in this work is a different calculation of the K value. In this paragraph the usual symbology of the Riedel equation has been changed in order to clearly depict the close relation between eqs 1and 4. However, we recall that with respect to the standard nomenclature the following relations hold:
10
-
b=C
18
I4 f6
c/(n
8-
u
6-
at!
; 1
ii ' */
; h B ;
Figure 1. a(TR)vs a, plot, at various equation.
d,
1 1 ;
rl
r:
aC
TR values, of the Riedel
(8)
Further, when the b and c values calculated through relations 6 and 7 are inserted in relations 3 and 4, the following equation holds for the (Y(TR) term
~ T R= )a, + w(TR)
(9)
with
By equating relations 8 and 9, Riedel derived the link between the term and the a constant u = K(n - l)*(a,- 3.758)
(11)
K = [tgb(TR)- l ] / d T ~ )
(12)
where
Both the tg@(TR)and the a(TR) terms vary widely with temperature, but the constancy of the ratio expressed by relation 12 is well verified experimentally. With the usual formalism for the Riedel equation (Reid et al., 19771, relation 11 can also be written as (13)
Riedel assumes K = 0.0838 as an universal parameter valid for any compound. While the Riedel restriction expressed by relation 5 was accepted in the so-called classical theory of vapor pressures, the application of relation 11was rejected in all subsequent works on vapor pressure prediction (Reid et al., 1977). The aim of this apparently redundant derivation of the Riedel equation is to show that relation 11has the same validity as the rules expressed by relations 6 and 7 since it is now clear that the link between a, and a is also a direct con-
(15) (16)
Calculation of the K Constant In order to calculate the K constant by avoiding a purely empirical method, it would be tempting to apply the rigorous relation linking "(TRb) to the heat of vaporization at the normal boiling point (Reid et al., 1987). (17)
From eqs 9-11 and 17, the derivation of the K value is immediate if a mean value of a b = 0.97 is assumed at T b for all the compounds. This method requires a new parameter, A H b , which is known for most compounds or can be calculated through reliable relationships based only on the molecular weight and the normal boiling temperature (Reid et al., 1987; Vetere, 1988). Another similar procedure, but independent from any enthalpic datum, is based on the application of relation 14 at two temperatures below Tb. Then the K constant can be calculated from the ratio a(TR,)/a(Tb)according to the following equation a = ac(A1
Q = K(3.758 - a,)
- c / ( n - 1) = A
a(TRb) = mb/RTbMb
to 7 (different values of n give rise to different values of the crossing point coordinates). From Figure 1, the following equation is given:
~ ( T R=)3.758 + (ac- 3.758)tg@(TR)
- 1) = D
(14)
- 1)/[(P(TR,)- A1'P(TR2)1
(18)
where Al is linked to the critical temperature only as it results from
which was derived by calculating the enthalpic data through the Watson relation. Unfortunately, both methods gave scattered results, and they cannot be confidently used in several cases. On the contrary, good results are obtained if the thermodynamic link between the Riedel constants is disregarded and the a, b, and c values are calculated from relation 4 applied to at least three temperatures in a range below T b (Vetere, 1988). A more empirical but useful procedure to calculate K resulted from the following steps. The compounds are grouped in families according to their chemical and physical properties. Some well-studied compounds are chosen as representative of any family considered. For these compounds, the best K value is obtained by correlating the available vapor pressure experimental data. Finally, the optimized K values are linked to a wellknown property of the compound through generalized correlations which are valid for all the compounds that belong to the same family.
2490 Ind. Eng. Chem. Res., Vol. 30,No. 11, 1991 Table 11. Rules tor Calculating the Riedel Constant K class of compound rules nonpolar compounds K = 0.066 + 0.0027H acids K = -0.120 0.025H alcohols K = 0.373 - 0.030H K = 0.106 - 0.0064H g1yc01s K = -0,008 + 0.14TRb other polar compounds
where P, must be expressed in atmospheres (for the use of H as a correlating quantity, see, for example, Gomez and Thodos, 1977). The only exception is represented by the family of water, ammonia, and polar nonassociated compounds, for which we have K = B2 + cpT~b (22)
Due to the results given in Table 11, in this work the compounds are subdivided into five families for which a linear relation of the type K = B1 + CIH (20)
The reasons for this different behavior can be found in the abnormally high value of the critical pressure of water and ammonia. If these compounds are disregarded, an eq 20 type relationship would be valid for this family of compounds also. In summary, the modified Riedel equation proposed in this paper can be applied following the procedure reported by Reid et al. (1977) for the unmodified Riedel equation provided that K is substituted for the 0.0838 value and a, is calculated according to the relation
+
links the Riedel constant to the easily obtained H parameter, defined by the relation
Table 111. Conmarison between Five Eauations Por Predicting the Vapor Pressures of Pure ComDounds % absolute average error pressure/ bar temp/K modified lit. source min max min max Riedel Riedel Miller Thek-Stiel Thodos methane a 90.7 190.5 0.47 0.17 0.12 45.96 0.41 0.49 0.16 b 37.69 108 363.0 3.58 4.53 propane 0.27 X 4.13 4.81 5.78 n-hexane C 0.13 X lo4 28.25 181.2 503.2 5.14 5.83 6.68 7.14 3.70 n-decane C 0.13 X lo-' 20.40 240.3 613.2 2.30 2.79 3.20 4.42 4.74 d 0.17 x 10-3 2.32 1.04 2.48 n-decane 268.1 483.0 0.49 5.42 3.85 n-dodecane e 0.59 X 0.018 263.9 371.3 17.15 3.69 5.16 14.64 28.65 0.17 x 10-3 2.41 n-dodecane 0.042 298.1 389.7 9.77 6.26 12.47 17.70 f n-tetradecane 0.72 x 10-3 0.013 343.2 394.7 13.19 0.45 9.51 21.57 16.79 f n-pentadecane 333.1 409.1 19.13 0.16 x 10-3 0.013 4.42 12.51 28.13 21.50 f 0.12 x 10-4 28.17 n-octadecane 0.01 335.2 439.8 2.56 31.16 42.47 39.15 f n-octadecane 0.36 X 10" e 43.47 0.0015 303.3 403.3 4.11 39.89 42.47 66.23 0.16 x 10-3 1.54 n-eicosane d 1.20 388.1 626.0 8.86 23.05 7.77 14.70 n-eicosane 0.23 x 10-3 e 363.3 467.4 4.33 0.013 21.50 55.13 25.37 22.64 ammonia 195.4 40.0 1.87 0.06 101.5 0.79 3.61 0.37 0.68 g h 258.2 643.2 4.46 0.0019 210.2 water 1.02 0.57 0.96 1.35 sulfur dioxide h 0.02 67.2 119.8 422.0 1.10 1.20 1.00 0.54 1.30 methylamine h 6.81 223.2 318.2 2.00 0.09 2.64 2.24 3.26 3.87 methyl chloride h 0.01 4.27 5.21 56.6 175.0 405.0 5.49 5.14 5.55 acetone i 213.8 487.7 3.29 2.82 0.0013 26.6 2.08 3.82 4.08 aniline 0.0013 53.1 308.0 699.2 4.29 4.30 5.09 5.55 11.68 j nitromethane k 260.0 580.0 6.93 0.0047 57.2 6.01 4.78 4.88 1.95 phenol k 1.18 0.0029 59.0 320.0 690.0 1.19 2.19 3.51 2.64 m-cresol 705.0 1.94 k 0.0048 45.8 1.10 4.94 1.17 340.0 3.30 ethyl acetate 0.0087 37.8 253.0 522.2 0.66 0.50 1.53 3.11 0.62 j methanol 230.0 505.0 7.47 0.0014 71.1 6.25 0.72 2.38 l,m ethanol 0.0011 i,l 57.4 240.0 510.0 3.93 4.18 1.28 2.26 m isopropanol 250.0 505.0 9.79 4.33 0.0014 45.6 9.98 7.07 2.00 isobutanol m 4.45 1.45 3.75 422.6 543.1 39.7 5.22 1.23 0.62 I-pentanol k 1.77 0.070 348.0 429.0 8.45 1.51 8.82 1.20 3.06 1.01 1-hexanol k 325.4 431.0 31.69 29.21 3.70 0.008 10.81 k 1.01 31.72 366.8 449.6 32.58 4.74 1-heptanol 0.006 17.88 1-octanol 1.35 k 293.2 479.0 51.17 5.62 0.007 45.02 27.54 1-nonanol k 1.02 18.70 364.9 486.8 21.53 1.67 0.007 33.21 1-decanol 1.78 k 400.5 528.4 10.58 1.16 0.030 24.22 9.00 cyc1opentano1 2.07 n 346.2 437.5 12.76 0.96 0.060 18.72 4.29 n cyclohexanol 0.034 434.0 456.5 1.89 0.46 17.23 14.17 7.91 0.001 61.0 ethylene glycol 6.82 320.0 635.0 31.38 22.66 32.85 36.71 P 1,3-propylene glycol 54.3 310.0 620.0 26.60 3.67 0.007 28.85 33.83 P diethylene glycol k 0.98 403. 516.0 35.76 7.92 0.010 41.37 49.76 formic acid 17.2 0 300.0 392.7 0.062 8.03 6.52 36.32 1.04 6.48 acetic acid 42.2 1 273.2 573.2 10.03 55.11 6.94 0.005 5.49 8.29 k propionic acid 0.68 329.7 401.5 4.16 0.028 4.39 4.77 3.88 12.37 butyric acid 0 1.01 0.010 293.2 436.4 5.60 6.06 20.16 5.27 18.27 2-methylpropionic acid 0 344.3 445.6 2.57 1.72 0.030 9.59 2.30 10.56 2.23 pentanoic acid 0 1.20 0.030 372.5 465.4 4.73 1.13 5.17 0.99 13.03 methylbutanoic acid 0 0.034 363.9 464.4 1.55 5.40 4.10 4.76 0.60 12.22 benzoic acid 0.53 0.010 405.3 500.2 13.15 12.43 3.62 23.14 j octanoic acid 0 417.2 513.6 11.33 1.04 0.030 19.75 8.59 0.38 'Kleinrahm and Wagner (1986). bKratzke (1980); Carruth and Kobayashi (1973). Wilhoit and Zwolinski (1971). dChirico et al. (1989) eSasse et al. (1988). !Allemand et al. (1985). #Din (1956); Baher et al. (1976). hWeast (1985). 'Ambrose et al. (1974). 'Vargatfik (1975). kBoublik et al. (1973). 'Timmermans (1950). "Kay and Donham (1955). "Ambrose and Ghiassee (1987b). "Ambrose and Giassee (1987a). PStephan and Hildwein (1987).
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2491 a, =
3.758K$'b + In P, K$'b
- In
TRb
(23)
where
Results The reliability of the modified Riedel equation with the K values calculated by using the Table I1 relations was evaluated by predicting the vapor pressures of nearly 50 compounds. The choice hinges, when possible, on recent data which cover a wide experimental range. However, in order to have a comparison based on complex molecules also, experimental data of lower accuracy were considered, at least in some cases. The results obtained are reported in Table 111, along with the experimental range investigated and the literature sources. The critical data were taken mainly from Reid et al. (1987). For some very polar compounds, reliable data for T,and P, are reported by Ambrose and Giassee (Ambrose and Giassee, 1987a,b; Ambrose, 1986) and Anselme and Teja (1988). As a test, the unmodified Riedel and three other wellknown literature equations were chosen: those of Gomez-Thodos, Miller, and Thek-Stiel (Reid et al., 1977). In order to have a fair comparison, the Thek-Stiel equation b data was applied only to compounds for which good m are known. It can be seen from Table I11 that the improvement of the modified Riedel equation over the original one is spectacular in the case of alcohols, with the exception of the very first compounds of this family. However, the improvement is appreciable also in the case of the other compounds examined. Among the reported results, those related to n-eicosane can be questioned since no reliable values are reported for the critical constants of this compound. As a general rule, the modified Riedel equation is better than the other investigated equations in the region of extremely low pressures. Another favorable feature of this equation is the capability of also predicting reliable data for very high molecular weight compounds from Tb and critical constants only. This point is important since the experimental data for this class of compounds are scarce and in some cases inaccurate. Regarding the difficult case of the prediction of vapor pressures for bifunctional alcohols, no definite conclusions can be drawn from the very few cases examined, but the results obtained appear encouraging.
The Riedel Equation as a Correlating Tool The importance of storing in a simple equation the literature experimental data with very little loss of accuracy is widely recognized. Therefore, it is interesting to verify whether the Riedel equation is a candidate for this task. The most obvious modification is to assume a temperature dependence for the K parameter which strongly affects the Riedel equation performances. A very simple rule is represented by the following relation K = d + eTR (25) The d and e parameters can be optimized by correlating the vapor pressure data in the whole experimental range. The results obtained for some well-studied compounds are reported in Table IV. They clearly show that the Riedel equation also in a modified form cannot compete with the Wagner relation when high-standard data are correlated. This conclusion confirms previous inquiries of several authors, notably McGarry (1983) and Wagner (1973).
Table IV. Correlation of the Vapor Pressure Data with the Riedel and the Wagner Equations absolute average error % comDoundsO Riedel Wagner methane 0.12 0.02 0.62 0.73 propane 1.68 n-hexane 0.64 n-decane 0.19 0.17 0.81 0.86 n-dodecane 0.41 n-tetradecane 0.46 2.69 3.16 n-pentadecane 2.48 2.54 n-octadecane 0.34 0.19 n-eicosane ammonia 0.18 0.20 0.01 0.24 water methanol 0.51 1.32 ethanol 0.27 0.50 0.16 cyclohexanol 0.50 Data sources are reported in Table 111.
Therefore, the outstanding success of the Riedel equation is restricted to the prediction of vapor pressures of pure compounds. When the experimental data must be correlated or extrapolated, the Wagner-type relations are much better. Further, it must be stressed that for strongly associated compounds the application of relation 25 gives no improvements over the use of a K constant value. Nomenclature constant defined by eq 6 A , B = constant of eq 1 Al = constant defined by eq 19 b = constant defined by eq 7 B , C = constants of eq 1 B1,C1 = constants of eq 20 Bz, Cz = constants of eq 22 c = constant of eq 4 d, e = constants of eq 25 H = constant defined by eq 21 AH = vaporization enthalpy at T , J mol-' m b = vaporization enthalpy at Tb, J mol-' K = constant defined by eq 12 m = constant of eq 2 n = constant of eq 4 P = vapor pressure, bar P, = critical pressure, bar Q = quantity defined by relation 13 R = universal constant of gases, bar cm3 mol-' K-I T = absolute temperature, K Tb = normal boiling temperature, K T, = critical temperature, K TR = reduced temperature TRb= reduced temperature at the normal boiling temperature V = molar volume, cm3 mol-' AZ = correction for the non-ideal behavior of the vapor phase Greek Letters a, = Riedel parameter, defined by d(ln PR)/d(ln TR)at TR a =
=1
p = angle of the a(TR) vs ac plot y, 6 = constants of eq 2 Literature Cited Allemand, W.; Jose, J.; Merlin, J. C. Measure de Faible Tensions de Vapeur d'Hydrocarbures Lourds. Second CODATA Symposium on Critical Evaluation and Prediction of Phase Equilibria in Multicomponent Systems. International Council for Scientific Unions: Paris, 1985;pp 35-43. Ambrose, D. The Eoaluation of Vapour-Pressure Data; University College: London, 1985. Ambrose, D. The Correlation and Estimation of Vapour Pressures. IV Observations on Wagner's methods of Fitting Equations to
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Znd. Eng. Chem. Res. 1991,30, 2492-2496
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Thermodynamic Model for the Adsorption of Toluene from Supercritical Carbon Dioxide on Activated Carbon Ying Yen Wu, David Shan Hill Wong,* and Chung-Sung Tan Department of Chemical Engineering, National Tsing Hua University, Hsin Chu, Taiwan 30043, Republic of China
A phenomenological thermodynamic model for the adsorption of toluene on activated carbon from supercritical carbon dioxide was developed. Peng-Robinson equation of state and real adsorption solution theory were used to calculate the fugacities of supercritical fluid and adsorbed phase, respectively. Experimental isothermal loading versus pressure data a t different concentrations of toluene were fitted to obtain parameters in the model. It was found that, in order to explain the data of adsorption of toluene, the effect of adsorption of carbon dioxide must be taken into account. Introduction Supercritical fluid (SCF) carbon dioxide is nonflammable, nontoxic, and inexpensive. It has a high masstransfer rate and good extractive power for organic compounds. Model1 et al. (1979), DeFilippi et al. (1980), Kander and Paulaitis (1983), and Tan and Liou (1988, 1989a,b) demonstrated that SCF carbon dioxide could be an efficient solvent for regenerating activated carbon loaded with organic compounds. Tan and Liou (1990a,b) provided extensive equilibria data for the system of toluene adsorbed on activated
* Author to whom correspondence should be addressed.
carbon from SCF carbon dioxide. Isotherms of toluene loading on activated carbon versus toluene concentration in the SCF carbon dioxide at 308,318, and 328 K under the condition of fixed carbon dioxide density were obtained. It was found that the experimental data at different densities could be fitted with the Langmuir expression. The heats of adsorption calculated at these densities were the same. Isotherms of toluene loading versus system pressure at various fixed toluene concentrations in the SCF phase were also reported. The crossover phenomenon was observed. Previously, it was believed that the adsorption of carbon dioxide on the activated carbon could be neglected and carbon dioxide merely acts as a carrier fluid. If this had
0888-5885/91/2630-2492$02.50/00 1991 American Chemical Society
