J. Chem. Eng. Data 1915, 30, 171-173 Vrlens, G. N.; Medcal, E. C. Ind. Eng. Chem. 1958, 40, 1098. EQen, E. 0.;Joffe, J. J. Chem. €ng. Data IW, 11, 480.
E b n , E. 0.;Desal, M. L. J . Chem. €ng. Data 1971, 16, 200. Ramma Rao, M. V.; Subba Reddy, M. V. chem. Eng. World 1978, 13, 79. Ramasubramanlan, J.; Srinlvasan, D. Chem. Eng. Commun. 1083, IS, 335.
Remesubramanlan, J.: Slinkasen, D. “Roceedlngs of the 32nd ana-
171
dlan Chemical Englneerlng Congress. Vancouver, Britlsh Columbia. 0133-6, 1982. (8) Sohoni. V. R.; Wahdpande, U. R. Ind. fng.Chem. 1962, 44, 1428. (9) Othmer, D. F.; Toblas, P. E. Ind. Eng. (2”.1942, 34, 693. (IO) Hand, D. B. J . phys. Chem. 1930, 34, 1961. Received for revlew February 1, 1984. Accepted September 4, 1984.
Vapor-Liquid Equilibria for the System Cyclohexane-fed -Butyl Alcohol Jaime 0. Trlday” and Claudlna Veas Depertamento de Procesos Quimlcos, UnlversMed T&nica Federico Santa Mat&, Valperako 110-V, Chile I8oth.nnal vapor pre88ure data over the whob range d compodtion were obtained for the Mnary systm cycbhexane-terf-butyi alcohol. Data wero taken at t.mp.ratures d 328.2 and 343.3 K by wlng a vapor-rocircuiating equlllbrlm stili. Data were correlated by the Wilson, NRTL, and modified UNIQUAC equaHonr. Th. Wilson equation gives the best flt for the two-parameter “his. The threeparameter NRTL aquatbn gives the best flt for ail the modek considered In this work. Introduction The vapor-liquid equilibria for the system cyciohexanetert-butyl alcohol have been previously investigated (7-6). Most of these studies have been carried out under isobaric condlfJo118 (2-5). Rigogine and Desmyter ( 7 ) have measured this system at 300 K for a range of composition up to 60% of the alcohol mole fraction. Buchowski and Bartel(6) have reported data at 303.15 K over the whole range of composition. The aim of this work was to provide equilibrium data for the binary system cyclohexane-fert-butyl alcohol at 328.2 and 343.3 K. This paper reportstheresuits of these measurements and their correlation by the Wilson, Renon-Prausnitz (NRTL), and modified Abrams-Prausnitz (UNIQUAC) equations. Experimental Sectlon
-.
Cyclohexane and tert-bulyi alcohol were Mer& analytrcal-grade reagents used without any further purification (minimum purltieg of 99.5%). some physical properties of the chemicals are Usted in Table Ialong with literature values. Vapor Pressure M.ssc#ementr. Vapor pressures were measured at constant temperatwe as a functbn of composition by using a vapor-recirculating equilibrium still. The equilibrium stili was a slmpRfied verskn of the one described by Hipkin and Myers (7). Instead of the vapor jacket used in the original deslgn, the contector is self-lagged with its own vapor assuring adiabatic condklons. A schematic view of the apparatus is shown in Figwe 1. The equilikkwn stili was connected through a cold trap to the regulating and measurement pressure d e vices. Pressures were measured by a mercury manometer. Mercury heights were determined with a cathetometer whose accuracy was f0.2 mm. All observed pressures were corrected to give the equivalent height of a mercury column at 273.2 K and standard gravity. Temperatures were measured Address conespondencsto thls author at the Deparbnent of Chemlcal Eng h e f h g , Unlverdty of CaMornia, Davls. CA 85616.
Table I. Physical Prowrties of Chemicals refractive index vapor press./kPa at 298.2 K 328.2 K 343.3 K exptl lit. exptl lit. exptl lit. cyclohexane 1.4235 1.42354O 43.72 43.68‘ 72.44 72.58’ tert-butyl alcohol 1.3860 1.385 2* 30.43 30.73‘ 60.98 60.82‘ (I
Reference 16. * Raference 17. Reference 18.
Table 11. Vapor-Liquid Equilibrium Data for the Binary System Cyclohexane (1)-tert-Butyl Alcohol (2)at 328.2 K
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
30.43 35.32 38.15 41.56 44.00 48.00 50.37 51.96 53.26 54.04 54.26 54.44 54.42 54.13 53.82 51.08 43.72
O.OO0
0.000
0.034 0.069 0.128 0.156 0.231 0.315 0.391 0.471 0.536 0.601 0.679 0.736 0.802 0.835 0.948 1.OOO
0.166 0.253 0.334 0.393 0.474 0.531 0.567 0.609 0.628 0.657 0.683 0.705 0.729 0.738 0.821 1.000
Table 111. Vapor-Liquid Equilibrium Data for the Binary System Cyclohexane (1)-tert-Butyl Alcohol (2)at 343.3 K P/kPa 21 Y1 1 60.98 O.OO0 0.000 65.33 2 0.018 0.073 69.61 3 0.073 0.187 4 74.40 0.111 0.264 5 0.144 79.26 0.329 83.64 6 0.202 0.391 7 0.342 90.89 0.496 0.444 8 93.57 0.523 0.489 93.94 9 0.575 0.504 94.40 10 0.587 11 0.599 95.10 0.628 94.81 12 0.618 0.623 94.96 13 0.643 0.643 14 0.655 94.93 0.630 93.41 15 0.783 0.695 0.941 87.76 16 0.790 17 0.994 77.85 0.924 18 1.OO0 72.44 1.000 with a certified U w ” e t e r (Will Scientific 7 10-5) with a stated accuracy of fO.l K. Compositions of the liquid and condensed vapor were obtained from measurements of their refractive indices at 298.2
QQ21-Q568/85/173O-Q171~Q1.5QlQ 0 1985 Amerlcan Chemical Society
-
172 Journal of Chemlcal and Englneerlng Data, Vol. 30, No. 2, 1985 Thermowell
g E(combinatoriai) RT
x 1 In
-
61
42
x1
x2
’[
- + x 2 in - + -
91x1
in
2
- + qg2In 42 41 81
1
(7)
where the coordination z is set equal to 10 and segment fraction 4 and area fractions 6 and 8‘ are given by
the parameters r , 9 ,and rf are pure-component molecular structure constants depending on the molecular size and the external surface area.
Vapor sample
Heater
rU= exp[-(q Flgure 1. Schematic view of the equillbrlum stlll.
K by using a Abbe-type refractometer with an accuracy of f0.0002. Compositions were estimated to be within f0.005 mole fraction accuracy for the liquid phase and fO.O1O for the vapor phase. Considering the accuracy of the measured variables, the experimental vapor pressures are accurate to better than 0.1 kPa at both temperatures.
Results and Dlwusdon The vapor-liquid equilibrium data for the system cyclohexane-M-butyl alcohol at 328.2 and 343.3 K are reported in Tables I1 and 111, respectively. The experhmntal data were correlated by the Wilson (8), Renon-Prausnitz (9),and modifled Abrams-Prausnftz equations (70, 77). For binary system these models give the following forms for the excess Gibbs energy, gE, Wilson g E / R T = -xl In (xl
+ X ~ A ,-~x)2 In ( x 2 + xlh2,) (1)
where
A,
is the binary energy interaction parameter for the i-j pair: V, is the liquid molar volume of component i.
NRTL
(3) where
gu is the binary energy interaction parameter for the i-) ’ pair: cry is the mixture nonrandomness parameter.
Mdfied UNIQUAC
+ gE(resMuai)
gE= gE(combinatorlai)
(6)
- udr)/RT]
(12)
where uuis the binary energy parameter for the i-j pair. When 9 = 9’,eq 6 reduces to the original UNIQUAC (5). The fugacity coefficients are calculated by the vkial equation of state in terms of pressure, truncated after the second term. Second viriai coefflclents were calculated by using the correlation of Hayden and O’Connell(72). The molar volumes were calculated by using the Rackett equation as modified by Spencer and Danner (73).For the liquid phase the standardstate fugacltles at zero pressure were calculated by the correlation of Prausnltz et al. (74). The computer program developed by Prausnitz et al. (74) was used in the m e l a t k n of the binary vapor-liquid equlllbrlum data. The adjustable binary parameters of the excess Gibbs energy equations were estimated by a nonlinear regression method based on the maximum-likelihood principle (75).The following objective function is minimized: 52
=
q-
( 4 - SI’
1-1
ap2
+-(r,Cr2
+
(x1,
- Rli)2 Ox
+ cvli CY
1
91/Y
(13)
where N is the total experimental points and C’S are the estimated standard deviation for each of the measured variables, Le., pressure, temperature, and liquktphase and vapor-phase compositions. A circumflex denotes the calculated variable. Theestknatedstandarddeviatknsforthe variables were 0.1 kPa for pressure, 0.1 K for temperature, and 0.001 and 0.010 for liquid-phase and vapor-phase compositions. The resulting parameters of the Wilson, NRTL, and modified UNIQUAC equations for the binary system cyclohexane-tertbutyl alcohol are shown in Table IV. Two alternatives were considered for the r w n equation depending ~n whether the alp parameter was fixed or not. As recommended by Renon and Prausnitz (9) the cyl2 parameter was set equal to 0.47 for systems formed by aromatic and alcohols. The compromise between goodness of fit and number of parameters requires some method of discriminating between models. A useful parameter for the comparison is obtained from the sum of the weighted squared residuals (eq 13)d W by the number of Uata points minus the number of degrees of freedom. This quantity is a measure of the overall fit of the equation to the experimental data and it approximates to the overall variance of errors. These estimated variances are also given in Table I V along with the obtained parameters.
Journal of Chemical and Engineering &fa, Vol. 30, No. 2, 1985 173
Table IV. Wilson, NRTL, and UNIQUAC Parameters for the Binary System Cyclohexane (1)-tert-Butyl Alcohol (2) ea Wilson
temp/K 328.2 343.3 NRTL‘ 328.2 343.3 NRTL 328.2 343.3 UNIQUACd 328.2 343.3
(AIz/R)~/ ( A d R ) ’ / K K 1148 f 67 235 f 33 1295 f 69 118 f 28 970 f 55 354 f 31 1095 f 59 240 f 29 1185 f 68 522 f 43 1187 f 65 512 f 56 937 f 41 -193 f 6 1027 f 40 -226 f 6
molecular-interaction area parameter for the pure component i molecular-volume parameter for the pure component i gas constant, J mol-’ K-’ sum of the weighted squared residuals defined by eq
9,’ r/
s2 b
a12
0.40 0.39 0.47 0.49 0.47 0.50 0.71 f 0.02 0.20 0.71 f 0.03 0.23 0.50 0.48
OAij is Xij - Xii for the Wilson equation, gij - gjj for the NRTL equation, and uij - ujj for the UNIQUAC equation. s2 is the estimated variance of the fit. was fixed. d r l = 3.97,q1 = ql’ = 3.01;r2 = 3.45,q2 = 3.05,q i = 0.88.
R S*
13 estimated variance of the fit absolute temperature, K UNIQUAC binary parameter for the i-j pair interaction, J mol-’ liquid moiar volume for the component i,cm3 mor’ liquid mole fraction for the component i vapor mole fraction for the component i coordination number
$2
T UI ”/
xi
Y/ z
Greek Letters
- .I
,
-.I[
0
0 0
- 1
0
,
,
,
,
,
,
,
,
5
1 I
XI
-Ol} O
, o ,
,
,
0
,
0
,
,
I
,
5
1 XI
Figure 2. Residuals for the three-parameter NRTL fit to the VLE data for the system cyclohexane (l)-tert-butyl alcohol (2) at 328.2 K.
The analysis of variances shows that the Wllson equation gives the best flt for twc-parameter models whHe the UNIQUAC and NRTL (al2= 0.47) show a similar flt. The three-perameter w n equation gives the best fit forthe models considered here. An analysis of residuals for the variables (Le., pressure, temperature, vapor and liquid mole fractions) can be used to detect any lack of fit. Figure 2 shows the obtained residuals when the three-parameter NRTL equation was used to correlate the equilibrium data at 328.2 K. A similar behavior was obtained for the data at 343.3 K. Since these pkts show a random distribution of the residuals, the threeparameter NRTL equation was considered suitable to represent the data. Glossary gE g9 GI
N P
Q/
excess Gibbs energy, J mol-’ NRTL binary parameter for the i-/ pair Interaction, J mol-’ defined by eq 5 total experimental points pressure, kPa moleculargeometric area parameter for the pure component i
R y
NRTL nonrandomness parameter Wilson binary parameter for the i-j pair Interaction, J mol-’ defined by eq 2 defined by eq 4 and 12 volume fraction defined by eq 9 area fraction defined by eq 10 area fraction defined by eq 11 estimated standard deviation y No. Cyclohexane, 110-82-7; tert-but) ~lcohol,75-65-0.
LHerature Clted (1) (2) (3) (4) (5) (8) (7) (8) (9) (10) (1 1) (12) (13) (14)
(15) (18) (17) (18)
Prigoglne. I.; Desmyter, A. Trans. Faraday Soc. 1951, 4 7 , 1137-42. Reddy. M. S.; Rao. C. V. Indian J . Technd. 1966, 3. 45-8. Reddy. M. S.; Reo, C. V. Indian J . Techno/. 1967, 5 . 86-8. Renker, W.; Qeiseler, G.; Quitzsch, K. Z.phys. Chem. (Le&@) 1974, 255. 549-57. Trlpethi, R. P.; ekrlula, S.; Gulati, 1. B. J . Chem. Eng. Deta 1976. 21, 44-7. Budrowski, H.; Bartel, L. f d . J . Chem. 1878, 52. 2417-29. Hipkin, H.; Myers, H. S. Ind. Eng. Chem. 1954, 46, 2525-8. Wllson, G. M. J . Am. Chem. Soc. 1964. 86, 127-30. Renon, H.; Prausnitz, J. M. A I M J . 1968, 14, 135-44. Abrams, D. S.; Prasnitz, J. M. A I C M J . 1975, 21, 116-28. Anderson. T. F.; Prausnitz, J.’M. Ind. Eng. Chem. Rocess Des. Dev. i.n..n.., 77.552-80. .. .. k y d e n , J. 0.; O’Connell, J. P. Ind. Eng. Chem. procesS Des. Dev. 1975. 14. 209-16. S p e n k , C. F.; Danner, R. P. J . Chem. Eng. Deta 1872, 17,236-41. Prausnitz,J. M.; Anderson. T. F.; @ens, E. A.; Edtert, C. A.; Hsleh, R.; OConneil, J. P. ”Computer Calculations for Multicomponent VaporLlquld and Llquid-Liquid Equillbrla”; PrenticeHeil: Englewood Cllffs, NJ. 1980. Anderson, T. F.; Abrams, D. S.; Grens, E. A. A I M J . 1976. 24, 20-9. Drelsbach, R. R. “Physical Propertles of Chemical Substances”; Dow Chsmlcai Co.: Midland, MI, 1952. Wiylolt, R. C.; Zwollnskl, B. J. “Physical Thermodynamic Propertles of Allphatlc Alcohols”; Amerlcan Chemical Soclety: Washington, DC, 1973; J. Phys. Chem. Ref. Data, Suppi. 1, Vol. 2. Reld, C. R.; Prausnltz, J. M.; Sherwood, T. K. “The Properties of Gases and Liquids”; McQraw-Hill: New York, 1977.
.
Recelved for review February 3, 1984. Accepted August 22. 1984. Financlal support for thls work was provided by the “Dlreccl6nGeneral Desaarrdlo Cienifflco y Tecnologico”, Unlversldad TBcnica Fededco Santa Marla, Chlb.
