Article pubs.acs.org/jced
Isobaric Vapor−Liquid Equilibrium Data for the Binary Mixtures 2Methyl Propan-2-ol with Tetraethoxysilane and 1-Phenyl Ethanone at 95.5 kPa Mamidipelli Pradeep Kumar, Mamilla Shyamsunder,* Bomma Satish Kumar, and Shuwana Tasleem Chemical Engineering Division, Indian Institute of Chemical Technology, Hyderabad 500007, India ABSTRACT: Isobaric vapor−liquid equilibrium data at an atmospheric pressure of 95.5 kPa are reported for the binary systems 2-methyl propan-2-ol (1) + tetraethoxylsilane (2) and 2-methyl propan-2-ol (1) + 1-phenyl ethanone (2). The experiments are done using a Swietoslawski-type ebulliometer. The liquid-phase mole fraction, x1, versus bubble-point temperature, T, measurements are found to be wellrepresented by the Wilson model. The optimum Wilson parameters are used to calculate the vapor-phase composition, activity coefficients, and excess Gibbs free energy. The results are discussed.
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INTRODUCTION The knowledge of vapor−liquid equilibria (VLE) forms a basis for the design of equipment used for different separation processes, specifically, the distillation operations. 2-Methyl propan-2-ol (CAS. RN: 75-65-0), commonly called tertbutanol, is used in different process industries in different capacities: in the manufacturing of perfumes and a variety of cosmetics, as a raw material in the production of isobutylene, which may be used to produce methyl tertiary butyl ether (a common gasoline additive), or to produce butyl elastomers used in the production of automobile tires. 2-Methyl propan-2ol is also used as a solvent in producing polymers from the hydrolysis of tetraethoxysilane1 (CAS RN: 78-10-4). Tetraethoxysilane is used as a cross-linking reagent in silicone polymers, and 1-phenyl ethanone (CAS RN: 98-86-2) is a typical precursor to various resins and also a raw material in the production of pharmaceuticals. In the present study experiments are carried out to measure the VLE data at a constant pressure of 95.5 kPa (local barometric pressure) for the two binary systems, namely, 2-methyl propan-2-ol (1) + tetraethoxysilane (2) and 2-methyl propan-2-ol (1) + 1-phenyl ethanone (2). The VLE data pertaining to mixtures presented in this paper are not available in the literature published so far.
index, nD. Good agreement was found between the measured values and literature values2 and is shown in Table 1. Table 1. Physical Properties of Pure Chemicals Used ρa/(kg·m−3)
a
component name
exptl
lit.2
exptl
lit.2
2-methyl propan-2-ol retraethoxysilane 1-phenyl ethanone
788.4 935.0 1024.5
788.7 935.60 1023.82
1.3877 1.3835 1.5370
1.3878 1.3832 1.5372
The values are reported at a temperature of 293.15 K.
Apparatus and Experimental Procedure. A Sweitoslawski type ebulliometer, very similar to the one described by Hala et al.,3 was used to carry out the experiments. The schematic is shown in Figure 1. One end of this ebulliometer was kept open to atmosphere to perform the experiments under a constant pressure equal to the atmospheric pressure, measured to be 95.5 kPa. A calibrated mercury thermometer (accurate to ± 0.5 K) and calibrated mercury manometer (accuracy of ± 0.133 kPa) are connected to the ebulliometer to measure the temperature and pressure, respectively. The thermometer bulb is located at the point where this gas−liquid mixture impinges. The thermometer was calibrated by means of pointto-point comparison with a platinum resistance thermometer certified by the National Institute of Standards and Technology (Boulder, CO, USA). The calibration was further confirmed against the triple point of water by using the triple point of water cell. The liquid mixtures for the studies were prepared gravimetrically, with the use of an electronic balance precise to ±
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EXPERIMENTAL SECTION Materials. The reagents 2-methyl propan-2-ol, tetraethoxysilane, and acetophenone (1-phenyl ethanone) are purchased from Sigma-Aldrich Chemicals Pvt. Limited, India. The purities of the reagents is checked by measuring the physical properties, namely, the density and refractive index, and further confirmed by gas chromatography with more than 0.99 mass fraction. Density, ρ, was measured by a DMA-4100 densimeter, with an uncertainty of ± 0.0001 g·cm−3. WZS-I Abbe refractometer (Shanghai Optical Instruments Factory, China) with an uncertainty of ± 0.0001 was used to measure the refractive © 2012 American Chemical Society
nDa
Received: January 23, 2012 Accepted: April 18, 2012 Published: April 26, 2012 1520
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Table 3. Critical Properties of the Pure Liquids9 property
2-methyl propan-2-ol
tetraethoxysilane
1-phenyl ethanone
Tb/K Tc/K Pc/kPa Vc/m3·kmol−1 Zc ω
355.5 506.2 3970 0.275 0.259 0.612
441.10 567.48 1710 0.591 0.214 0.870
475.26 713.00 4030 0.380 0.258 0.361
ln γ1 = −ln(x1 + Λ12x 2) + x 2[{Λ12 /(x1 + Λ12x 2)} − {Λ 21/(x 2 + Λ 21x1)}
(1)
ln γ2 = −ln(x 2 + Λ 21x1) − x1[{Λ12 /(x1 + Λ12x 2)} − {Λ 21/(x 2 + Λ 21x1)}
(2)
where
(4)
(2/7)
/Pc
(5)
ln Vs = ln(RTc/Pc) + [1 + (1 − Tr)(2/7)]ln Z
(6)
The parameter Z has a unique value for each compound, depending on the acentric factor, ω. Z is evaluated using the method proposed by Yamada and Gunn.6 Tc is the critical temperature, Pc is the critical pressure, and Tr is the ratio of boiling temperature to critical temperature. Z = 0.29056 − 0.08775ω
Antoine constants8,9
ϕ=
Bi
Ci
2-methyl propan-2-ola tetraethoxysilaneb 1-phenyl ethanonea
16.8548 16.784 16.2384
2658.29 3942.79 3781.07
−95.50 −53.797 −81.15
(7)
The optimum values for the Wilson parameters are obtained by minimizing the objective function, ϕ using the Nelder−Mead optimization technique described in detail by Kuester and Mize.7 The objective function, ϕ, is defined as
Table 2. Antoine Coefficients A, B, and C for Pure Liquids in Equation 10 Ai
]
Alternatively,
RESULTS AND DISCUSSION The experimental values of bubble temperatures, T and the liquid-phase composition of 2-methyl propan-2-ol, x1, are
component name
V2L
[1 + (1 − Tr) Vs = RTZ c
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Sinnot.
Λ 21 = (V1L /V2 L)exp{−(λ 21 − λ 22)/RT }
and are the pure component molar volumes, and (λ12 − λ11) and (λ21 − λ22) are the Wilson parameters. Each λ represents the energy of interaction between the molecules indicated the corresponding subscripts. The liquid molar volume for each pure species is computed using the modified Rackett equation as given by Spencer and Danner,5 which is written as
0.0001 g. The desired amount of the two components were weighed and stirred well before charging into the ebulliometer. The flow rate of cold water was adjusted to yield a desired drop rate at about 30 per minute in accordance with the suggestion of Hala et al.3 The equilibrium temperature was recorded after steady state conditions were judged by the constant temperature and uniform drop rate of at least 30 per minute. The samples were taken after waiting for approximately for 30 min to ensure completed VLE. The equilibrium temperature (T) was noted down, and the samples were withdrawn from the liquid and condensate and analyzed using Agilent GC analyzer, model 7890A, equipped with a TC detector.
8 b
(3)
V1L
Figure 1. Schematic diagram of ebulliometer: (a) boiler; (b) Cottrell tube; (c) drop counter; (d) thermowell; (e) condenser; (f) feed inlet and connection manostat; (g) heater; (h) themometer.
a
Λ12 = (V2 L /V1L)exp{−(λ12 − λ11)/RT }
∑ [(Pcal/Pexptl) − 1]2
(8)
The excess Gibbs free energy is evaluated using the following Wilson relation4 g E /RT = −x1 ln(x1 + Λ12x 2) − x 2 ln(x 2 + Λ 21x1)
9
Huang et al.
(9)
In the above equation the excess Gibbs energy is defined with reference to an ideal solution in the sense of Raoult's law; eq 7 obeys the boundary condition that gE vanishes as either x1 or x2 becomes zero. The saturated vapor pressures are calculated using Antoine's equation given as
tabulated along with the experimental and calculated values of the vapor-phase mole fraction of 2-methyl propan-2-ol, y1, the liquid phase activity coefficients γ1 and γ2, and the excess Gibbs free energy, gE. These results are shown in Tables 4 and 5. Wilson4 equations are used for the calculation of the activity coefficients and the Gibbs energy. The equations are summarized below for quick reference.
ln(Pi sat /mmHg) = Ai − Bi /[(T /K) + Ci]
(10)
The Antoine constants (A, B, C) are obtained from literature8,9 and are given in Table 2. 1521
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Table 4. Experimental VLE Data and Calculated Results for the Binary System 2-Methyl Propan-2-ol (1) + Tetraethoxysilane (2) at 95.5 kPaa calculated by Wilson
a
gE
calculated by UNIFAC
T/K
x1
y1
γ1
γ2
y1
γ1
γ2
y1
kJ·kmol−1
439.35 390.15 377.15 372.65 371.15 370.15 369.65 368.65 367.65 367.15 366.65 364.65 363.15 362.15 361.15 360.15 359.15 357.65 356.65 353.61
0.000 0.136 0.239 0.321 0.386 0.440 0.486 0.524 0.557 0.586 0.611 0.680 0.727 0.752 0.780 0.809 0.842 0.876 0.914 1.0000
0.000 0.726 0.853 0.896 0.919 0.935 0.943 0.951 0.956 0.960 0.964 0.972 0.977 0.980 0.982 0.985 0.987 0.990 0.993 1
1.0007 1.0600 1.0738 1.0751 1.0725 1.0690 1.0650 1.0616 1.0583 1.0548 1.0517 1.0423 1.0352 1.0313 1.0267 1.0220 1.0167 1.0115 1.0062 1.0000
1.0000 0.9998 1.0003 1.0018 1.0040 1.0070 1.0107 1.0150 1.0197 1.0247 1.0299 1.0498 1.0694 1.0828 1.1004 1.1223 1.1528 1.1934 1.2504 1.4653
0.0000 0.7273 0.8505 0.8972 0.9208 0.9355 0.9455 0.9527 0.9582 0.9625 0.9658 0.9740 0.9788 0.9811 0.9835 0.9859 0.9884 0.9910 0.9937 1.0000
1.2821 1.2681 1.2682 1.2400 1.2316 1.2015 1.1873 1.1653 1.1519 1.1408 1.1296 1.0977 1.0773 1.0660 1.0558 1.0436 1.0309 1.0217 1.0096 1.0000
1.0000 1.0005 1.0043 1.0148 1.0197 1.0401 1.0499 1.0709 1.0873 1.1032 1.1194 1.1832 1.2409 1.2821 1.3252 1.3915 1.4733 1.5685 1.7379 1.9710
0.0000 0.7612 0.8700 0.9086 0.9293 0.9404 0.9490 0.9544 0.9590 0.9626 0.9655 0.9723 0.9764 0.9784 0.9807 0.9829 0.9855 0.9883 0.9913 1.0000
0.00 25.05 54.00 75.75 90.92 102.41 110.88 117.64 122.88 126.36 128.80 132.51 131.22 129.08 124.99 118.72 108.65 94.86 73.84 0.00
Wilson parameters: [(λ12 − λ11)/R] = 177.77; [(λ12 − λ11)/R] = 33.101; standard deviation = 0.18 K.
Table 5. Experimental VLE Data and Calculated Results for the Binary System 2-Methyl Propan-2-ol (1) + 1-Phenyl Ethanone (2) at 95.5 kPaa calculated by Wilson
a
gE
calculated by UNIFAC
T/K
x1
y1
γ1
γ2
y1
γ1
γ2
y1
kJ·kmol−1
472.25 403.15 386.65 377.65 370.65 368.65 367.15 365.65 364.65 363.65 362.15 361.15 359.65 358.15 356.15 354.65 354.65
0.000 0.141 0.247 0.330 0.397 0.451 0.497 0.535 0.568 0.613 0.655 0.703 0.760 0.826 0.904 0.966 1.0000
0.000 0.887 0.947 0.961 0.974 0.979 0.983 0.985 0.987 0.989 0.991 0.993 0.995 0.996 0.998 0.999 1
1.1938 1.2608 1.2470 1.2247 1.2033 1.1811 1.1618 1.1459 1.1319 1.1128 1.0955 1.0762 1.0546 1.0322 1.0114 1.0016 1.0000
1.0000 1.0028 1.0111 1.0235 1.0392 1.0554 1.0729 1.0907 1.1087 1.1378 1.1716 1.2187 1.2916 1.4072 1.6135 1.8673 2.0569
0.0000 0.8947 0.9506 0.9683 0.9769 0.9811 0.9840 0.9860 0.9875 0.9893 0.9908 0.9922 0.9938 0.9955 0.9974 0.9990 1.0000
2.3624 2.2185 1.9440 1.7445 1.6013 1.4980 1.4186 1.3587 1.3107 1.2511 1.2014 1.1513 1.1010 1.0548 1.0176 1.0023 1.0000
1.0000 1.0167 1.0564 1.1083 1.1673 1.2285 1.2924 1.3551 1.4179 1.5186 1.6314 1.7882 2.0247 2.3933 3.0306 3.7894 4.3523
0.0000 0.9365 0.9664 0.9757 0.9804 0.9827 0.9842 0.9854 0.9862 0.9873 0.9883 0.9894 0.9907 0.9925 0.9951 0.9980 1.0000
0.00 117.50 201.88 258.91 297.85 320.87 335.54 344.13 348.39 349.05 344.45 331.35 304.43 254.98 166.37 67.27 0.00
Wilson parameters: [(λ12 − λ11)/R] = 231.95; [(λ12 − λ11)/R] = 43.17; standard deviation = 0.34 K.
The critical input data corresponding to the pure components required in the computations are taken from Reid et al.10 and are presented in Table 3. The activity coefficient values, thus calculated, are then used to find the corresponding vapor phase mole fraction, yi, from the relation ϕiyP = γixiPi i exptl
sat
At low pressures, vapor phases usually approximate ideal gases, for which ϕ̂ i = ϕi = 1, and the pointing factor also becomes equal to 1. Thus, the vapor-phase fugacity coefficient, ϕi, equals approximately 1. Therefore, for low pressure VLE data eq 11 reduces to yP = γixiPi sat i exptl
(11)
The results obtained and shown in Tables 4 and 5 indicate that the binary systems under study deviate very marginally from ideality. Therefore a comparison is made for the values of vapor-phase composition calculated using Wilson's model with
where ϕi = (ϕî/ϕi s)exp[−Vi L(Pexptl − Pi sat)/RT ]
(13)
(12) 1522
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Figure 6. Plot of ln(γ1/γ2) vs x1 of 2-methyl propan-2-ol (1) + tetraethoxysilane (2).
Figure 2. Equilibrium diagram for the binary system 2-methyl propan2-ol (1) + tetraethoxysilane (2). ×, experimental; −·−, Wilson equation; , Raoult's law; ---, UNIFAC.
Figure 7. Plot of ln(γ1/γ2) vs x1 of 2-methyl propan-2-ol (1) + 1phenyl ethanone (2). Figure 3. Equilibrium diagram for the binary system 2-methyl propan2-ol (1) + 1-phenyl ethanone (2). ×, experimental; −·−, Wilson equation; , Raoult's law; ---, UNIFAC.
Table 6. Result of Herington's Thermodynamic Consistency Test system 1. 2-methyl propan-2-ol (1) + tetraethoxysilane (2) 2. 2-methylpropan-2-ol (1) + 1-phenyl ethanone (2)
Herington's test11 |D − J| 9.05 8.83
propan-2-ol (1) + 1-phenyl ethanone (2), respectively. Figures 4 and 5 show the T−x1−y1 diagrams. The data are checked for thermodynamic consistency using the Herington test;11 the results are shown in Figures 6 and 7, and a summary is given in Table 6. The data are found to be thermodynamically consistent.
Figure 4. T−x1−y1 diagram for 2-methyl propan-2-ol (1) + tetraethoxysilane (2). ●, measured T−x1 data; ◆, measured T−y1 data; −−, T−y1 computed from the Wilson model.
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CONCLUSIONS Phase equilibria in the binary mixtures of 2-methyl propan-2-ol (1) + tetraethoxylsilane (2) and 2-methyl propan-2-ol (1) + 1phenyl ethanone (2) have been investigated. The observed values of the liquid-phase mole fraction versus bubble point on all of the mixtures investigated could be well-represented by the Wilson model. The UNIFAC model tends to overestimate the activity coefficients for the systems presented here. None of the systems investigated formed an azeotrope. The experimental data presented are expected to be useful for design purposes.
Figure 5. T−x1−y1 plot for 2-methyl propan-2-ol (1) + 1-phenyl ethanone (2). ●, measured T−x1 data; ◆, measured T−y1 data; −−, T−y1 computed from the Wilson model.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected].
the values calculated using Raoult's law. A comparison with the predictive universal functional activity coefficient (UNIFAC) model is also done and tabulated in Tables 4 and 5. The equilibrium data are shown graphically in Figures 2 to 5. Figures 2 and 3 show the plot of the equilibrium vapor-phase composition versus liquid-phase composition for the systems 2methyl propan-2-ol (1) + tetraethoxylsilane (2) and 2-methyl
Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Peace, B. W.; Mayhan, K. G.; Montle, J. F. Polymers from Hydrolysis of Tetraethoxysilane. Polymer 1973, 14 (9), 420−422.
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(2) Weast, R. C.; Astle, M. J. CRC Handbook of Data on Organic Compounds; CRC Press: Boca Raton, FL, 1985. (3) Hala, E. Vapor-Liquid Equilibrium; Pergamon Press: Elmsford, NY, 1958. (4) Wilson, G. Vapor-liquid equilibrium. XI. A New Expression for the Excess Gibbs Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127− 130. (5) Spencer, C. F.; Danner, R. P. Improved Equation of Saturated Liquid Density. J. Chem. Eng. Data 1972, 17, 236. (6) Yamada, T.; Gunn, R. D. Saturated Liquid Molar Volumes. The Rackett equation. J. Chem. Eng. Data 1973, 18 (2), 234. (7) Kuester, R. T.; Mize, J. H. Optimization Techniques with Fortran; McGraw-Hill: New York, 1973. (8) Sinnot, R. K. Coulson and Richardson's Chemical Engineering Series, Vol. 6, 3rd ed.; Butterworth-Heinemann: Woburn, MA, 2001. (9) Huang, J.; Lee, Y.; Lee, L. Vapor Liquid Equilibrium Measurements for Tetraethysilicate + Ethanol at 24.00 and 53.32 kPa. J. Chem. Eng. Data 2004, 49, 1175−1179. (10) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977. (11) Wisniak, J. The Herington Test for Thermodynamic Consistency. Ind. Eng. Chem. Res. 1994, 33 (1), 177−180.
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