Article pubs.acs.org/jced
Isobaric Vapor−Liquid Equilibrium Data for Binary Mixtures of 1‑Phenylethanone with a Few Alcohols at 95.2 kPa Mamidipelli Pradeep Kumar,* G. Rakesh Kumar, and Shuwana Tasleem Energy and Chemical Engineering Division, Indian Institute of Chemical Technology, Hyderabad − 500007, India ABSTRACT: Bubble point temperatures at atmospheric pressure of 95.2 kPa are measured for the binary systems propan-1-ol (1) + 1-phenylethanone (2), propan-2-ol (1) + 1phenylethanone (2), 2-methyl-1-propanol (1) + 1-phenylethanone (2), and 2-butanol (1) + 1-phenylethanone (2) using a Swietoslawski-type ebulliometer. The liquid-phase mole fraction, x1, versus bubble point temperature, T, measurements are found to be well represented by the Wilson model. The optimum Wilson parameters are used to calculate the vapor-phase composition, activity coefficients, and excess Gibbs free energy and the results compared with the values of activity coefficients of the mixtures calculated using the UNIFAC group contribution method. The results are discussed.
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between the measured values and the literature5 and is shown in Table 1.
INTRODUCTION Propan-1-ol (CAS RN: 71-23-8), propan-2-ol (CAS RN: 67-630), 2-methyl-1-propanol (CAS RN: 78-83-1), and 2-butanol (CAS RN: 78-92-2) are used as solvent in the pharmaceutical industry1 and for resins and cellulose esters, whereas 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.2,3 The separation of mixtures of these compounds is usually carried out using distillation operation, which requires the vapor−liquid equilibrium data. The vapor− liquid equilibrium (VLE) data pertaining to binary mixtures of these compounds are not available in the literature published so far except for 2-butanol (1) + 1-phenylethanone (2). Therfore, a study was taken up to experimentally determine the VLE data for the binary systems comprising propan-1-ol (1) + 1phenylethanone (2), propan-2-ol (1) + 1-phenylethanone (2), 2-methyl-1-propanol (1) + 1-phenylethanone (2), and 2butanol (1) + 1-phenylethanone (2). A comparison is made for the 2-butanol (1) + 1-phenylethanone (2) system with the available literature.4
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Table 1. Comparison of Experimental Density and Refractive Index with the Literature Data5 ρ (kg·m−3)a,b component name
exptl
lit.4
exptl
lit.4
propan-1-ol propan-2-ol 2-methyl-1-propanol 2-butanol 1-phenylethanone
802.8 786.0 801.3 806.2 1028.2
803.5 785.5 801.8 806.3 1028.1
1.3854 1.3788 1.3926 1.3985 1.5370
1.3850 1.3776 1.3955 1.3978 1.5372
a
The experimental measurements for density and also refractive index are done at 293.15 K. bu(ρ) = ± 0.0001 g·cm−3; u(nD) = ± 0.0001.
Apparatus and Experimental Procedure. A Sweitoslawski-type ebulliometer, very similar to the one described by Hala et al.,6 was used to carry out the experiments. The experimental setup and the procedure are explained in detail in our previous publication.7
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EXPERIMENTAL SECTION
RESULTS AND DISCUSSION Wilson’s equation,8 based on molecular considerations and the UNIFAC9 group contribution method, was used for calculation of liquid-phase activity coefficients. The vapor-phase nonideality is assumed to be negligible as the experiments are performed at a local atmospheric pressure of 95.2 kPa. At such low pressure, the nonidealities in the vapor phase can be safely neglected.
Materials. The reagents propan-1-ol, propan-2-ol, 2-methyl1-propanol, 2-butanol, and acetophenone (1-phenyl ethanone) were purchased from Sigma-Aldrich Chemicals Pvt. Limited, India. The purities of the reagents were checked by gas chromatography and confirmed to be more than 0.99 mass fraction. The physical properties, viz., density and refractive index, were measured at 293.15 K. Density, ρ, was measured by a DMA-4100 densimeter, with an accuracy of ± 0.0001 g·cm−3. The WZS-I Abbe refractometer (Shanghai Optical Instruments Factory, China) with an uncertainty of ± 0.0001 was used to measure the refractive index, nD. Good agreement was found © 2012 American Chemical Society
nDa,b
Received: July 2, 2012 Accepted: August 27, 2012 Published: September 6, 2012 2832
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The equations involved and the calculation strategy using Wilson’s method have been explained in an earlier publication7of the authors. According to Wilson’s8 model, the activity coefficients are given as
li = (z /2) ·(ri − qi) − (ri − 1)
(1)
Table 2. UNIFAC Group Specifications9
(2)
group numbers
where
main
Λ12 = (V2 L /V1L)exp{−(λ12 − λ11)/RT }
(3)
Λ 21 = (V1L /V2 L)exp{−(λ 21 − λ 22)/RT }
(4)
1 1 1 3 3 5 9
V1 and V2 are the pure component molar volumes, and (λ12 − λ11) and (λ21 − λ22) are the Wilson’s parameters. Each λ represents the energy of interaction between the molecules indicated by the corresponding subscripts. The liquid molar volume for each pure species is computed using the modified Rackett equation as given by Spencer and Danner.10 The Nelder−Mead optimization technique described in detail by Kuester and Mize11 is used for the determination of the optimum values for the Wilson’s parameters which are obtained by minimizing the objective function, defined as L
ϕ=
(16)
Rk and Qk are the group parameters available in the literature.9 The group interaction parameters amn are evaluated from experimental phase equilibrium data, and for many groups the values of these parameters are calculated and listed.9 All the parameters (Rk, Qk, and amn) corresponding to the systems under study are given in Table 2.
ln γ2 = −ln(x 2 + Λ 21x1) − x1[{Λ12 /(x1 + Λ12x 2)} − {Λ 21/(x 2 + Λ 21x1)}]
(15)
Ψmn = exp( −amn /T )
ln γ1 = −ln(x1 + Λ12x 2) + x 2[{Λ12 /(x1 + Λ12x 2)} − {Λ 21/(x 2 + Λ 21x1)}]
z = 10
L
∑ [(Pcal/Pexptl) − 1]2
(6)
5
9
61.13 0 89.60 140.10
986.5 636.1 0 164.5
476.4 25.77 84.00 0
(17)
Table 3. Antoine Coefficients A, B, and C for Pure Liquids in Equation 17 Antoine constants12
(7)
component name
Ai
Bi
Ci
propan-1-ol propan-2-ol 2-methyl-1-propanol 2-butanol 1-phenylethanone
17.5439 18.6929 16.8712 17.2102 16.2384
3166.38 3640.20 2874.73 3026.03 3781.07
−80.15 −53.54 −100.3 −86.65 −81.15
(8)
The critical input data corresponding to the components are used to estimate the pure component molar volumes required in the computations in Wilson’s7 equations. The data are taken from Sinnot et al.12 and are presented in Table 4. Tables 5, 6, 7, and 8 give the experimental values of the bubble point, T, liquid-phase mole fraction, x1, vapor-phase mole fraction, y1, and the calculated values of liquid-phase activity coefficients, γ1, γ2, calculated vapor-phase mole fractions, y1c, and the excess Gibbs free energy, gE. The values of activity coefficients computed using the Wilson Method show marginal deviation from ideality for all the systems studied, whereas the values of activity coefficients computed using the UNIFAC method indicate slight excess variations. The vapor-phase nonideality is assumed to be negligible as the
(9)
ln Γk = Q k[1 − ln(Σm(θm Ψmk)) − Σm{θm Ψkm/(Σn(θn Ψnm))}]
3
0 −11.12 156.40 26.76
The Antoine constants (A, B, C) are obtained from Sinnot et al.12 and are listed in Table 3.
ln γi C = ln(Φi /xi) + (z /2)·qi · ln(θi/Φi) + li
ln γi R = Σk[νk(ln Γk − ln Γk(i))]
n=1
ln(Pi sat /mmHg) = Ai − Bi /[(T /K + Ci]
where
− (Φi /xi) ·Σj(xjl j)
surface area Qk
The saturated vapor pressures of the components are calculated using the Antoineequation given as
(5)
The UNIFAC group contribution method is based on the assumption that the activity coefficient for a component is the sum of the contributions made by the molecule’s functional groups. In a binary mixture, the UNIFAC equation for the activity coefficient of component i is
ln γi = ln γi C + ln γi R
volume Rk
name
1 CH3 0.9011 0.848 2 CH2 0.6744 0.540 3 CH 0.4469 0.228 9 ACH 0.5313 0.400 10 AC 0.3652 0.120 14 OH 1.0000 1.200 18 CH3CO 1.6724 1.488 UNIFAC group−group interaction parameter, amn in Kelvin
m=1 3 5 9
The activity coefficient values, thus calculated, are then used to find the corresponding vapor-phase mole fraction, yi, from the relation yP = γixiPi sat i exptl
secondary
(10)
θi = qixi /Σj(qjxj)
(11)
Φi = rx i i / Σj(rjxj)
(12)
ri = Σk(νk(i)R k)
(13)
qi = Σk(νk(i)Q k)
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Table 4. Critical Properties of the Pure Liquids12 property
propan-1-ol
propan-2-ol
2-methyl-1-propanol
2-butanol
1-phenylethanone
Tb/K Tc/K Pc/kPa Vc/m3·kmol−1 Zc ω
370.3 536.8 5168 0.219 0.253 0.626
355.4 508.3 4762 0.220 0.248 -
381.0 547.7 4296 0.273 0.257 0.588
372.7 536.0 4195 0.268 0.252 0.576
475.0 701.0 3850 0.376 0.250 0.420
Table 5. Experimental VLE Data for Temperature T, Pressure p = 95.2 kPa, Liquid-Phase Mole Fraction x, and Vapor-Phase Mole Fraction y and Calculated Activity Coefficients γ, Vapor-Phase Mole Fraction yc, and Excess Gibbs Free Energy gE for the Binary System Propan-1-ol (1) + 1-Phenylethanone (2)a,b calculated by Wilson
gE
calculated by UNIFAC
T/K
x1
y1
γ1
γ2
y1c
γ1
γ2
y1c
kJ·kmol−1
472.25 413.15 400.65 392.15 388.15 385.15 383.15 382.15 380.15 379.15 377.15 376.15 374.15 369.65 369.15 368.65
0.000 0.147 0.257 0.341 0.409 0.464 0.509 0.547 0.609 0.655 0.708 0.746 0.776 0.933 0.950 1.0000
0.000 0.856 0.924 0.933 0.961 0.967 0.977 0.981 0.983 0.986 0.988 0.990 0.992 0.995 0.998 1
1.349 1.332 1.274 1.229 1.192 1.164 1.141 1.122 1.095 1.076 1.057 1.044 1.035 1.004 1.002 1.000
1.000 1.006 1.021 1.040 1.061 1.084 1.106 1.127 1.168 1.205 1.255 1.298 1.336 1.618 1.662 1.801
0.000 0.847 0.918 0.944 0.956 0.964 0.969 0.973 0.978 0.981 0.984 0.986 0.988 0.996 0.997 1.000
2.500 2.022 1.805 1.655 1.531 1.445 1.382 1.332 1.252 1.199 1.149 1.115 1.091 1.009 1.006 1.000
1.000 1.015 1.050 1.097 1.152 1.211 1.266 1.320 1.441 1.555 1.715 1.859 1.997 3.242 3.465 4.000
0.000 0.893 0.939 0.956 0.963 0.968 0.971 0.973 0.976 0.978 0.980 0.982 0.983 0.993 0.994 1.000
0.00 162.20 258.02 313.90 345.72 362.92 370.82 372.70 366.52 353.64 330.58 307.26 285.65 110.23 83.82 0.00
Wilson parameters: [(λ12 − λ11)/R] = 183.44; [(λ12 − λ11)/R] = 34.147; standard deviation = 0.22 K. bu(T) = 0.5 K, u(p) = ± 0.133 kPa, and u(x1) = u(y1) = 0.005. a
Table 6. Experimental VLE Data for Temperature T, Pressure p = 95.2 kPa, Liquid-Phase Mole Fraction x, and Vapor-Phase Mole Fraction y and Calculated Activity Coefficients γ, Vapor-Phase Mole Fraction yc, and Excess Gibbs Free Energy gE for the Binary System Propan-2-ol (1) + 1-Phenylethanone (2)a,b calculated by Wilson
gE
calculated by UNIFAC
T/K
x1
y1
γ1
γ2
y1c
γ1
γ2
y1c
kJ·kmol−1
472.25 412.15 391.65 383.65 378.65 375.15 371.15 369.15 367.15 366.15 364.15 363.15 360.65 356.65 353.84
0.000 0.145 0.253 0.336 0.403 0.458 0.503 0.542 0.575 0.603 0.650 0.717 0.809 0.931 1.0000
0.000 0.877 0.948 0.962 0.971 0.976 0.983 0.986 0.987 0.988 0.990 0.994 0.996 0.999 1
1.098 1.109 1.100 1.088 1.077 1.067 1.060 1.053 1.047 1.042 1.035 1.024 1.012 1.002 1.000
1.000 1.002 1.007 1.013 1.021 1.029 1.038 1.046 1.054 1.062 1.076 1.101 1.146 1.233 1.303
0.000 0.886 0.946 0.965 0.974 0.979 0.983 0.986 0.987 0.989 0.991 0.993 0.996 0.999 1.000
2.215 2.019 1.834 1.667 1.561 1.470 1.403 1.347 1.304 1.270 1.213 1.146 1.071 1.012 1.000
1.000 1.015 1.048 1.098 1.147 1.205 1.267 1.326 1.385 1.443 1.563 1.773 2.212 3.295 4.543
0.000 0.933 0.966 0.975 0.980 0.983 0.984 0.986 0.987 0.988 0.989 0.990 0.992 0.996 1.000
0.00 56.53 94.74 118.22 132.66 141.28 146.42 148.60 149.15 148.34 144.75 133.74 107.44 47.88 0.00
Wilson parameters: [(λ12 − λ11)/R] = 99.237; [(λ12 − λ11)/R] = 8.65; standard deviation = 0.21 K. bu(T) = 0.5 K, u(p) = ± 0.133 kPa, and u(x1) = u(y1) = 0.005. a
plotted against the liquid-phase mole fraction, x1, for the systems propan-1-ol (1) + 1-phenylethanone (2), propan-2-ol (1) + 1-phenylethanone (2), 2-methyl-1-propanol (1) + 1phenylethanone (2), and 2-butanol (1) + 1-phenylethanone
experiments are performed at a local atmospheric pressure of 95.2 kPa; at such low pressures, the vapor behaves ideally. The results are presented graphically in Figures 1 to 8. Figures 1 to 4 show the equilibrium vapor composition, y1, 2834
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Table 7. Experimental VLE Data for Temperature T, Pressure p = 95.2 kPa, Liquid-Phase Mole Fraction x, and Vapor-Phase Mole Fraction y and Calculated Activity Coefficients γ, Vapor-Phase Mole Fraction yc, and Excess Gibbs Free Energy gE for the Binary System 2-Methyl-1-propanol (1) + 1-Phenylethanone (2)a,b calculated by Wilson
gE
calculated by UNIFAC
T/K
x1
y1
γ1
γ2
y1c
γ1
γ2
y1c
kJ·kmol−1
472.25 403.15 399.306 394.15 391.15 389.15 388.65 388.15 387.15 386.15 385.15 384.65 384.15 383.65 382.65 380.65 379.65
0.000 0.296 0.354 0.456 0.557 0.627 0.677 0.716 0.746 0.771 0.791 0.808 0.822 0.855 0.894 0.955 1.000
0.000 0.881 0.921 0.948 0.953 0.964 0.971 0.972 0.977 0.978 0.982 0.984 0.985 0.988 0.990 0.993 1.000
1.635 1.368 1.311 1.223 1.149 1.107 1.081 1.064 1.051 1.042 1.035 1.030 1.026 1.018 1.010 1.002 1.000
1.000 1.049 1.073 1.129 1.206 1.275 1.334 1.386 1.433 1.474 1.510 1.543 1.571 1.641 1.735 1.912 2.070
0.000 0.907 0.924 0.945 0.958 0.966 0.970 0.974 0.977 0.979 0.981 0.982 0.984 0.986 0.990 0.996 1.000
2.201 1.673 1.566 1.410 1.280 1.202 1.156 1.120 1.097 1.081 1.067 1.058 1.050 1.034 1.020 1.005 1.000
1.000 1.072 1.187 1.201 1.332 1.464 1.577 1.701 1.801 1.895 1.984 2.050 2.130 2.310 2.549 3.022 3.666
0.000 0.921 0.930 0.949 0.958 0.964 0.967 0.970 0.972 0.974 0.976 0.977 0.978 0.981 0.985 0.993 1.000
0.00 422.78 468.58 515.95 521.33 500.05 471.37 441.77 413.63 387.49 364.30 343.13 323.99 276.92 213.72 98.77 0.00
Wilson parameters: [(λ12 − λ11)/R] = 200.6; [(λ12 − λ11)/R] = 82.72; standard deviation = 0.16 K. bu(T) = 0.5 K, u(p) = ± 0.133 kPa, and u(x1) = u(y1) = 0.005. a
Table 8. Experimental VLE Data for Temperature T, Pressure p = 95.2 kPa, Liquid-Phase Mole Fraction x, and Vapor-Phase Mole Fraction y and Calculated Activity Coefficients γ, Vapor-Phase Mole Fraction yc, and Excess Gibbs Free Energy gE for the Binary System 2-Butanol (1) + 1-Phenylethanone (2)a,b calculated by Wilson
gE
calculated by UNIFAC
T/K
x1
y1
γ1
γ2
y1c
γ1
γ2
y1c
kJ·kmol−1
472.25 412.15 399.15 393.15 388.15 384.65 381.65 379.65 377.65 376.15 375.15 374.65 374.15 373.65 373.15 372.15 371.65 371.15 370.95
0.000 0.145 0.253 0.336 0.403 0.458 0.503 0.542 0.575 0.603 0.628 0.650 0.670 0.703 0.7417 0.8085 0.8941 0.9311 1.0000
0.000 0.855 0.914 0.948 0.953 0.965 0.966 0.970 0.972 0.976 0.977 0.981 0.984 0.990 0.992 0.995 0.996 0.997 1.000
1.638 1.537 1.413 1.325 1.263 1.217 1.183 1.156 1.135 1.118 1.103 1.092 1.082 1.067 1.050 1.028 1.009 1.004 1.000
1.000 1.011 1.037 1.068 1.102 1.136 1.169 1.201 1.231 1.260 1.287 1.313 1.336 1.380 1.436 1.549 1.728 1.822 2.025
0.000 0.851 0.917 0.940 0.952 0.960 0.965 0.969 0.972 0.974 0.976 0.978 0.979 0.981 0.984 0.988 0.993 0.995 1.000
2.214 1.995 1.770 1.615 1.505 1.423 1.359 1.306 1.271 1.237 1.212 1.186 1.168 1.138 1.104 1.061 1.018 1.008 1.000
1.000 1.015 1.051 1.098 1.150 1.205 1.261 1.322 1.373 1.431 1.484 1.537 1.588 1.682 1.823 2.100 2.670 2.963 3.765
0.000 0.880 0.932 0.949 0.958 0.964 0.967 0.970 0.972 0.974 0.975 0.976 0.977 0.979 0.980 0.984 0.989 0.993 1.000
0.00 245.64 379.12 451.81 490.06 508.05 513.77 512.02 505.65 496.49 485.73 474.08 462.02 437.77 403.29 328.47 203.08 138.27 0.00
a Wilson parameters: [(λ12 − λ11)/R] = 229.23; [(λ12 − λ11)/R] = 44.55; standard deviation = 0.11 K. bu(T) = 0.5 K, u(p) = ± 0.133 kPa, and u(x1) = u(y1) = 0.005.
(2), respectively. The corresponding T−x1−y1 plots are shown in Figures 5 to 8. The comparison of the VLE data for the system 2-butanol (1) + 1-phenylethanone (2) with the available literature4 is also shown in Figure 8. The comparative study shows a small variation in the data which might be a result of the difference in the pressure conditions. The earlier published4 data are reported at 101.3 kPa (1 atm), whereas the present paper reports the VLE data at a local atmospheric pressure of 95.2 kPa.
The results shown in Tables 5 to 8 and Figures 1 to 8 indicate that the Wilson model adequately represents the phase equilibrium data studied in the present work. Further, the data were tested for thermodynamic consistency using Herrington’s area test.13 The empirical criteria as modified by Wisnaik13 requires a value for two parameters for the test. The said parameters are given as follows. D = 100 × |(A − B)| /|(A + B)| 2835
(18)
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Figure 1. Equilibrium diagram for the binary system propan-1-ol (1) + 1-phenylethanone (2) at 95.2 kPa.
Figure 5. T−x1−y1 diagram for propan-1-ol (1) + 1-phenylethanone (2) at 95.2 kPa.
Figure 2. Equilibrium diagram for the binary system propan-2-ol (1) + 1-phenylethanone (2) at 95.2 kPa. Figure 6. T−x1−y1 diagram for propan-2-ol (1) + 1-phenylethanone (2) at 95.2 kPa.
Figure 3. Equilibrium diagram for the binary system 2-methyl propan1-ol (1) +1 phenylethanone (2).
Figure 7. T−x1−y1 diagram for 2-methyl propan-1-ol (1) + 1phenylethanone (2) at 95.2 kPa.
Figure 4. Equilibrium diagram for the binary system 2-butanol (1) + 1-phenylethanone (2) at 95.2 kPa.
J = 150 × |ΔTmax /Tmin|
(19)
where A is the area above the zero line on the plot of ln(γ1/γ2) against x1 and B is the area below the zero line; ΔTmax is the maximum difference in the boiling temperatures of the mixture; and Tmin is the boiling temperature of the more volatile component. According to Wisniak,13 for isobaric data sets, the test criteria for passing is |D − J| < 10. The result of the test proves the data to be thermodynamically consistent. The results are presented in Table 9.
Figure 8. T−x1−y1 diagram for 2-butanol (1) + 1-phenylethanone (2) at 95.2 kPa.
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CONCLUSIONS Phase equilibria in the binary mixtures of propan-1-ol (1) + 1phenylethanone (2), propan-2-ol (1) + 1-phenylethanone (2), 2-methyl-1-propanol (1) + 1-phenylethanone (2), and 2butanol (1) + 1-phenylethanone (2) have been investigated. 2836
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Table 9. Result of Herrington’s Thermodynamic Consistency Test system 1 2 3 4
propan-1-ol (1) + 1-phenylethanone (2) propan-2-ol (1) + 1-phenylethanone (2) 2-methyl propan-1-ol (1) + 1-phenylethanone (2) 2-butanol (1) + 1-phenylethanone (2)
Herrington’s test13 |D − J| 8.91 8.72 7.86 9.64
The observed values of the liquid-phase mole fraction and vapor-phase mole fraction versus bubble point of all the mixtures investigated could be well represented by the Wilson model. The UNIFAC model tends to overestimate the activity coefficients by a small margin for the systems propan-1-ol (1) + 1-phenylethanone (2) and propan-2-ol (1) + 1-phenylethanone (2). However, the systems 2-methyl-1-propanol (1) + 1phenylethanone (2) and 2-butanol (1) + 1-phenylethanone (2) are well represented by both the methods. None of the systems investigated form an azeotrope. The experimental data presented are expected to be useful for design purposes.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: mpk.iict@gmail.com. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Perkin, W. H.; Kipping, F. S. Organic Chemistry; W. & R. Chambers: London, 1922. (2) Sittig, M. Pharmaceutical Manufacturing Encyclopedia; William Andrew Publishing: New York, 1988. (3) Kumar, G.; Braish, T. Process Chemistry in the Pharmaceutical Industry; CRC Press: Boca Raton, FL, 2007; Vol. 2. (4) Miller, K. J.; Wu, J. L. Heat of Mixing and Vapor-Liquid Equilibrium of Acetophenone-2-Butanol System. J. Chem. Eng. Data 1973, 18 (3), 262−263. (5) Weast, R. C.; Astle, M. J. CRC Handbook of Data on Organic Compounds; CRC Press: Boca Raton, FL, 1985. (6) Edward, H. Vapor-Liquid Equilibrium; Pergamon Press: Elmsford, NY, 1958. (7) Pradeep Kumar, M.; et al. Isobaric Vapor−Liquid Equilibrium Data for the Binary Mixtures 2-Methyl Propan-2-ol with Tetraethoxysilane and 1-Phenyl Ethanone at 95.5 kPa. J. Chem. Eng. Data 2012, 57 (5), 1520−1524. (8) Wilson, G. Vapor-liquid equilibrium. XI. A New Expression for the Excess Gibbs Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127− 130. (9) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977. (10) Spencer, C. F.; Danner, R. P. Improved Equation of Saturated Liquid Density. J. Chem. Eng. Data 1972, 17, 236. (11) Kuester, R. T.; Mize, J. H. Optimization Techniques with Fortran; McGraw-Hill: New York, 1973. (12) Sinnot, R. K. Coulson and Richardson’s Chemical Engineering Series, 3rd ed.; Butterworth-Heinemann Publication: Woburn, MA, 2001; Vol. 6. (13) Wisniak, J. The Herington Test for Thermodynamic Consistency. J. Ind. Eng. Chem. Res. 1994, 33 (1), 177−180.
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