VaporâLiquid Equilibrium Data for the Morpholine-4-carbaldehyde + n

Article pubs.acs.org/jced

Vapor−Liquid Equilibrium Data for the Morpholine-4-carbaldehyde + n‑Hexane or n‑Heptane Binary Systems Using a Static-Synthetic Apparatus Kuveneshan Moodley, Paramespri Naidoo, Johan David Raal, and Deresh Ramjugernath* Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, Durban 4041, South Africa S Supporting Information *

ABSTRACT: Precise isothermal binary vapor−liquid equilibrium (VLE) measurements were performed for the morpholine4-carbaldehyde + n-hexane or n-heptane systems at (343.15, 363.15, and 393.15) K using a static-synthetic apparatus. The P−x data measured were processed using both the model-dependent and model-independent approaches. Infinite dilution activity coefficients were estimated by the extrapolation of VLE data by three different methods. Excess enthalpy and entropy data were predicted from VLE data using the Gibbs−Helmholtz relation.

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INTRODUCTION It is often difficult, and sometimes impossible, to separate a mixture of components with similar volatility that exhibits azeotropic behavior by conventional distillation. Extractive distillation provides an efficient and effective solution to accomplish such a separation. The selection of a suitable solvent for this type of separation process is imperative, as it dictates the efficiency and degree of separation obtainable for the process. It is therefore important that the phase behavior of mixtures with the solvent be experimentally determined to facilitate an accurate design, simulation, and optimization of the extractive distillation process. The solvent morpholine-4-carbaldehyde (NFM, C5H9NO2) has proved to be an effective physical solvent in the extractive distillation of mixtures composed of aromatic constituents (Al Qattan and Al-Sahhaf,1 Cincotti et al.,2 Ko et al.,3 Park and Gmehling,4 Xiong and Zhang,5 and Huang et al.6). However the assessment of the efficiency of NFM as an extractive solvent in the separation of mixtures composed of alkane constituents is limited by the lack of published vapor−liquid equilibrium (VLE) data for systems of NFM + alkanes available in the literature within the temperature ranges employed in the majority of industrial separation processes (343.15 to 393.15) K. The static-synthetic method provides a particularly accurate and convenient method of determining isothermal P−x data for binary systems with large differences in volatility. A limitation of the method is that thermodynamic consistency testing cannot be performed, as the Gibbs−Duhem relation is utilized in the calculation of vapor compositions. It is therefore prudent that larger P−x data sets be produced, than in analytical-type methods, to ensure that accuracy and repeatability in measurements is maintained. © XXXX American Chemical Society

Table 1. Chemical Suppliers and Purities refractive index at 293.15 K

a

component

supplier

exptl

lit.

propan-1-ol butan-2-ol n-pentane n-hexane n-heptane morpholine-4carbaldehyde

Sigma Aldrich Sigma Aldrich Sigma Aldrich Merck Fluka Merck

1.3852 1.3972 1.3575 1.3748 1.3877 1.4844

1.3851 1.3978 1.3575 1.3749 1.3876 1.4845

a

minimum purity claimed

GC peak area fraction

≥ 0.995 ≥ 0.990 ≥ 0.990 ≥ 0.990 ≥ 0.990 ≥ 0.990

0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

Literature: Lide15 at 293.15 K.

The static-synthetic apparatus of Raal et al.7 was extended for measurements up to 1500 kPa and subsequently used to measure P−x data for the {n-hexane or n-heptane} + morpholine4-carbaldehyde systems at (343.15, 363.15, and 393.15) K. The data was modeled using the model-dependent method of Barker8 and the model-independent method that involved the integration of the coexistence equation derived by Van Ness.9 The usefulness of the measured P−x data was maximized as infinite dilution activity coefficients calculated by extrapolation of VLE data, and by the Maher and Smith10 method were possible. Excess enthalpy and entropy data were predicted from VLE data, using the Gibbs−Helmholtz relation. Received: May 6, 2013 Accepted: July 31, 2013

A

dx.doi.org/10.1021/je4004417 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. Method used for integration of coexistence equation of Van Ness.9

Table 2. Second Virial Coefficients and Component Liquid Molar Volumes for Systems Considered Bii

a

Bij

−1

m ·mol ·10 3

6

‑1

m ·mol ·10 3

Bii 6

−1

Bij

m ·mol ·10 3

6

m ·mol‑1·106 3

T

Vi

component

K

m ·mol ·10

a

a

b

b

water (i = 2) propan-1-ol (i = 1) n-hexane (i = 1) butan-2-ol (i = 2) n-hexane (i = 1) morpholine-4-carbaldehyde (i = 2) n-hexane (i = 1) morpholine-4-carbaldehyde (i = 2) n-hexane (i = 1) morpholine-4-carbaldehyde (i = 2) n-heptane (i = 1) morpholine-4-carbaldehyde (i = 2) n-heptane (i = 1) morpholine-4-carbaldehyde (i = 2) n-heptane (i = 1) morpholine-4-carbaldehyde (i = 2)

313.15 313.15 329.15 329.15 343.15 343.15 363.15 363.15 393.15 393.15 343.15 343.15 363.15 363.15 393.15 393.15

16.53 74.94 138.93 94.13 140.50 103.98 145.39 105.70 154.15 108.46 156.13 103.98 160.86 105.70 169.08 108.46

−1436.5 −1853.6 −2591.8 −1346.0 −1777.4 −6666.8 −1471.0 −5275.7 −1140. 6 −3878.5 −2604.5 −6666.8 −2121.4 −5275.7 −1618.9 −3878.5

−1431.6

−1061.1 −1684.5 −1428.0 −1659.9 −1279.7 −6968.9 −1106.1 −5423.0 −906.8 −3939.3 −1856.9 −6968.9 −1589.1 −5423.0 −1286.9 −3939.3

−1258.6

3

−1

6

Hayden−O’Connell correlation.20 bModified Tsonopoulos Correlation (Long et al. B

19

−1306.2 −2850.3 −2338.2 −1799.5 −3610.3 2923.8 −2217.4

−1530.4 −2558.8 −2141.5 −1697.0 −3176.7 −2636.4 −2066.1

). dx.doi.org/10.1021/je4004417 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 3. Measured Vapor Pressure Data, with Corresponding Values from Literature Correlations p/kPa component propan-1-ol

butan-2-ol

n-hexane

n-heptane

morpholine-4carbaldehyde

T/K

this work a

b

312.60 343.40a 352.40a 324.80a 328.40a 345.00a 354.20a 328.10a 337.00a 343.20a 363.95a 391.95a 411.95a 386.15a 391.95a 403.65a 412.05a 343.15a

6.93 32.98b 49.19b 11.73b 14.50b 32.80b 49.15b 64.67b 86.77b 105.88c 187.23c 387.77c 600.68c 151.97c 177.71c 239.78c 290.34c 0.15c

363.15a 393.15a

0.49c 2.18c

Poling et al.16

DDB17

6.82 32.98 49.16 11.72 14.19 32.26 48.42 64.29 86.59 105.42 187.83 388.42 600.78 152.77 178.74 240.65 290.86

6.75 32.88 49.03 12.18 14.69 32.95 49.16 64.46 86.65 105.38 186.84 383.96 592.53 152.86 178.06 238.96 291.58 0.15

Figure 4. P−x plot for the n-hexane (1) + butan-2-ol (2) at 329.15 K showing the dilute region of n-hexane. ×, P−x, experimental; −, NRTL+V-mTS model; ---, mod. UNIQUAC+V-mTS model; □, Uusi-Kyyny et al.;27 ◊, Raal et al.7

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EXPERIMENTAL EQUIPMENT AND PROCEDURES The measurements presented were performed using a pressureextended version of the static-synthetic apparatus commissioned and described in detail by Raal et al.7 The addition of a (0 to 1.6) MPa WIKA-P-10 pressure transducer allows for measurements above atmospheric pressure. The standard uncertainty in the equilibrium pressure reading, within the (0 to 100) kPa range was calculated to be ± 0.106 kPa and ± 1.06 kPa for the (0.1 to 1.6) MPa pressure range. The standard uncertainty in the equilibrium temperature was calculated as ± 0.05 K. The uncertainty in the volume delivered to the cell was determined by the calibration of the piston injectors, and was found to be ± 0.025 cm3. The cell interior volume is an essential parameter, required for the calculation of vapor compositions via the Gibbs−Duhem relation. This volume was determined experimentally, by the method of Raal et al.7 and was confirmed to be 189.9 cm3. The suppliers and purities of the components used for measurement are presented in Table 1. The purities of the components used were determined by refractive index, and gas chromatography using a thermal conductivity detector. A final purity of ≥ 0.999 (GC peak area fraction) was determined for all components; therefore no further purification was necessary. In addition, the water used for measurement in this work was distilled deionized water with a conductivity of 177.5 μS. The chemical components were fully degassed for 8 h using the virtual total reflux distillation method of Van Ness and Abbott.11 The degassing apparatus commissioned by Narasigadu et al.12 was used. Pure component vapor pressure measurements were carried out for the chemicals used, and were compared to literature to verify that each component loaded into the cell was thoroughly degassed. Loading of the solvent was done in a few steps to verify constancy of pressure with each addition. The measurement procedure using the static-synthetic method is relatively simple and involves determining system pressure as a function of liquid composition. The composition of each phase is not analyzed, however the overall composition (zi) is determined exactly by the metered introduction of each component into the cell, using very precise piston dispensers. The cell and piston loading procedures have been described in detail by Raal et al.7 and Motchelaho.13

0.49 2.17

Uncertainty in T = ± 0.05 K. bUncertainty in p = ± 0.106 kPa. Uncertainty in p = ± 1.06 kPa.

a c

Figure 2. P−x−y plot for the water (1) + propan-1-ol (2) system at 313.15. ×, P−x experimental; −, NRTL+V-HOC model; ---, T-K Wilson + V-HOC model; ···, coexistence equation; □, P−x, Zielkiewicz and Konitz;26 ○, P−y, Zielkiewicz and Konitz;26 ◊, P−x, Raal et al.7

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THEORETICAL MODELS For the reduction of the vapor−liquid equilibrium measurements, P−zi data were converted to P−xi data using the method described previously by Raal and Ramjugernath.18 The model-dependent

Figure 3. P−x−y plot for the n-hexane (1) + butan-2-ol (2) system at 329.15 K: ×, P−x, experimental; −, NRTL-V+mTS model; ---, mod. UNIQUAC+V-mTS model; ···, coexistence equation; □, Uusi-Kyyny et al.;27 ◊, Raal et al.7 C



Article

Table 4. Model Parameters and Average Pressure Residuals for Measured Test Systems n-hexane (1) + butan-2-ol (2)

water (1) + propan-1-ol (2) model and parameters T-K Wilson (λ12 − λ11)/J·mol−1 (λ12 − λ22)/J·mol−1 ΔPAVG/kPaa NRTL (g12 − g11)/J·mol−1 (g12 − g22)/J·mol−1 α12 ΔPAVG/kPaa modified UNIQUAC (u12 − u11)/J·mol−1 (u12 − u22)/J·mol−1 ΔPAVG /kPaa a

313.15 K (V-HOC)

313.15 K (V-mTS)

329.15 K (V-HOC)

329.15 K (V-mTS)

4315.45 −2083.65 0.046

4316.88 −2082.37 0.047

699.79 5355.48 0.281

644.42 5269.37 0.289

6713.60 280.3 0.30 0.008

6714.70 281.70 0.30 0.009

4021.52 1401.87 0.30 0.151

3973.40 1354.94 0.30 0.134

4470.55 525.19 0.055

4472.92 526.61 0.557

8821.74 −1565.01 0.284

8714.19 −1582.53 0.282

ΔpAVG = 1/n ∑n1|pexp − pcalc|.

Table 5. Regressed Data for the n-Hexane (1) +Morpholine-4-carbaldehyde (2) System at 343.15 Ka Using the Wilson + V-mTS Model exptl z1 0.000 ± 0.0000 0.008 ± 0.0004 0.015 ± 0.0004 0.024 ± 0.0004 0.030 ± 0.0004 0.035 ± 0.0004 0.040 ± 0.0004 0.045 ± 0.0004 0.069 ± 0.0004 0.102 ± 0.0004 0.162 ± 0.0004 0.222 ± 0.0004 0.279 ± 0.0004 0.363 ± 0.0004 0.552 ± 0.0003 0.290 ± 0.0003 0.323 ± 0.0004 0.395 ± 0.0005 0.444 ± 0.0006 0.490 ± 0.0007 0.547 ± 0.0005 0.646 ± 0.0007 0.748 ± 0.0008 0.790 ± 0.0009 0.836 ± 0.0009 0.889 ± 0.0009 0.948 ± 0.0007 0.961 ± 0.0013 0.967 ± 0.0017 0.994 ± 0.0004 1.000 ± 0.0000 a

p/kPa b

0.16 11.73b 20.48b 30.36b 36.90b 41.90b 45.67b 49.12b 63.88b 78.03b 88.88b 93.93b 96.52b 99.10b 100.15b 96.90b 98.30b 99.40b 99.63b 99.87b 100.05c 100.37c 100.51c 100.65c 100.80c 100.92c 102.73c 103.11c 103.51c 104.30c 105.47c

Wilson + V-mTS p /kPa

x1

y1

Δp/kPad

γ1

γ2

α12

0.16 10.69 19.92 31.06 36.29 41.26 45.90 50.07 64.59 77.35 88.97 94.08 96.64 98.54 100.16 96.92 97.73 98.90 99.42 99.76 100.09 100.50 100.86 101.04 101.29 101.72 102.70 103.09 103.32 104.91 105.47

0.000 0.005 0.011 0.018 0.023 0.027 0.032 0.037 0.058 0.090 0.150 0.210 0.270 0.355 0.549 0.279 0.311 0.381 0.430 0.476 0.533 0.633 0.737 0.780 0.828 0.883 0.945 0.959 0.965 0.994 1.000

0.000 0.985 0.992 0.995 0.996 0.996 0.996 0.997 0.997 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.999 0.999 0.999 0.999 0.999 1.000

0.00 1.04 0.56 −0.70 0.61 0.64 −0.23 −0.95 −0.71 0.68 −0.09 −0.15 −0.12 0.56 −0.01 −0.02 0.57 0.50 0.21 0.11 −0.04 −0.13 −0.35 −0.39 −0.49 −0.80 0.03 0.02 0.19 −0.61 0.00

21.411 19.765 18.304 16.510 15.653 14.827 14.045 13.331 10.747 8.269 5.660 4.256 3.409 2.636 1.733 3.304 2.987 2.463 2.194 1.990 1.784 1.506 1.298 1.229 1.160 1.092 1.030 1.019 1.015 1.001 1.000

1.000 1.000 1.001 1.002 1.004 1.005 1.007 1.008 1.019 1.041 1.095 1.165 1.250 1.404 1.981 1.265 1.319 1.460 1.580 1.713 1.915 2.427 3.363 3.996 5.064 7.270 13.897 17.147 19.265 39.359 49.172

12493.35 11464.79 10205.85 9567.37 9169.32 8426.93 7972.77 6230.44 4816.46 2976.79 2203.81 1591.75 1066.95 513.44 1518.31 1301.59 1012.51 826.49 687.48 547.83 361.63 222.33 175.90 129.53 88.03 44.45 35.68 29.92 15.34

calc

Uncertainty in T = ± 0.05 K. bUncertainty in p = ± 0.106 kPa. cUncertainty in p = ± 1.06 kPa. dΔp = p − pcalc

combined (γ−Φ) method of Barker8 was used to calculate activity coefficients and vapor mole fractions. Vapor phase nonidealities were accounted for using the virial equation of state with the modified Tsonopoulos (Long et al.19) (V-mTS) and Hayden−O’Connell20 (V-HOC) second virial coefficient correlations.

The Nelder-Mead simplex method was used to minimize the pressure residual (|pexp − pcalc|) defined by Barker.8 The activity coefficient models (Wilson,21 T-K Wilson,22 NRTL,23 or mod. UNIQUAC24) that provided the lowest absolute average relative deviation (AARD) in pressure are presented where the AARD is given by D



Article

Table 6. Regressed Data for the n-Hexane (1) +Morpholine-4-carbaldehyde (2) System at 363.15 Ka Using the T-K Wilson + V-mTS Model exptl Z1 0.000 ± 0.0000 0.008 ± 0.0004 0.015 ± 0.0004 0.024 ± 0.0004 0.030 ± 0.0004 0.035 ± 0.0004 0.040 ± 0.0004 0.045 ± 0.0004 0.069 ± 0.0004 0.102 ± 0.0004 0.162 ± 0.0004 0.222 ± 0.0004 0.279 ± 0.0004 0.363 ± 0.0004 0.552 ± 0.0003 0.290 ± 0.0003 0.323 ± 0.0004 0.395 ± 0.0005 0.444 ± 0.0006 0.490 ± 0.0007 0.547 ± 0.0005 0.646 ± 0.0007 0.748 ± 0.0008 0.790 ± 0.0009 0.836 ± 0.0009 0.889 ± 0.0009 0.948 ± 0.0007 0.961 ± 0.0013 0.967 ± 0.0017 0.994 ± 0.0004 1.000 ± 0.0000 a

T-K Wilson + V-mTS p/kPa b

0.49 12.31b 22.87b 34.90b 42.61b 49.03b 55.36b 60.89b 84.79b 108.92c 137.32c 153.19c 162.82c 168.78c 174.43c 163.26c 165.64c 170.04c 172.36c 173.97c 174.29c 175.84c 176.80c 178.30c 178.45c 179.64c 183.95c 184.90c 185.50c 189.88c 190.95c

pcalc/kPa

x1

y1

Δp/kPad

γ1

γ2

α12

0.49 12.20 22.49 35.81 42.60 49.19 55.36 61.26 84.31 109.15 137.54 153.10 161.86 168.81 174.74 162.80 165.70 169.98 171.88 173.17 174.36 175.84 177.23 177.93 178.95 180.65 184.11 185.29 185.94 189.82 190.95

0.000 0.006 0.011 0.019 0.024 0.028 0.033 0.037 0.058 0.089 0.148 0.209 0.268 0.354 0.549 0.276 0.308 0.377 0.425 0.470 0.526 0.627 0.732 0.775 0.824 0.880 0.944 0.958 0.964 0.994 1.000

0.000 0.960 0.978 0.986 0.988 0.990 0.991 0.992 0.994 0.995 0.996 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.998 0.998 0.998 0.998 0.999 1.000

0.00 0.11 0.38 −0.91 0.01 −0.16 0.00 −0.37 0.48 −0.23 −0.22 0.09 0.96 −0.03 −0.31 0.46 −0.06 0.06 0.48 0.80 −0.07 0.00 −0.43 0.37 −0.50 −1.01 −0.16 −0.39 −0.44 0.06 0.00

11.971 11.420 10.934 10.299 9.973 9.654 9.353 9.064 7.907 6.597 4.946 3.893 3.194 2.513 1.674 3.111 2.839 2.376 2.129 1.938 1.742 1.474 1.272 1.206 1.140 1.077 1.023 1.014 1.010 1.000 1.000

1.000 1.000 1.001 1.001 1.002 1.003 1.004 1.005 1.012 1.027 1.067 1.124 1.195 1.331 1.860 1.207 1.253 1.375 1.480 1.597 1.775 2.229 3.052 3.598 4.498 6.264 10.866 12.803 13.972 22.548 25.658

4061.03 3871.58 3616.93 3479.90 3368.65 3241.57 3109.76 2646.28 2162.29 1505.60 1112.72 851.68 606.46 292.69 841.88 722.85 549.42 465.37 387.72 309.34 212.05 135.44 107.24 81.99 54.36 29.77 24.55 23.10 15.84

Uncertainty in T = ± 0.05 K. bUncertainty in p = ± 0.106 kPa. cUncertainty in p = ± 1.06 kPa. dΔp = p − pcalc.

Table 7. Regressed Data for the n-Hexane (1) +Morpholine-4-carbaldehyde (2) System at 393.15 Ka Using the T-K Wilson + V-mTS Model exptl z1 0.000 0.008 0.015 0.024 0.030 0.035 0.040 0.045 0.069 0.102 0.162 0.222 0.279 0.363 0.552 0.290 0.323 0.395 0.444 0.490

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

T-K Wilson + V-mTS p/kPa

0.0000 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 0.0003 0.0004 0.0005 0.0006 0.0007

b

2.18 24.17b 42.98b 69.88b 82.99b 97.19b 110.26c 122.95c 171.25c 227.23c 291.50c 325.96c 345.31c 358.94c 366.73c 346.96c 352.20c 359.23c 362.91c 365.03c

pcalc/kPa

x1

y1

Δp/kPad

γ1

γ2

α12

2.18 24.17 44.56 69.60 83.99 96.98 109.66 121.72 172.21 227.70 292.49 326.68 344.75 357.97 368.01 346.15 351.45 359.23 362.62 364.88

0.000 0.005 0.009 0.015 0.019 0.022 0.026 0.030 0.048 0.077 0.134 0.195 0.256 0.345 0.546 0.263 0.293 0.359 0.406 0.450

0.000 0.909 0.950 0.967 0.973 0.976 0.979 0.981 0.986 0.989 0.991 0.992 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.993

0.00 0.00 −1.58 0.28 −1.00 0.21 0.60 1.23 −0.96 −0.47 −0.99 −0.72 0.56 0.97 −1.28 0.81 0.75 0.00 0.29 0.15

14.345 13.717 13.134 12.417 12.004 11.630 11.264 10.914 9.431 7.738 5.578 4.243 3.395 2.606 1.691 3.321 3.024 2.515 2.245 2.035

1.000 1.000 1.000 1.001 1.002 1.002 1.003 1.004 1.010 1.023 1.063 1.122 1.197 1.341 1.897 1.207 1.251 1.367 1.467 1.578

2199.15 2083.34 1935.55 1866.61 1790.09 1722.79 1657.39 1394.81 1099.47 742.45 523.79 389.01 265.03 121.60 375.88 333.04 249.70 207.80 175.98

E



Article

Table 7. continued exptl

a

T-K Wilson + V-mTS

z1

p/kPa

p /kPa

x1

y1

γ1

γ2

α12

0.547 ± 0.0005

367.55c

366.90

0.506

0.993

0.65

1.820

1.748

140.74

0.646 ± 0.0007

368.94c

369.41

0.607

0.993

−0.47

1.526

2.181

94.64

0.748 ± 0.0008

370.76c

371.86

0.715

0.993

−1.10

1.303

2.970

59.24

0.790 ± 0.0009

373.05c

373.18

0.760

0.993

−0.13

1.230

3.494

47.64

0.836 ± 0.0009

374.21c

375.16

0.811

0.994

−0.95

1.158

4.367

35.62

0.889 ± 0.0009

378.39

c

378.60

0.871

0.994

−0.21

1.087

6.097

24.20

0.948 ± 0.0007

385.34c

385.82

0.939

0.995

−0.48

1.026

10.761

12.88

0.961 ± 0.0013

388.11c

388.31

0.954

0.996

−0.20

1.016

12.783

10.62

0.967 ± 0.0017

389.52c

389.70

0.961

0.996

−0.18

1.012

14.020

9.75

0.994 ± 0.0004

398.28

c

397.93

0.993

0.999

0.35

1.001

23.426

5.61

1.000 ± 0.0000

400.27c

400.27

1.000

1.000

0.00

1.000

26.945

calc

Δp/kPad


Table 8. Regressed Data for the n-Heptane (1) +Morpholine-4-carbaldehyde (2) System at 343.15 Ka Using the Wilson + V-mTS Model exptl

a

Wilson + VmTS b

z1

p/kPa

0.000 ± 0.0000 0.007 ± 0.0007 0.009 ± 0.0007 0.009 ± 0.0007 0.019 ± 0.0007 0.026 ± 0.0007 0.038 ± 0.0007 0.054 ± 0.0007 0.095 ± 0.0007 0.164 ± 0.0007 0.209 ± 0.0007 0.319 ± 0.0006 0.376 ± 0.0006 0.436 ± 0.0006 0.503 ± 0.0006 0.562 ± 0.0005 0.613 ± 0.0005 0.643 ± 0.0004 0.576 ± 0.0005 0.735 ± 0.0006 0.778 ± 0.0009 0.827 ± 0.0009 0.882 ± 0.0008 0.945 ± 0.0006 0.958 ± 0.0010 0.965 ± 0.0012 0.972 ± 0.0011 0.987 ± 0.0007 0.994 ± 0.0007 1.000 ± 0.0000

0.15 10.40 13.60 14.20 23.88 27.81 31.61 33.37 34.39 34.85 34.94 35.02 35.15 35.38 35.44 35.54 35.90 35.90 35.60 36.41 36.66 37.02 37.62 38.40 38.70 39.00 39.20 39.76 40.10 40.40

p /kPa

x1

y1

Δp/kPac

γ1

γ2

α12

0.15 10.57 13.65 14.30 23.84 27.73 31.39 33.12 34.38 34.82 34.94 35.13 35.24 35.36 35.51 35.67 35.84 35.95 35.71 36.38 36.66 37.05 37.67 38.75 39.07 39.25 39.45 39.91 40.17 40.40

0.000 0.003 0.004 0.004 0.010 0.015 0.027 0.042 0.083 0.154 0.200 0.312 0.371 0.432 0.499 0.559 0.611 0.642 0.571 0.731 0.775 0.824 0.880 0.943 0.957 0.964 0.972 0.986 0.994 1.000

0.000 0.986 0.989 0.989 0.994 0.994 0.995 0.995 0.996 0.996 0.996 0.996 0.996 0.996 0.996 0.996 0.996 0.996 0.996 0.996 0.996 0.996 0.997 0.998 0.998 0.998 0.999 0.999 1.000 1.000

0.00 −0.17 −0.05 −0.10 0.04 0.08 0.22 0.25 0.01 0.03 0.00 −0.11 −0.09 0.02 −0.07 −0.13 0.06 −0.05 −0.10 0.03 0.00 −0.03 −0.05 −0.35 −0.37 −0.25 −0.25 −0.15 −0.07 0.00

134.389 103.416 93.880 91.814 59.921 45.164 29.016 19.536 10.209 5.586 4.319 2.784 2.350 2.027 1.759 1.578 1.450 1.386 1.547 1.230 1.170 1.112 1.059 1.016 1.009 1.007 1.004 1.001 1.000 1.000

1.000 1.000 1.001 1.001 1.004 1.007 1.017 1.031 1.075 1.163 1.229 1.427 1.557 1.720 1.945 2.198 2.478 2.673 2.254 3.470 4.047 4.955 6.578 10.167 11.448 12.217 13.097 15.284 16.662 17.924

27309.33 24435.52 23614.71 15286.16 11504.76 7226.37 4830.28 2434.51 1213.42 884.34 498.73 383.79 298.11 227.09 182.60 147.18 132.44 174.26 89.34 72.46 56.07 40.16 24.94 22.26 20.47 19.46 17.22 15.08

calc

Uncertainty in T = ± 0.05 K. bUncertainty in p = ± 0.106 kPa. cΔp = p − pcalc.

Δpavg =

1 n

n

integration of the coexistence equation. The specific procedure used to accomplish this integration has been described in detail by Moodley,14 and is similar in concept to the methods described by Sayegh and Vera.25 A fourth-order Runge−Kutta technique was employed for numerical integration by a marching procedure. The calculation method employed in this work is

∑ |pexp − pcalc | 1

(1)

where pexp and pcalc are experimental and calculated pressures, respectively. Additionally, the VLE data were processed by the model-independent method that involved the numerical F



Article

Table 9. Regressed Data for the n-Heptane (1) +Morpholine-4-carbaldehyde (2) System at 363.15 Ka Using the Wilson + V-mTS Model exptl

a

Wilson + V-mTS

z1

p/kPab

pcalc/kPa

x1

y1

Δp/kPac

γ1

γ2

α12

0.000 ± 0.0000 0.007 ± 0.0007 0.009 ± 0.0007 0.009 ± 0.0007 0.019 ± 0.0007 0.026 ± 0.0007 0.038 ± 0.0007 0.054 ± 0.0007 0.095 ± 0.0007 0.164 ± 0.0007 0.209 ± 0.0007 0.319 ± 0.0006 0.376 ± 0.0006 0.436 ± 0.0006 0.503 ± 0.0006 0.562 ± 0.0005 0.613 ± 0.0005 0.643 ± 0.0004 0.576 ± 0.0005 0.735 ± 0.0006 0.778 ± 0.0009 0.827 ± 0.0009 0.882 ± 0.0008 0.945 ± 0.0006 0.958 ± 0.0010 0.965 ± 0.0012 0.972 ± 0.0011 0.987 ± 0.0007 0.994 ± 0.0007 1.000 ± 0.0000

0.49 9.89 12.91 13.62 25.22 32.11 42.41 51.09 61.80 66.91 68.09 69.28 69.55 69.58 69.94 70.18 70.20 70.34 70.10 71.32 71.60 72.33 73.30 75.11 75.58 76.06 76.50 77.60 78.52 78.59

0.49 9.84 13.03 13.62 25.22 32.10 42.48 51.08 61.74 66.74 67.83 68.96 69.29 69.57 69.88 70.18 70.47 70.66 70.23 71.38 71.85 72.53 73.60 75.53 76.11 76.45 76.82 77.68 78.18 78.59

0.000 0.003 0.004 0.005 0.010 0.014 0.024 0.037 0.075 0.146 0.193 0.307 0.366 0.428 0.496 0.557 0.610 0.640 0.566 0.728 0.772 0.821 0.878 0.943 0.957 0.964 0.971 0.986 0.994 1.000

0.000 0.950 0.962 0.964 0.980 0.984 0.988 0.990 0.992 0.992 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.994 0.994 0.996 0.996 0.997 0.997 0.999 0.999 1.000

0.00 0.05 −0.12 0.00 0.00 0.01 −0.07 0.01 0.06 0.17 0.26 0.32 0.26 0.02 0.06 0.00 −0.27 −0.32 −0.13 −0.06 −0.25 −0.20 −0.30 −0.42 −0.53 −0.39 −0.32 −0.08 0.34 0.00

44.695 40.104 38.514 38.221 32.314 28.690 22.964 17.838 10.434 5.801 4.472 2.857 2.403 2.065 1.788 1.600 1.467 1.401 1.575 1.245 1.182 1.121 1.064 1.018 1.011 1.008 1.005 1.001 1.000 1.000

1.000 1.000 1.000 1.000 1.002 1.003 1.007 1.015 1.047 1.124 1.185 1.373 1.499 1.655 1.873 2.120 2.393 2.584 2.164 3.339 3.904 4.806 6.452 10.257 11.669 12.532 13.530 16.070 17.712 19.244

6071.67 5862.08 5856.31 4875.87 4291.07 3391.65 2598.55 1465.16 752.59 554.40 303.50 235.46 181.96 140.00 109.76 89.52 79.73 107.14 54.71 43.91 33.83 23.91 14.46 12.56 11.70 10.95 9.31 7.67

Uncertainty in T = ± 0.05 K. bUncertainty in p = ± 0.106 kPa. cΔp = p − pcalc.

Table 10. Regressed Data for the n-Heptane (1) +Morpholine-4-carbaldehyde (2) System at 393.15 Ka Using the T-K Wilson + V-mTS Model exptl z1 0.000 0.006 0.007 0.009 0.021 0.026 0.038 0.054 0.095 0.166 0.200 0.221 0.249 0.286 0.332 0.399 0.554 0.623 0.454 0.499 0.665

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

T-K Wilson + V-mTS p/kPa

0.0000 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0006 0.0006 0.0005 0.0005 0.0005 0.0005 0.0005

b

2.18 12.56b 14.21b 19.05b 39.91b 46.85b 67.07b 88.05b 129.32c 162.95c 167.94c 169.13c 171.74c 173.01c 174.13c 175.22c 175.95c 175.51c 175.20c 175.52c 176.03c

pcalc/kPa

x1

y1

Δp/kPad

γ1

γ2

α12

2.18 12.26 14.19 19.15 38.89 46.85 66.10 87.65 129.54 162.95 169.23 171.63 173.66 175.13 175.90 175.97 175.01 174.70 175.66 175.36 174.62

0.000 0.002 0.003 0.004 0.010 0.012 0.020 0.030 0.061 0.131 0.167 0.190 0.220 0.259 0.310 0.381 0.546 0.618 0.443 0.488 0.654

0.000 0.821 0.845 0.885 0.943 0.952 0.966 0.974 0.982 0.985 0.986 0.986 0.986 0.987 0.987 0.987 0.986 0.986 0.987 0.987 0.986

0.00 0.30 0.02 −0.10 1.02 0.00 0.97 0.40 −0.22 0.00 −1.29 −2.50 −1.92 −2.12 −1.77 −0.75 0.94 0.81 −0.46 0.16 1.41

25.446 24.414 24.215 23.705 21.661 20.830 18.794 16.455 11.568 6.736 5.473 4.879 4.263 3.644 3.061 2.487 1.729 1.525 2.139 1.939 1.439

1.000 1.000 1.000 1.000 1.001 1.001 1.003 1.006 1.023 1.082 1.122 1.150 1.191 1.251 1.341 1.496 2.047 2.438 1.662 1.810 2.696

1903.90 1875.85 1821.02 1656.19 1583.09 1411.41 1217.99 830.72 447.72 351.30 304.86 257.60 208.96 164.11 119.47 60.36 44.89 92.03 76.82 38.35

G



Article

Table 10. continued exptl

a

T-K Wilson + V-mTS

z1

p/kPa

p /kPa

x1

y1

γ1

γ2

0.712 ± 0.0006

176.25c

174.64

0.702

0.986

1.61

1.341

3.130

30.77

0.767 ± 0.0006

176.35c

174.87

0.758

0.987

1.48

1.244

3.838

23.34

0.797 ± 0.0007

176.37c

175.12

0.789

0.987

1.25

1.196

4.387

19.51

0.831 ± 0.0007

177.15c

175.54

0.824

0.987

1.61

1.149

5.194

15.87

0.867 ± 0.0007

177.31c

176.21

0.861

0.987

1.10

1.103

6.451

12.26

0.906 ± 0.0006

177.61

c

177.33

0.902

0.988

0.28

1.060

8.685

8.74

0.949 ± 0.0005

180.04c

179.33

0.947

0.990

0.71

1.023

13.607

5.37

0.963 ± 0.0007

180.60c

180.26

0.961

0.991

0.34

1.013

16.487

4.40

0.977 ± 0.0006

181.21c

181.36

0.976

0.993

−0.15

1.006

20.635

3.50

0.986 ± 0.0006

181.90c

182.25

0.986

0.995

−0.35

1.002

24.777

2.91

0.996 ± 0.0003

182.99c

183.26

0.996

0.998

−0.27

1.000

30.751

2.34

1.000 ± 0.0000

183.70c

183.70

1.000

1.000

0.00

1.000

34.017

calc

Δp/kPad

α12


Table 11. Model Parameters and Average Pressure Residuals for the n-Hexane (1)/n-Heptane (1) + Morpholine-4-carbaldehyde (2) Systems at Measured Temperatures V-mTS eq

343.15 K

V-HOC

363.15 K

393.15 K

343.15 K

363.15 K

393.15 K

5213.15 9511.36 0.373

4082.74 8630.19 0.541

5264.09 9331.19 1.149

3683.60 4302.30 4876.56 8223.20 8986.60 9007.32 0.307 0.490 0.391 n-heptane (1) + morpholine-4-carbaldehyde (20) 7590.90 6624.80 1041.63 7338.30 11115.30 6621.66 0.175 0.815 0.109

3739.79 8270.90 0.309

4630.47 9043.62 0.519

7620.74 7380.78 0.176

6675.51 11158.48 0.816

7047.20 6758.37 0.416

5800.40 9742.13 0.856

n-hexane (1) + morpholine-4-carbaldehyde (2) Wilson λ12 − λ11/J·mol−1 λ12 − λ22/J·mol−1 ΔpAVG/kPaa T-K Wilson λ12 − λ11/J·mol−1 λ12 − λ22/J·mol−1 ΔpAVG/kPaa λ12 − λ11/J·mol−1 λ12 − λ22/J·mol−1 ΔpAVG/kPaa T-K Wilson λ12 − λ11/J·mol−1 λ12 − λ22/J·mol−1 ΔpAVG/kPaa a

5169.70 9465.00 0.371 4832.10 8980.60 0.377 1039.60 6591.00 0.103 9778.10 5924.70 0.309

4026.30 8564.80 0.531

7013.50 6723.20 0.401

5187.40 9239.30 1.145

5738.70 9794.70 0.798

9799.60 5950.24 0.315

ΔpAVG = 1/n∑n1|pexp − pcalc|.

Figure 5. P−x−y plot for the n-hexane (1) + morpholine4-carbaldehyde (2) system at 343.15 K. ×, P−x, experimental; −, Wilson model; ---, T-K Wilson model; ···, coexistence equation.

Figure 6. P−x−y plot for the n-hexane (1) + morpholine4-carbaldehyde (2) system at 363.15 K. ×, P−x experimental; −, Wilson model; ---, T-K Wilson model; ···, coexistence equation. H



Article

Figure 7. P−x−y plot for the n-hexane (1) + morpholine4-carbaldehyde (2) system at 393.15 K. ×, P−x, experimental; −, Wilson model; ---, T-K Wilson model; ···, coexistence equation.

Figure 10. P−x−y plot for the n-heptane (1) + morpholine4-carbaldehyde (2) system at 393.15 K. ×, P−x experimental; −, Wilson model; ---, T-K Wilson model; ···, Coexistence Equation.

Figure 8. P−x−y plot for the n-heptane (1) + morpholine4-carbaldehyde (2) system at 343.15 K. ×, P−x experimental; −, Wilson model; ---, T-K Wilson model; ···, coexistence equation.

Figure 11. γi−x plot for the n-hexane (1) + morpholine-4-carbaldehyde (2) system at 393.15 K. −, Wilson model; ---, T-K Wilson model; ···, coexistence equation.

procedure used in this work, involved plotting ln γ1 vs x22 for the dilute region, and the subsequent extension of the plot to x2 = 1, to determine ln γ∞ 1 . If this extrapolation method did not produce a suitable linear relationship between ln γ1 and x22, then direct extrapolation, using the regressed activity coefficient model parameters was performed. The dependence of infinite dilution activity coefficient (γ∞ i ) on second virial coefficient values (Bii and Bij) was determined using the method outlined by Raal et al.,7 who give the dependence of the limiting activity coefficients on second virial coefficients by the following equations: ⎡ ∂γ ∞ ⎤ 2γ ∞P2sat ⎢ 1 ⎥= 1 RT ⎣ ∂B12 ⎦

Figure 9. P−x−y plot for the n-heptane (1) + morpholine4-carbaldehyde (2) system at 363.15 K. ×, P−x experimental; −, Wilson model; ---, T-K Wilson model; ···, coexistence equation.

(2)

⎡ ∂γ ∞ ⎤ γ ∞P2sat ⎡ ⎛ ∂B ⎞ P sat ⎤ ⎢2⎜ 12 ⎟ − 1sat ⎥ ⎢ 1 ⎥= 1 RT ⎢⎣ ⎝ ∂B11 ⎠ P2 ⎥⎦ ⎣ ∂B11 ⎦

presented in Figure 1. The method is very sensitive to the starting values used to estimate the boundary conditions for the dy/dP relationship. The expressions for the limiting conditions given by Van Ness9 were used. The limiting activity coefficients were calculated for the systems measured by extrapolation methods (see below) or by the method of Maher and Smith.10 The extrapolation methods were applied to the original measured data, as well as to the data calculated by the coexistence equation. The Maher and Smith10 method is virtually model independent, except for the calculation of xi from zi. The extrapolation

⎡ ∂γ ∞ ⎤ ⎢ 1 ⎥= ⎣ ∂B22 ⎦

(3)

⎤ ⎡ ⎛ ∂B ⎞ Φ∞ ⎛ ∂P ⎞ P2sat ⎢2⎜ 12 ⎟ − 1⎥ + 1 ⎜ ⎟ ⎥⎦ RT ⎢⎣ ⎝ ∂B22 ⎠ RT ⎝ ∂X1 ⎠ P1sat

γ1∞p2sat

∞

(4)

where γ∞ i is the infinite dilution activity coefficient of component i, Psat i is the saturation pressure of component i in kPa, R is the universal gas constant in J·mol·K−1, T is the temperature in K, Bii and Bij are the second virial coefficients in m3·mol−1, and Φ∞ 1 , is the vapor correction factor at infinite dilution. I



Article

Table 12. Infinite Dilution Activity Coefficients for the Systems Measured this work system

extrapolation

γ∞ 1 γ∞ 2

3.662 14.638

γ∞ 1 γ∞ 2

4.196 6.542

γ∞ 1 γ∞ 2

21.411 49.172

γ∞ 1 γ∞ 2

11.971 25.658

γ∞ 1 γ∞ 2

14.345 26.945

γ∞ 1 γ∞ 2

134.389 17.924

γ∞ 1 γ∞ 2

44.695 19.244

γ∞ 1 γ∞ 2

25.446 34.017

Maher and Smith10 method

coexistence equation

water (1) + propan-1-ol (2) at 313.15 K 3.825 3.807 14.03 14.336 n-hexane (1) + butan-2-ol (2) at 329.15 K 5.986 4.615 10.202 7.708 n-hexane (1) + morpholine-4-carbaldehyde (2) at 343.15 K 20.377 24.46 29.135 n-hexane (1) + morpholine-4-carbaldehyde (2) at 363.15 K 11.886 14.75 28.086 n-hexane (1) + morpholine-4-carbaldehyde (2) at 393.15 K 15.639 21.49 27.163 n-heptane (1) + morpholine-4-carbaldehyde (2) at 343.15 K 115.054 70.813 13.136 n-heptane (1) + morpholine-4-carbaldehyde (2) at 363.15 K 42.039 50.09 11.37 n-heptane (1) + morpholine-4-carbaldehyde (2) at 393.15 K 28.881 43.093 34.111

Raal et al.7

Uusi-Kyyny et al.27

3.83 18.42 4.66 13.13

4.41 10.54

The dependence of γ∞ 1 on the second virial coefficients (eqs 2 to 4) was calculated for the case of B12 ≠ f(Bii, Bij), and for the case of B12 = − B11B22

(5) 7

Equation 5 is an empirical relation used by Raal et al. The temperature dependences of the model parameters for the new systems measured that provided the lowest AARD (Wilson and T-K Wilson Gibbs excess energy models) have been calculated. A second order polynomial was used (λij − λjj) = a + bT1 + cT 2

(6)

Figure 12. Plot of PD/x1x2 vs x1 to determine infinite dilution activity coefficient by the method of Maher and Smith10 for the n-heptane (1) + morpholine-4-carbaldehyde (2) system at 363.15 K.

where a, b, and c are the polynomial constants and T is the temperature in K.

Figure 13. Plot of ln γ1 vs x22 for the direct extrapolation of γ∞ 1 for the n-hexane (1) + morpholine-4-carbaldehyde (2) system at 363.15 K.

RESULTS AND DISCUSSION The calculated second virial coefficients calculated using the Tsonopoulos (Long et al.19) (V-mTS) and Hayden-O’Connell20 (V-HOC) correlations are presented in Table 2. The results of the pure component vapor pressure measurements are presented in Table 3. These results compare well with the data of Poling et al.16 and DDB software.17 Test measurements for the water + propan-1-ol system at 313.15 K and n-hexane + butan-2-ol system at 329.15 K were performed. The results of both test measurements were found to be in good agreement with the results of Raal et al.,7 Zielkiewicz and Konitz,26 and Uusi-Kyyny et al.27 Regressed data for the test systems measured, including calculated activity coefficient (γi) and relative volatility (α12) values are presented in Tables S1 to S2 in the Supporting Information, for the model that provided the best fit for each system. These results are presented graphically (P−x1−y1 plots) in Figures 2 and 3 for the water + propan-1-ol and the n-hexane + butan-2-ol

■

J



Article

Table 13. Calculated Molar Excess Property Data for the n-Hexane (1) + Morpholine-4-carbaldehyde System at Measured Temperatures T/K 343.15

363.15

excess molar property/J·mol‑1


x1

GE

HE

TSE

GE

HE

TSE

0 0.01 0.02 0.03 0.05 0.07 0.09 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.92 0.93 0.94 0.95 0.96 0.97 0.99 1

0 83.29 162.95 239.25 382.66 515.04 637.55 695.40 954.29 1168.69 1344.55 1485.84 1595.26 1674.62 1725.07 1747.20 1741.11 1706.41 1642.17 1546.80 1417.83 1251.51 1042.01 779.67 656.41 590.08 520.24 446.54 368.55 285.73 102.57 0.00

0 50.69 96.00 136.71 206.66 264.35 312.49 333.61 416.71 473.02 511.67 537.96 555.18 565.41 570.00 569.84 565.41 556.90 544.17 526.69 503.31 471.80 427.79 361.75 324.69 302.67 277.66 248.97 215.64 176.40 71.98 0.00

0 −32.60 −66.95 −102.54 −176.00 −250.68 −325.06 −361.80 −537.58 −695.67 −832.88 −947.88 −1040.08 −1109.21 −1155.06 −1177.36 −1175.70 −1149.51 −1098.00 −1020.11 −914.53 −779.71 −614.22 −417.92 −331.72 −287.41 −242.57 −197.57 −152.91 −109.33 −30.58 0.00

0 73.73 145.06 214.11 345.67 469.05 584.78 639.92 890.26 1101.85 1278.30 1422.19 1535.34 1618.99 1673.86 1700.29 1698.15 1666.91 1605.53 1512.35 1384.93 1219.63 1011.02 750.53 628.84 563.63 495.23 423.40 347.84 268.20 94.87 0.00 T/K

0 56.77 107.52 153.11 231.45 296.07 349.98 373.63 466.70 529.77 573.05 602.50 621.78 633.23 638.38 638.20 633.24 623.71 609.46 589.88 563.68 528.40 479.11 405.14 363.64 338.98 310.97 278.83 241.51 197.56 80.62 0.00

0 −16.96 −37.54 −61.00 −114.22 −172.98 −234.80 −266.29 −423.56 −572.08 −705.25 −819.69 −913.56 −985.75 −1035.48 −1062.09 −1064.91 −1043.20 −996.07 −922.48 −821.24 −691.23 −531.91 −345.38 −265.20 −224.65 −184.26 −144.57 −106.33 −70.64 −14.25 0.00

393.15 excess molar property/J·mol‑1 E

x1

G

HE

TSE

0 0.01 0.02 0.03 0.05 0.07 0.09 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

0 85.44 167.76 247.14 397.62 537.87 668.72 730.83 1011.06 1245.69 1439.74 1596.69 1718.97 1808.22 1865.49 1891.28 1885.59 1847.92 1777.24

0 66.54 126.02 179.45 271.27 347.00 410.19 437.91 547.00 620.91 671.64 706.16 728.76 742.18 748.22 748.00 742.18 731.01 714.31

0 −18.90 −41.74 −67.69 −126.35 −190.87 −258.53 −292.92 −464.06 −624.78 −768.10 −890.53 −990.21 −1066.04 −1117.28 −1143.28 −1143.40 −1116.91 −1062.93

K



Article

Table 13. continued T/K 393.15 excess molar property/J·mol‑1 x1

GE

HE

TSE

0.70 0.75 0.80 0.85 0.90 0.92 0.93 0.94 0.95 0.96 0.97 0.99 1

1671.79 1528.97 1344.86 1113.58 825.81 691.65 619.82 544.52 465.47 382.34 294.76 104.25 0.00

691.36 660.66 619.31 561.54 474.84 426.20 397.30 364.47 326.81 283.06 231.55 94.49 0.00

−980.43 −868.31 −725.55 −552.04 −350.97 −265.46 −222.52 −180.04 −138.66 −99.28 −63.21 −9.76 0.00

Table 14. Calculated Molar Excess Property Data for the n-Heptane (1) + Morpholine-4-carbaldehyde System at Measured Temperatures T/K 343.15

363.15 ‑1


excess molar property/J·mol x1

GE

HE

TSE

GE

HE

TSE

0.00 0.01 0.02 0.03 0.05 0.07 0.09 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.92 0.93 0.94 0.95 0.96 0.97 0.99 1.00

0.00 124.45 233.07 330.83 503.26 653.17 786.10 847.26 1110.30 1316.16 1476.40 1597.70 1684.32 1739.04 1763.71 1759.50 1727.04 1666.47 1577.49 1459.36 1310.75 1129.69 913.34 657.54 542.91 482.72 420.52 356.22 289.75 221.01 76.26 0.00

0.00 228.10 381.86 490.76 627.29 698.60 730.90 736.96 704.31 611.30 488.25 349.35 202.36 52.13 −97.91 −244.94 −386.31 −519.12 −639.85 −743.80 −824.20 −870.64 −865.87 −778.54 −708.06 −662.30 −608.12 −544.16 −468.73 −379.74 −149.46 0.00

0.00 103.65 148.79 159.93 124.03 45.42 −55.20 −110.30 −405.99 −704.86 −988.15 −1248.36 −1481.96 −1686.91 −1861.62 −2004.44 −2113.34 −2185.58 −2217.34 −2203.15 −2134.95 −2000.34 −1779.21 −1436.09 −1250.97 −1145.02 −1028.64 −900.38 −758.48 −600.74 −225.71 0.00

0.00 106.84 206.08 298.89 468.43 620.23 757.39 821.15 1099.44 1321.44 1497.13 1632.62 1731.92 1797.70 1831.74 1835.14 1808.44 1751.67 1664.39 1545.64 1393.80 1206.46 980.13 709.62 587.42 523.02 456.28 387.11 315.38 240.97 83.45 0.00

0.00 256.82 430.35 553.60 708.94 791.09 829.41 837.21 805.17 704.70 569.81 416.43 253.32 85.93 −81.83 −246.80 −405.95 −556.01 −693.00 −811.65 −904.34 −959.39 −957.45 −863.42 −786.08 −735.66 −675.81 −605.02 −521.40 −422.60 −166.48 0.00

0.00 149.99 224.27 254.70 240.52 170.86 72.03 16.05 −294.27 −616.74 −927.32 −1216.19 −1478.60 −1711.77 −1913.58 −2081.94 −2214.38 −2307.67 −2357.40 −2357.29 −2298.13 −2165.86 −1937.58 −1573.04 −1373.50 −1258.67 −1132.09 −992.13 −836.78 −663.57 −249.93 0.00

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Table 14. continued T/K 393.15 excess molar property/J·mol‑1 x1

GE

HE

TSE

0.00 0.01 0.02 0.03 0.05 0.07 0.09 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.92 0.93 0.94 0.95 0.96 0.97 0.99 1.00

0.00 103.04 200.98 294.27 468.42 627.94 774.64 843.62 1150.15 1401.32 1605.25 1767.22 1890.80 1978.39 2031.52 2051.08 2037.34 1990.00 1908.14 1790.12 1633.35 1433.86 1185.57 878.69 736.05 659.74 579.76 495.80 407.49 314.39 111.44 0.00

0.00 301.01 504.39 648.84 830.92 927.20 972.11 981.24 943.70 825.95 667.84 488.08 296.90 100.72 −95.91 −289.26 −475.79 −651.66 −812.23 −951.29 −1059.93 −1124.45 −1122.18 −1011.97 −921.33 −862.22 −792.08 −709.11 −611.11 −495.31 −195.12 0.00

0.00 197.97 303.41 354.57 362.49 299.25 197.47 137.62 −206.45 −575.37 −937.41 −1279.15 −1593.90 −1877.67 −2127.44 −2340.34 −2513.13 −2641.66 −2720.38 −2741.41 −2693.27 −2558.31 −2307.75 −1890.65 −1657.38 −1521.96 −1371.84 −1204.91 −1018.60 −809.70 −306.56 0.00

Figure 14. Excess thermodynamic properties (GE, HE, and TSE) for the n-hexane (1) + morpholine-4-carbaldehyde (2) system. ◊, GE; ⧫, HE; ■, TSE at 343.15 K. ●, GE; ○, HE; +, TSE at 363.15 K. ▰, GE; Δ, HE; □, TSE at 393.15 K, using the T-K Wilson + V-mTS model.

Figure 15. Excess thermodynamic properties (GE, HE, and TSE) for the n-heptane (1) + morpholine-4-carbaldehyde (2) system. ⧫, GE; ◊, HE; ■, TSE at 343.15 K. ○, GE; ●, HE; +, TSE at 363.15 K. ▰, GE; Δ, HE; □, TSE at 393.15 K, using the T-K Wilson + V-mTS model.

systems. The results obtained from the integration of the coexistence equation are also presented in these plots. The results from the integration of the coexistence equation are only presented graphically, as a very large number of data points were generated in the numerical integration procedure. A plot of the results obtained for the dilute region of n-hexane in butan-2-ol is presented in Figure 4. Model parameters for the

best fit models for the test systems are presented in Table 4 along with the AARD between calculated and experimental pressures. The regressed data for the two new systems measured, n-hexane + morpholine-4-carbaldehyde and n-heptane + morpholione-4-carbaldehyde at (343.15, 363.15, and 393.15) K are given in Tables 5 to 10 along with calculated activity coefficients for the best fit models. It was found that the modified M



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some cases, and is much larger than the dependence of γ∞ 1 on B22 and B12 values. This confirms the difficulty in finding reliable values of γ2∞ for systems with very large relative volatilities. The high precision of the P−xi data for the new systems measured permitted satisfactory calculation of the excess enthalpy (HE), (useful for distillation process design), using the Gibbs−Helmholtz relation. These results are presented in Tables 13 and 14 and graphically in Figures 14 and 15. It is interesting to note that for the n-hexane + morpholine-4carbaldehyde system endothermic mixing is observed for the entire composition range, whereas the n-heptane + morpholine4-carbaldehyde system exhibits a combination of both endothermic and exothermic mixing over the composition range. Excess entropies were then calculated using the excess property relation. The temperature dependence of the model parameters for the two models that provided the lowest AARD was determined by a fit to eq 6. These results are presented in Table 15.

Table 15. Temperature Dependence of Wilson and T-K Wilson Model Parameters polynomial constantsa

system

model parameter

a

b

c

J·mol−1

J·mol−1·K−2

J·mol−1·K−1

J·mol−1

n-hexane (1) + morpholine-4-carbaldehyde (2) (λ12 − λ22) 193124 −998.42 (λ12 − λ11) 263730 −1411.50 T-K Wilson model (λ12 − λ22) 179780 −932.28 (λ12 − λ11) 219057 −1159.90 n-heptane (1) + morpholine-4-carbaldehyde (2) Wilson model (λ12 − λ22) −632487 3273.00 (λ12 − λ11) −1008014 5409.65 T-K Wilson model (λ12 − λ22) 147889 −842.36 (λ12 − λ11) 295816 −1490.60

Wilson model

a

1.35 1.92 1.27 1.56 −4.16 −7.20 1.25 1.91

■

As in eq 6.

CONCLUSIONS Isothermal P−x data for the n-hexane or n-heptane + morpholine-4-carbaldehyde systems at (343.15, 363.15, and 393.15 K) have been presented. This data was obtained by employing precise experimental techniques, and using a modified version of the static-synthetic apparatus of Raal et al.7 extended for measurement up to 1.5 MPa. In addition infinite dilution activity coefficients, excess enthalpy and entropy data, as well as the temperature dependence of the Wilson and T-K Wilson model parameters were calculated from the measured P−x data. The dependence of the infinite dilution activity coefficients on second virial coefficients was calculated using the method of Raal et al.7 The dependence of γ∞ 2 on B22 and B12 values was found to be exceptionally large and has considerable implications on the calculation of γ∞ 2 values, for systems with large relative volatilities.

Tsonopoulos correlation (Long et al.19) (V-mTS) provided the best fits for all the new systems measured. The correlated model parameters are presented in Table 11 with the AARD between calculated and experimental pressures. The P−x1−y1 plots are shown in Figures 5 to 10. A smooth continuation at the midpoint is evident in all systems, and indicates the uniformity of measurements even though the measurements were initiated from either of the pure component points. These plots also include the results obtained by the integration of the coexistence equation. The activity coefficient plot for the n-hexane + morpholine-4-carbaldehyde at 393.15 K is shown as an example in Figure 11. This plot also includes calculated activity coefficients obtained from the integration of the coexistence equation. It was found that for both the {C6 or C7} hydrocarbon + morpholine-4-carbaldehyde systems studied, strong positive deviation from Raoult’s law was exhibited. No azeotrope was formed under the temperature conditions measured. This may be attributed to the large vapor pressure ratios between the sat components of the systems considered (Psat 1 /P2 ± 700 for C6 and ± 300 for C7 compounds). Stability analyses were carried out on the alkane + morpholine4-carbaldehyde systems measured to ensure that two-liquidphase formation did not occur at the experimental conditions (T ≥ 343.15 K). However it must be mentioned that the binary systems measured form two liquid phases at lower temperatures, as reported by Al Qattan and Al-Sahhaf1 and Cincotti et al.2 The results of the calculation of infinite dilution activity coefficients by extrapolation, the method of Maher and Smith,10 and the coexistence equation, are presented in Table 12, with available literature values. The plots of PD/x1x2, or its inverse, vs x1 were found to be sufficiently linear with a Pearson productmoment correlation coefficient greater than 0.95 for all cases presented. Those cases that are not presented did not meet this linearity criterion. An example of the plot of PD/x1x2 vs x1 for the n-heptane + morpholine-4-carbaldehyde system at 363.15 K is presented in Figure 12. The plot of ln γ1 vs x22 is presented as an example for the n-hexane + morpholine-4-carbaldehyde system at 363.15 K in Figure 13. The results of the calculation of the dependence of infinite dilution activity coefficients on second virial coefficient values are presented in Table S3 of the Supporting Information. It was found that γ∞ 2 has an exceptionally large dependence on B22 and B12 values for both systems measured, with orders of 1·103 in

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ASSOCIATED CONTENT

S Supporting Information *

Tables S1, S2, and S3. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +27 31 260 2969. Fax: +27 31 260 1118. Funding

This work is based upon research supported by the National Research Foundation of South Africa under the South African Research Chair Initiative of the Department of Science and Technology and the National Research Foundation Thuthuka Programme. Notes

The authors declare no competing financial interest.

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REFERENCES

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