Excess properties and isothermal vapour-liquid equilibrium data for the ((toluene + pyridine)) system from 343 K to 383 K

J. Chem. Thermodynamics 141 (2020) 105946

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Excess properties and isothermal vapour-liquid equilibrium data for the ((toluene + pyridine)) system from 343 K to 383 K Kuveneshan Moodley Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, Durban 4041, South Africa

a r t i c l e

i n f o

Article history: Received 18 July 2019 Received in revised form 4 September 2019 Accepted 5 September 2019 Available online 7 September 2019 Keywords: Vapour-liquid equilibrium Excess properties Densities

a b s t r a c t Isothermal vapour-liquid equilibrium (VLE) data for the ((toluene + pyridine)) system has been measured at four temperatures from approximately 343 K to 383 K, using a dynamic-analytic apparatus. The densities of ((toluene + pyridine)) mixtures were also measured from 298 K to 363 K using an Anton Paar DMA-5000 densitometer. The vapour-liquid phase equilibrium data were modelled by the c
U approach and the Non-Random Two-Liquid and UNIQUAC activity coefficient models. The consistency of the experimental isothermal VLE data were checked by the area and point tests. The experimental density data were modelled using an 8-parameter empirical correlation which allowed for the simultaneous representation of temperature and liquid composition. The experimental data were used to determine the excess properties for volume, Gibbs energy, enthalpy and entropy. The excess volume was modelled using Redlich-Kister polynomials. Ó 2019 Elsevier Ltd.

1. Introduction Pyridine dehydration is commonly accomplished using enhanced distillation with aromatic solvents such as benzene or toluene [1]. The resulting pyridine-toluene mixture must then be separated for solvent recovery. A further need for the separation of pyridine and toluene arises from coal coking processes. Toluene, obtained from this process, often contains small quantities of pyridine, which is an impurity [2]. The mixture phase behaviour has been studied previously in the literature at a limited set of conditions which include Krasavin et al. [3] at 27.56–104.77 kPa, Hollo et al. [4] and Korotkova et al. [5] at 101.32 kPa, Jose et al. [6] at 298.15–333.15 K, Bratton et al. [7] at 363.15, Rogalski and Bylicki [8] at 373.124 K. The isothermal phase behaviour has not been considered at conditions close to the normal boiling point of the mixture. This is likely due to the close-boiling nature of the system and the associated difficulties in measuring the phase equilibrium data. Additionally, the mixture density (or excess volume) has not been well studied in the literature at conditions above ambient temperature (Bratton et al. [7]) at 298.14 and 363.12, Woycicki and Sadowska [9] at 298.14, Liu et al. [10] at 298.15). Precise VLE and density data is very useful as it allows for the calculation of several excess properties that include excess Gibbs energy, excess enthalpy, excess entropy, and excess volume. These properties are necessary for characterizing the non-ideal behaviours of

mixtures which is required for accurate process design. Since the ((toluene + pyridine)) system is known to be highly non-ideal due to an azeotrope, excess properties are likely to be significant in magnitude, and hence their characterization is essential. In this work the isothermal vapor-liquid equilibrium phase behaviour of the (toluene + pyridine) mixture has been measured at (343.1, 353.0, 363.2, and 382.7) K, and the density at atmospheric pressure has been measured at (298.15, 343.15, 353.15, 363.15) K. From these data the excess Gibbs energy, excess enthalpy, excess entropy, and excess volume have been calculated. The vapour-liquid equilibrium data were correlated by the c
U method with the Non-Random Two-Liquid [11] and UNIQUAC [12] liquid-phase models and with the virial equation of state with the Hayden and O’Connell correlation [13] for the vapour phase. The density data were correlated using an 8-parameter empirical correlation proposed in a previous work [14]. The calculated excess volume was then fitted to Redlich-Kister polynomials [15]. 2. Theory 2.1. Vapour-liquid equilibrium For vapour-liquid equilibrium by the combined approach, Smith et al. [16] show that

yi Ui P ¼ xi ci Psat i E-mail address: [email protected] https://doi.org/10.1016/j.jct.2019.105946 0021-9614/Ó 2019 Elsevier Ltd.

ð1Þ

2

K. Moodley / J. Chem. Thermodynamics 141 (2020) 105946

Here yi and xi are the vapour and liquid mole fractions respectively, P is the total system pressure, ci is the activity coefficient of species, i, in the liquid phase and Psat is the vapour pressure of i the pure component i. Ui is a correction factor for the vapour phase, calculated from:

"  # b
V i P
Psat / i i Ui ¼ sat exp RT /i

ð2Þ

b is the fugacity coefficient in solution, /sat is the fugacity The / i i coefficient at saturation, V i is the liquid molar volume of component i, R is the universal gas constant and T is the equilibrium temperature. For the virial equation of state, this reduces to:

"

Ui ¼ exp

  Bii
Vil P
Psat þ Py2j dij i RT



ð3Þ

where

dij ¼ 2Bij
Bii
Bjj

ð4Þ

and where Bij are the second virial coefficients which were estimated by the Hayden and O’Connell [13] correlation. The NonRandom Two-Liquid (NRTL) model [11] and UNIQUAC model [12] were used to determine the activity coefficients, similarly to recent published work [17–19]. 2.2. Density and excess volume

0  E 1 @ nG RT A HE ¼
RT 2 @ @T

ð8Þ

P;xi

The excess entropy, SE , is determined by the excess property axiom:

SE ¼

HE
GE T

ð9Þ

By definition, the excess volume is given by the following expression:

VE ¼

2 X

 
1 xi V i q
1 m
qi

ð10Þ

i¼1

Mi is the molar mass of component i, qm is the density of the mixture and qi is the density of component i. Redlich-Kister expansions were used to correlate excess properties (volume). For binary systems the expansion is given by:

ME ¼

J X

rMk;12 x1 x2 ðx1
x2 Þk

ð11Þ

k¼0

where ME is the excess property for the binary system, J is the total number of Redlich-Kister binary parameters,rM k;21 , where the subscript (k,21) denotes fitting parameter k between components 2 and 1. xi is the component mole fraction of the mixture. The rM k;21 parameters are property dependent.

To correlate density, temperature and composition simultaneously, an empirical correlation was proposed in a previous work [14]. The T-xi-qm relationship was correlated by the following polynomial:

3. Materials and methods

qm ðx2 ; T Þ ¼ b1 T 2 þ b2 T þ b3 x22 þ b4 T 2 þ b5 T þ b6 x þ b7 T

The chemicals used were procured from Sigma-Aldrich and had a stated mass fraction purity of >0.99. This was confirmed by a Shimadzu GC 2014 Plus with a 4 m  3 mm (1/8-inch) stainless steel CRS Porapak Q packed column and with helium as the carrier gas. This same GC and column were used for phase sampling analysis. An ATAGO RX-7000a refractometer (sodium D-line = 589 nm, temperature uncertainty from repeatability is 0.01 K) with an uncertainty of 0.0001 was used to perform pure component refractive index measurements at 101.3 kPa, within 0.1 kPa confirmed by a Mensor standard (CPC6000). The pyridine was dried under molecular sieve for 48 h prior to use. The water content of the pyridine was determined, by Karl-Fischer titration using an MKS 500 apparatus, to be less than 0.0003 mass fraction. The chemical properties are provided in Table 1.









2

þ b8

ð5Þ
3

where qm, is the mixture density in kg∙m , T is the temperature in Kelvin and bi (i = 1. . .8) are the model fitting parameters. It was found that the correlation provided continuous P-V-T functions that could be further correlated by theoretically superior models such as cubic equations of state. Note that this model only allows for a linear temperature dependence of component 1. The empirical model above is correlated by minimizing the following root mean square deviation in density (RMSDq ):

2

31=2 0 exp calc 2 6XN1 @ qk
qk Þ 5 RMSDq ¼ 4 k N1

ð6Þ

3.1. Materials

3.2. Experimental procedure exp k

calc k

where q and q are the experimental and calculated densities respectively of the data point k and N1 is the total number of density data points measured. 2.3. Excess properties Using the fundamental excess property relation at constant temperature and pressure, the excess Gibbs energy can be expressed as:

GE ¼ RT

N X

xi lnci

ð7Þ

i¼1

Additionally, applying the fundamental excess property relation at constant pressure and composition results in the GibbsHelmholtz relation, providing an expression for the excess enthalpy:

3.2.1. Density measurements An Anton-Paar DMA 5000 vibrating tube densitometer was used to perform the density measurements. The temperature is maintained within the device to 0.01 K by a solid-state thermostat. The apparatus was calibrated with air and ultra-pure distilled, deionized, degassed water (conductivity of 19.3 lS∙m
1). The uncertainty in temperature was determined considering supplier uncertainty, calibration, accuracy, repeatability using the standard procedures of JCGM [21]. The binary mixtures were prepared gravimetrically by mixing degassed pure components using a Mettler-Toledo mass balance (model AB204-S, uncertainty of 0.0001 g) in gastight stopper vials, shaken thoroughly, and conveyed by gastight syringes. A standard uncertainty in the mixture mole fraction of u(x1) = 0.0004 was calculated using the procedure of JCGM [21] and includes uncertainty introduced by component purities. The standard operating procedure for the Anton-Paar

3

K. Moodley / J. Chem. Thermodynamics 141 (2020) 105946 Table 1 Chemical identifiers and purities. CAS-RN

Supplier

toluene

108–88-3

Sigma Aldrich

110–86-1

Sigma Aldrich

b

pyridine a b

Refractive index (RI) at 0.101 MPaa

Component

Experimental

Literature [20]

1.4942 (298.15 K) 1.5098 (293.15 K)

1.4941 (298.15 K) 1.5095 (293.15 K)

Minimum stated mass fraction purity

GC peak relative area (mass fraction purity)

0.990

0.995

0.990

0.995

Sodium D-line (Wavelength = 589 nm), Standard uncertainties u are uðRIÞ ¼ 0:0001, uðT Þ ¼ 0:01K, uðP Þ ¼ 1 kPa. Purified by molecular sieve.

DMA 5000 was followed. Density measurements were conducted three times for each mixture with a maximum deviation of 0.0025% observed among repeated runs. The standard uncertainty in density was calculated to be 0.00017 g∙cm
3 for pure components and 0.00019 g∙cm
3 for mixtures. The uncertainty in the derived excess molar volume was calculated to be u(VE) 0.0011 cm3∙mol
1. 3.2.2. Vapour-liquid equilibrium measurements Vapour-liquid equilibrium experiments were performed on the apparatus of Joseph et al. [22]. The procedure has been described in that work and in a more recent work [23]. Temperature was measured using a Pt-100 probe calibrated using a WIKA CTB 9100 and WIKA CTH 6500 kit, and the overall uncertainty in temperature was subsequently estimated as u(T) = 0.1 K considering supplier uncertainty, calibration, accuracy, repeatability and using the standard procedures of JCGM [21]. Pressure was measured with a WIKA P-10 0–100 kPa absolute transducer calibrated using a WIKA CPH 6000 unit. The overall standard uncertainty in pressure was u(P) = 0.08 kPa again using propagation of errors and the standard procedures of JCGM [21]. Phase analysis by gas chromatography was conducted in triplicate using the apparatus described above. The thermal conductivity detector used was calibrated by the area ratio method Raal and Mühlbauer [24], using gravimetry with the mass balance mentioned above. The standard uncertainty in mole fraction from the phase sampling was determined to be 0.005 using the procedures of JCGM [21] and includes uncertainty introduced by component purities, and the influence of the uncertainties of temperature and pressure.

4. Results and discussion In Table 2, the pure component vapour pressures and densities, from this work, are compared to values from the literature. A close correlation between experimental and literature data is observed. This confirms the precision and accuracy of the various measurement devices used.

Fig. 1. Experimental and correlated (exp., corr.) density for the system toluene (1) + pyridine (2) at 298.15 K (d, ─), 343.15 K (j, . . ..), 353.15 K (+. —), 363.15 K (▲,
∙
). Literature data at 298.14 K (s), 363.12 K (D), (Bratton et al. [7]).

Table 2 Experimental pure component liquid density and vapour pressures compared to data from literature. Component

Densitya

Vapour Pressureb

T/K

P/kPa

This work q/g.cm

298.15

101.3

0.86200

343.15

101.3

0.82018

353.15

101.3

0.80980

363.15

101.3

0.79990

298.15

101.3

0.97799

343.15

101.3

0.93264

353.15

101.3

0.92199

363.15

101.3

0.91140


3


3

Literature q/g∙cm

T/K

This work P/kPa

Literature P/kPa

0.86194 0.86217 0.81920 0.82030 0.80970 0.81054 0.79996 0.79970

343.1

27.15

353.0

38.60

363.2

54.30

382.7

98.30

27.11 27.15 38.63 38.68 54.32 54.38 98.27 98.31

[27] [28] [27] [28] [27] [28] [27] [28]

343.1

22.10

353.0

32.00

363.2

45.90

382.7

85.70

22.09 22.07 32.08 32.05 45.93 45.91 85.66 85.68

[37] [28] [37] [28] [37] [28] [37] [28]

toluene [25] [26] [29] [30] [31] [32] [33] [34]

pyridine

a b

Standard uncertainties u are u(T) = 0.05 K, u(P) = 1 kPa, u(q) = 0.00017 g∙cm
3. Standard uncertainties u are u(T) = 0.1 K, u(P) = 0.08 kPa.

0.97756 [35] 0.97840 [36] 0.93180 [38] 0.92195 0.92250 0.91110 0.91160

[39] [40] [38] [7]

4

K. Moodley / J. Chem. Thermodynamics 141 (2020) 105946

Densities for the (toluene + pyridine) system at 298.15 and 363.15 K have been reported previously in the literature. These are compared to experiments performed in this work in Fig. 1. Again, a close correlation was observed which confirms the experimental procedure for mixture density measurements. The density data at previously unmeasured conditions are presented in Table 3 and in Fig. 1, where the correlation by the empirical model is also presented. The model parameters and RMSDq for this correlation are presented in Table 4. In Fig. 2, the deviations between the model trained in this work and the existing literature data are presented with the maximum relative deviation within 0.003. The density data were also used to calculate excess volumes for the toluene-pyridine mixture at various temperatures and compositions. These data are presented graphically in Fig. 3, along with correlations by the Redlich-Kister expansion. The model parameters for these expansions are presented in Table 3, along with the RMSDV E . A good correlation is observed, with a smoother trend in the excess volume measured in this work, in comparison to the literature data also presented in Fig. 3. This is likely due to the greater accuracy of the device used in this work for measurement, in comparison to the older techniques used in the previously reported literature data. The excess volume increases with increasing temperature, and changes from exhibiting a minimum at 298.15 K to duel local maxima at higher temperatures. This behaviour is attributed to possible van der Waals forces at lower temperatures that may cause the mixture molecules to occupy a smaller volume. With increasing temperature, the molecules have a higher average energy and hence may cause each other to occupy more space than in the pure state. The excess volumes are also compared to data available in the literature in Fig. 3. There is a

significant discrepancy with the data of Liu et al. [10]. This is attributed to the differences in the technique used (a dilatometer was used in that work). A reasonable correlation is observed with the data of Bratton et al. [7]. The vapour-liquid equilibrium data for the (toluene + pyridine) system at 343.1, 353.05, 363.2 and 382.7 K are presented in Table 5 and Figs. 4 and 5.

Fig. 2. Deviations between literature and model calculated (Eq. (5)) densities, 298.14 K Bratton et al. [7] (s), approximately 363.12 K Bratton et al. [7] (h).

Table 3 Measured and regressed liquid densities for the toluene (1) + pyridine (2) system at 0.101 MPa.a Composition

Experimental density/(g∙cm3)

x1

T/K 298.15

343.15

353.15

363.15

0 0.0755 0.1566 0.2541 0.3573 0.461 0.5802 0.6811 0.7716 0.8588 1

0.97799 0.96721 0.95604 0.94340 0.93060 0.91837 0.90490 0.89392 0.88441 0.87560 0.86200

0.93264 0.92158 0.91062 0.89832 0.88591 0.87407 0.86100 0.85032 0.84110 0.83272 0.82018

0.92199 0.91069 0.89961 0.88731 0.87499 0.86318 0.85013 0.83945 0.83037 0.82209 0.80980

0.91140 0.89997 0.88884 0.87648 0.86428 0.85257 0.83963 0.82908 0.82008 0.81193 0.79990

a Standard uncertainty (u) in pressure is u(P) = 1 kPa, Standard uncertainty (u) in density is u(q) = 0.00019 g∙cm
3, Standard uncertainty (u) in composition is u(x1) = 0.0004, Standard uncertainty (u) in temperature is u(T) = 0.05 K.

Table 4 Fitting parameters for liquid density and excess volume correlations for the toluene (1) + pyridine (2) system. Density correlation (Eq. (5)) (g∙cm
3)

b1
1.84477E
07 b5 7.16942E
04

Excess volume correlation (Eq. (11)) (cm3.mol
1)

x1;21

b2 2.20629E
04 b6
8.09295E
04

x2;21

b4
1.35075E
06 b8 1.14580E+00

RMSDq 5.137E
04 (g∙cm
3)

x4;21

x5;21

RMSDV E (cm3∙mol
1)

8.74116E
02
1.34822E
02
2.68739E
01
2.26446E
01


2.10801E
01 6.31930E
02
1.72140E
01
3.26076E
01

1.460E
03 2.393E
03 1.679E
03 1.105E
03

b3
2.72397E
02 b7
9.51753E
04

x3;21

T = 298.15 K
7.97197E
01
1.25789E
01 3.29197E
01 T = 343.15 K
5.31311E
01
4.91490E
03 7.99830E
01 T = 353.15 K
3.81708E
01 6.02101E
02 1.12939E+00 T = 363.15 K
2.23241E
01
2.41382E
03 1.34994E+00 2 31=2 0 2 E exp E calc 6P @ V k
V k Þ 5 RMSDV E ¼ 4 N2 , where N2 equals the number of experimental compositions. k N2

5

K. Moodley / J. Chem. Thermodynamics 141 (2020) 105946

Fig. 3. Excess volume and correlation for the system toluene (1) + pyridine (2) at (exp., corr.) 298.15 K, (d,
∙∙
), 343.15 K (r,
∙
), 353.15 K (▲,


), 363.15 K (j, ∙∙∙∙). Literature data at 298.14 (s), (Bratton et al. [7]), at 298.14 (), (Woycicki and Sadowska [9]), at 298.15 (+), (Liu et al. [10]), at 363.12 (h), (Bratton et al. [7]).

The VLE data were correlated with the Non-Random Two-Liquid + Hayden and O’Connell (NRTL-HOC) and Universal Quasichemical Activity Coefficient + Hayden and O’Connell (UNIQUAC-HOC) model combinations. This is also presented in Figs. 4 and 5. The model parameters, root mean square deviation in pressure (RMSDP) and absolute average deviation in vapor composition (dy1 ) are presented in Table 6. The UNIQUAC-HOC was found to provide a slightly superior fit to the experimental data than the NRTL-HOC combination with fixed non-randomness parameter (a12). The experimental data has passed the area and point tests [15,41] with conditions of 0.02 and 0.01 tolerance respectively. These results are summarized in Table 7 and residual plots are provided in the supplementary data. The system is highly non-ideal and exhibits an azeotrope at all temperatures considered that shifts toward the pyridine rich region with increasing temperature. Some isobaric data at similar conditions were available in the literature for the (toluene + pyridine) system and isothermal systems at approximately 333.13 K, (Jose et al. [6]), 363 K (Bratton et al. [7]), at 373.12 K (Rogalski et al. [8]). This data is also presented in Figs. 4 and 5 for comparison. There is approximately a 0.1 kPa difference between the literature data from isobaric measurements and this work. This difference is attributed to

Fig. 4. Vapour-liquid equilibrium data for the system toluene (1) + pyridine (2). (Px1, P-y1) at: 343.1 K (d, s), 353.0 K (j, h). UNIQUAC-HOC model correlation (P-x1, P-y1) at: 343.1 K ( , –), 353.0 K ( , – – –). Data of Krasavin et al. [3] at 343.15 K (, +), data of Jose et al. [6] at 333.15 K (r).

Fig. 5. Vapour-liquid equilibrium data for the system toluene (1) + pyridine (2). (Px1, P-y1) at: 363.2 K (d, s) (left axis), 382.7 K (j, h) (right axis). UNIQUAC-HOC model correlation (P-x1, P-y1) at: 363.2 K ( , –) (left axis), 382.7 K ( , – – –) (right axis). Data of Krasavin et al. [3] at 363.15 K (▲, D) (left axis), data of Bratton et al. [7] at 363.15 K (P-x1) () (left axis), data of Rogalski and Bylicki [8] at 373.12 K (P-x1) (+) (left axis), data of Korotkova et al. [5] at 382.52 K (P-x1) (r) (right axis).

Table 5 Experimental vapour-liquid equilibrium data toluene (1) + pyridine (2) at various temperatures.a T = 343.1 K

T = 353.0 K

T = 363.2 K

T = 382.7 K

P/kPa

x1

y1

P/kPa

x1

y1

P/kPa

x1

y1

P/kPa

x1

y1

22.10 22.40 22.70 23.00 23.40 24.40 25.30 26.10 26.80 27.10 27.40 27.60 27.70 27.65 27.45 27.25 27.15

0.000 0.011 0.028 0.046 0.068 0.149 0.240 0.340 0.448 0.529 0.604 0.723 0.809 0.890 0.965 0.991 1.000

0.000 0.018 0.045 0.073 0.107 0.215 0.319 0.419 0.514 0.580 0.639 0.733 0.805 0.880 0.959 0.989 1.000

32.00 32.35 32.65 33.20 33.95 34.90 36.35 37.15 37.95 38.45 38.90 39.25 39.35 39.10 38.88 38.75 38.60

0.000 0.011 0.024 0.047 0.085 0.142 0.247 0.333 0.429 0.505 0.601 0.723 0.799 0.936 0.979 0.990 1.000

0.000 0.017 0.038 0.072 0.126 0.201 0.320 0.405 0.493 0.557 0.634 0.732 0.796 0.927 0.975 0.988 1.000

45.90 46.55 46.85 47.15 48.35 49.60 51.45 52.65 53.65 54.30 54.95 55.25 55.40 55.20 54.90 54.65 54.30

0.000 0.022 0.033 0.043 0.087 0.142 0.249 0.338 0.440 0.521 0.623 0.701 0.792 0.913 0.973 0.989 1.000

0.000 0.033 0.049 0.064 0.125 0.196 0.317 0.406 0.499 0.567 0.649 0.712 0.788 0.901 0.967 0.987 1.000

85.70 86.30 86.60 87.30 88.80 90.85 93.60 95.40 97.10 98.50 99.50 99.70 99.60 99.50 98.70 98.50 98.30

0.000 0.018 0.026 0.045 0.084 0.143 0.243 0.333 0.430 0.515 0.617 0.680 0.799 0.914 0.986 0.993 1.000

0.000 0.024 0.035 0.061 0.111 0.183 0.297 0.390 0.482 0.558 0.644 0.696 0.796 0.903 0.983 0.992 1.000

a Standard uncertainty (u) in pressure is u(P) = 0.08 kPa, Standard uncertainty (u) in composition is u(x1) = u(y1) = 0.005, Standard uncertainty (u) in temperature is u(T) = 0.1 K.

6

K. Moodley / J. Chem. Thermodynamics 141 (2020) 105946

Table 6 Regressed NRTL and UNIQUAC model parameters for the toluene (1) + pyridine (2) system. Parameter

Model NRTLa

UNIQUACb

a12, NRTL

0.6394
0.2010 0.3000 0.0113 0.0075


0.5867 0.3870 – 0.0024 0.0016

a12, NRTL

0.6898
0.2599 0.3000 0.0037 0.0014


0.6165 0.4117 – 0.0036 0.0012

a12, NRTL

0.8196
0.3597 0.3000 0.0060 0.0029


0.6949 0.4592 – 0.0055 0.0026

a12, NRTL

1.0749
0.5762 0.3000 0.0123 0.0021


0.8314 0.5484 – 0.0112 0.0016

T = 343.1 K a12 a21 RMSDP/kPac dy1d T = 353.0 K a12 a21 RMSDP/kPac dy1d T = 363.2 K a12 a21 RMSDP/kPac dy1d T = 382.7 K a12 a21 RMSDP/kPac dy1d

Fig. 6. Experimental and model calculated activity coefficients (c1-x1, c2-x1) for the toluene (1) + pyridine (2) system at: 343.1 K (d, s), 353.0 K (j, h). UNIQUAC-HOC model correlation at: 343.1 K ( , ), 353.0 K (–, – – –).

Model parameters can be related to those described in the original works by the following expressions:   a sij ¼ aij ,Gij ¼ exp aij;NRTL sij b Aij ¼ exp aij "   2 1=2 PN3 Pexp
Pcalc c k Þ k RMSDP ¼ , k N3 PN3 d

dy1 ¼ isotherm.

k

absðyexp
ycalc k Þ k , N3

where N3 are the number of experimental VLE points per

Table 7 Results of the area and point consistency tests. System

NRTL-HOC model T/K = 343.1 T/K = 353.0 T/K = 363.2 T/K = 382.7 UNIQUAC-HOC model T/K = 343.1 T/K = 353.0 T/K = 363.2 T/K = 382.7

Calculated criterion

Consistency test result

Area test D/(%)a

Point testb

0.089 0.043 0.011 0.015

0.006 0.006 0.005 0.006

Passed Passed Passed Passed

both both both both

tests tests tests tests

0.252 0.390 0.526 0.869

0.005 0.006 0.007 0.006

Passed Passed Passed Passed

both both both both

tests tests tests tests

 R  1 c1   0 lnc2 dx1    Criteria: D ¼ 100 R 1    2. lncc12 dx1 0 exp calc P jyi
yi j b Criteria: N  0:01 and random scatter of D yi and DP residuals about i¼1 N the zero axis. a

experimental uncertainty and differences in procedures/apparatuses between both studies. The data of Bratton et al. [7] at 363 K, is clearly of poor quality, and no reasonable comparison can be made to this work. The dependence of the activity coefficients on composition at each isotherm is presented in Figs. 6 and 7 and exhibits a typical trend with increasing temperature. The relative volatilities for each isotherm are presented in Fig. 8. The relative volatility trend with temperature is conventional, with a21 increasing with increasing temperature of the isotherm.

Fig. 7. Experimental and model calculated activity coefficients (c1-x1, c2-x1) for the toluene (1) + pyridine (2) system at: 363.2 K (d, s), 382.7 K (j, h). UNIQUAC-HOC model correlation at: 363.2 K ( , ), 382.7 K (–, – – –).

The experimental data and models were used to calculate the excess Gibbs energy (GE), excess enthalpy (HE) and excess entropy (SE) and are presented in Figs. 9–11. The Gibbs excess energy is positive for the entire composition range as observed in Fig. 9. Also presented in Fig. 9 is the predicted Gibbs excess energy when all four isotherms were simultaneously regressed using temperature dependent model parameters and the UNIQUAC-HOC model. The parameters are presented in the supporting information in Table S1. It is clear that the individually regressed isotherm model parameters provide a superior representation of the Gibbs excess energy, which is expected. In Fig. 10, the results of the excess enthalpy predictions are presented which were based on model predictions of the simultaneously regressed isotherms. Experimental excess enthalpy data was available in the literature at temperatures below those considered here. However, predictions were also made at the lower temperature conditions. A good correlation can be observed between predicted and experimental literature data, which confirms the fitting procedure and strengthens the confidence in the experimental VLE data.

K. Moodley / J. Chem. Thermodynamics 141 (2020) 105946

Fig. 8. Experimental and model calculated relative volatility a21 ¼

y2 x2 y1 x1

vs. x1 (exp.,

UNIQUAC-HOC model) for the toluene (1) + pyridine (2) system at: 343.1 K (d, ), 353.0 K (s, – – –) 363.2 K (j, ), 382.7 K (h, –).

7

Fig. 10. Calculated excess enthalpy (HE) for the system toluene (1) + pyridine (2) at: 298.14 ( ), 308.14 ( ), 318.13 ( ), 343.1 K (–), 353.0 K (– – –) 363.2 K (–.–.–), 382.7 K (– – –). Literature data at 298.14 K (+) (Findlay [42]), () (Woycicki and Sadowska [9]), 308.14 K (s) (Singh and Verma [43]), 318.13 K (h) (Findlay [42]).

Fig. 9. Excess Gibbs energy (GE) vs. x1 for the system toluene (1) + pyridine (2) (exp., UNIQUAC-HOC model) at: 343.1 K (d,–), 353.0 K (+, – – –) 363.2 K (j,–.–.–), 382.7 K (h, –..–..–). Black lines are based on model prediction by simultaneous fitting of all isotherms. Red lines are based on model prediction by individual fitting of each isotherm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 11. Calculated excess entropy (SE) for the system toluene (1) + pyridine (2) at: 343.1 K (–), 353.0 K (– – –) 363.2 K (–.–.–), 382.7 K (– – –).

The excess entropy was calculated from the difference between the Gibbs excess energy and the excess enthalpy. Since GE, HE and SE were found to be positive for each temperature for the entire composition range, the system conforms to the classification of Smith et al. [16] for systems where weak/negligible hydrogen bonding is exhibited.

simultaneously represents temperature and composition variation, with a root mean square deviation within the order of magnitude of the density uncertainty. The VLE data showed that the system exhibited an azeotrope at all temperatures measured. The experimental VLE data were successfully correlated by the UNIQUAC-HOC model combination with root mean square deviation in pressure and absolute average deviation in composition within experimental uncertainty. The VLE data were found to be thermodynamically consistent.

5. Conclusion Excess equilibrium and volumetric properties for the toluenepyridine system were successfully derived from experimental measurements of density and isothermal vapour-liquid equilibrium at several temperatures. Positive GE, HE and SE, were determined at the conditions measured with decreasing magnitude with increasing temperature, while VE transitioned from negative toward positive with increasing temperature. The excess volume was correlated using Redlich-Kister expansions. The density data were successfully correlated using an 8-parameter model, that

Acknowledgements This work is based upon research supported by the JW Nelson Fund awarded by the University of KwaZulu-Natal.

Notes The author declares no competing financial interest.

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JCT 2019-594