Excess Properties and Phase Equilibria for the Potential Biofuel

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Excess Properties and Phase Equilibria for the Potential Biofuel System of Propan-2-ol and 2‑Methyl-propan-1-ol at 333.15, 343.15, and 353.15 K Kuveneshan Moodley,† Carey-Lee Dorsamy,† Caleb Narasigadu,*,‡ and Youlita Vemblanathan† †

Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, Durban, 4041 South Africa ‡ Chemical Engineering Department, Faculty of Engineering, Mangosuthu University of Technology, 511 Mangosuthu Highway, Umlazi, 4031 South Africa ABSTRACT: Experimental vapor−liquid equilibrium (VLE) data using a dynamic apparatus and densities at atmospheric pressure using an Anton Paar DMA-5000 densitometer were measured for the potential biofuel system of propan-2-ol (1) + 2-methyl-propan-1-ol (2) at 333.15, 343.15, and 353.15 K. From these data, the excess properties for volume, Gibbs energy, enthalpy, and entropy were determined. The VLE data were correlated using the γ−Φ approach and non-random twoliquid activity-coefficient models. Thermodynamic consistency testing was conducted, and the VLE data passed the area and point tests. The experimental density data were modeled with an eight-parameter correlation to simultaneously represent composition and temperature. The excess volume was correlated with a Redlich−Kister expansion.

1. INTRODUCTION Biologically derived hydrocarbons are increasingly being used as fuel or fuel additives for transport and power generation and as chemical components for industrial and domestic use. Currently, biologically derived ethanol (bioethanol) is the most-popular biofuel on the market, with approximately 26.5 billion gallons being produced globally in 2016.1 In recent years, however, the potential uses of biologically derived propanols (biopropanols) and butanols (biobutanols) as alternatives to bioethanol as transportation fuel have been increasingly studied.2−4 This is because propanols and butanols have a higher carbon number and, therefore, a higher-energy density than ethanol; they are less soluble in water due to a longer nonpolar chain that lowers their corrosiveness and their propensity to absorb moisture from the atmosphere, as is the case with ethanol. Their lower hydrophilic nature, in comparison to ethanol, also makes blending with diesel and other fuels easier. More specifically, 2-methyl-propan-1-ol (isobutanol) has a motor octane number that is approximately 10% higher than nbutanol. It is also slightly less toxic than n-butanol,5 with several companies (Gevo and Dupont with BP (Butamax)) exploring different process routes for optimal production using corn- or sugar-based feed stocks. Fermentation using various types of bacteria, including Clostridium aurantibutyricum6 and Corynebacterium glutamicum,7,8 are used for 2-methyl-propan-1-ol production. Other common byproducts of these fermentation processes include acetone, ethanol, n-propanol, propan-2-ol, and n-butanol. To be incorporated into fuel blends, these product © XXXX American Chemical Society

mixtures must be chemically characterized or separated so that the target physical and chemical properties of the final fuel blend can be achieved, e.g., mixture densities, enthalpies, and vapor pressures. To characterize these fluid properties, thermodynamic excess properties for volume, enthalpy, entropy and Gibbs energy must be known. Excess properties are a convenient and practical means of quantifying nonidealities in chemical mixtures. These properties can be determined from precise density and vapor−liquid equilibrium measurements. For many of the constituent binary pairs that comprise the fermentation products from a biobutanol process mentioned above, excess-property and phase-equilibrium data are available in the literature under typical separation process conditions (323−363 K and up to atmospheric pressure).9−12 However, little data is available for the crucial system of propan-2-ol with 2-methyl-propan-1-ol. This system is of great interest as both components are a useful alternate biofuel with several superior characteristics to ethanol. However, their differences in physical and chemical properties are significant and must be accounted for in blending calculations. In this work, the density at atmospheric pressure and vapor− liquid equilibrium data for the system of propan-2-ol (1) + 2methyl-propan-1-ol (2) was measured at 333.15, 343.15, and 353.15 K. This thermodynamic data was then used to determine Received: February 2, 2018 Accepted: May 18, 2018

A

DOI: 10.1021/acs.jced.8b00103 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

δij = 2Bij − Bii − Bjj

the excess volume, excess Gibbs energy, excess enthalpy, and excess entropy at the measured conditions. The density data was modeled using an eight-parameter empirical correlation. Excess volume was correlated using Redlich−Kister expansions.13 The vapor−liquid equilibrium data was modeled using the γ−Φ approach and the non-random two-liquid (NRTL) activity coefficient model.

Bij are the second virial coefficients and were estimated by the Hayden and O’Connell correlation.15 To calculate the activity coefficients, the NRTL model was used. 2.3. Non-Random Two-Liquid model. Renon and Prausnitz16 reported the NRTL activity coefficient as: ⎡ ⎛

2. THEORY 2.1. Density and Excess Volume. The densities of most hydrocarbon components or mixtures at constant pressure conventionally decrease with temperature and increase with the increasing composition of the denser component. It is difficult to simultaneously model density, temperature, and composition, with cubic equations of state generally performing poorly for liquids. The xi−ρm−T relationship can be correlated by the following proposed empirical polynomial:

ln γi =

Gij = exp( −αijτij)

RMSD =

(1)

τij = aij + bij /T

(2)

N

VE =

(11)

where xi is the mole fraction of component i, Mi is the molar mass of component i, ρm is the density of the mixture and ρi is the density of component i. N is the total number of components in the mixture. The fundamental excess property relation is given by Smith et al.:14 ⎛ nHE ⎞ ⎛ nGE ⎞ ⎛ nV E ⎞ d⎜ ⎟d P − ⎜ 2 ⎟d T + ⎟=⎜ ⎝ RT ⎠ ⎝ RT ⎠ ⎝ RT ⎠

(3)

E

E

N

∑ ln γidni i=1

(12)

E

where G , V , and H are the excess Gibbs energy, volume, and enthalpy, respectively. ni is the total number of moles of component i. At constant temperature and pressure, the excess Gibbs energy can be determined from eq 12:

ϕî

N

GE = RT ∑ xi ln γi

(4)

(13)

i=1

When the virial equation of state, truncated to the second virial coefficient, is employed, eq 4 is expressed by: ⎡ (B − V l)(P − P sat) + Py 2 δ ⎤ ii i i j ij ⎥ Φi = exp⎢ ⎥ ⎢ RT ⎦ ⎣

∑ xiV(i ρm−1 − ρi−1) i=1

In the above equation, yi and xi are the vapor and liquid mole fractions, respectively; P is the total pressure of the system; and Psat i is the vapor pressure of the pure component i. γi is the activity coefficient of species, i, in the liquid phase, and Φi is a correction factor for the vapor phase, given by: ⎡ −V l(P − P sat) ⎤ i i ⎥ ⎢ exp ⎥⎦ ϕisat ⎢⎣ RT

(10)

where aij and bij are adjustable fitting parameters. 2.4. Excess Properties. The experimental excess molar volumes can be calculated from the experimental densities using the following expression:

and calculated densities, respectively, of the data point k, and Q is the total number of data points measured. 2.2. Vapor−Liquid Equilibrium. The criterion for phaseequilibrium states that the fugacities of a component in each phase at equilibrium must be equal. Smith et al.14 for instance show that the following expression can be derived for VLE systems at low pressures:

Φi =

(9)

RT

In eq 9, T is the temperature in Kelvin and R is the universal gas constant in J mol−1·K−1. The cross-interaction parameters (gij− gii) are determined by regression of experimental phaseequilibrium data. It has been recommended by Walas17 that the nonrandomness parameter αij be set to a value of 0.3 for nonaqueous systems, although this parameter can be regressed if it provides a superior fit to the experimental data. A temperature-dependent τij can be incorporated for simultaneous representation of multiple isotherms:

calc where ρexp k and ρk are the experimental

yi ΦiP = xiγiPisat

(8)

gij − gjj

τij =

⎛⎛ ρ exp − ρ calc ⎞2 ⎞1/2 ⎜⎜ k ρ exp k ⎟ ⎟ ⎠⎠ ⎝⎝ k Q

(7)

and

where ρm is the mixture density in kg·m−3, xi is the mole fraction of component 1, T is the temperature in Kelvin and βi (i = 1···8) are the model fitting parameters. This type of empirical correlation is useful to provide continuous P−V−T functions for further correlation by theoretically superior models such as cubic equations of state, associating fluid theory, etc. The model parameters were determined via regression by minimizing the following objective function (root-mean-square deviation, RMSD): Q ∑k

⎞⎤ ⎞2 ⎛ τijGij ⎟⎥ ⎟⎟ + ⎜⎜ 2 ⎟⎥ x x G + x x G ( + ) j ji ⎠ ⎝ j i ij ⎠⎦ ⎣ ⎝ i Gji

xj2⎢τji⎜⎜ ⎢

where:

ρm (x1 , T ) = (β1T 2 + β2T + β3)x12 + (β4 T 2 + β5T + β6)x1 + β7T + β8

(6)

Alternatively, if constant pressure and composition is assumed in eq 12, then the Gibbs−Helmholtz relation results: ⎛ nGE ⎜ ∂ RT HE = −RT 2⎜ ⎜ ∂T ⎝

( ) ⎞⎟⎟

(5)

where: B

⎟ ⎠P , x

i

(14) DOI: 10.1021/acs.jced.8b00103 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 1. Chemical Suppliers and Purities refractive index (RI) at 293.15 K and 0.101 MPaa component

CAS RN

supplier

experimental

literatureb

minimum stated mass-fraction purity

GC peak relative area (mass fraction purity)

propan-2-olc 2-methyl-propan-1-olc

67-63-0 78-83-1

Sigma-Aldrich Sigma-Aldrich

1.3774 1.3962

1.3776 1.3960

≥0.990 ≥0.990

0.9999 0.9999

a

Standard uncertainties, u. are u(RI) = 0.0001, u(T) = 0.01K, u(P) = 0.0002 MPa. bLide19 at 293.15 K. cPurified by molecular sieving,

Table 2. Comparison of Pure Component Density and Vapor Pressures to Literature Valuesa density component propan-2-ol

2-methyl-propan-1-ol

a

T/K

P/kPa

333.15

101.3

vapor pressure this work ρ/g·cm

−3

−3

literature ρ/g·cm

38.428

343.15

61.1

0.739 46

353.15

101.3

0.729 10

0.728324

353.15

92.3

333.15

101.3

0.769 49

333.15

12.3

343.15

101.3

0.760 79

343.15

20.5

20.614

353.15

101.3

0.751 86

0.769 3030 0.770 62931 0.769 4432 0.769 4627 0.760 3030 0.761 27931 0.752 22131

60.528 60.729 92.228 92.629 12.314

353.15

32.7

32.914

HE − GE T

38.629

23

2014 Plus with a 4 m × 1/8 in. stainless-steel CRS Porapak Q packed column was used with helium as the carrier gas. The refractive indices were also determined using a ATAGO RX7000α refractometer (sodium D-line = 589 nm; temperature uncertainty from repeatability is 0.01 K) with an uncertainty of 0.0001. Refractive index measurements were carried out at 0.1013 MPa within 0.0002 MPa, confirmed by a Mensor standard model CPC6000. The alcohols were dehydrated by employing molecular sieves for 48 h prior to usage. The purities and chemical suppliers are provided in Table 1. 3.2. Experimental Procedure. Density Measurements. The binary and pure component density measurements were conducted on an Anton-Paar DMA 5000 vibrating tube densitometer. The temperature is controlled within 0.01 K in the apparatus using a solid-state thermostat. Prior to use the apparatus was calibrated with air and ultrapure distilled deionized degassed water (degassed using a Vigreux-type column). The conductivity of the water was 22.1 μS·m−1 prior to degassing. The binary mixtures were prepared synthetically by mass in gastight stopper vials and using gas-tight syringes for transfer. The sealed vials were shaken thoroughly to ensure good mixing and were used immediately. The mass balance used for the preparation was from Mettler-Toledo (model AB204-S) with a supplier uncertainty of 0.0001 g. The standard uncertainty in the mole fraction was estimated to be lower than 0.0005. The sample was then extracted from the sealed vial via a septum using a gastight syringe and loaded into the DMA 5000. After thermal equilibrium is established, the density measurement can be taken. Each density measurement was conducted in triplicate with a maximum percent difference of 0.002% between parallel runs. The standard uncertainty of the density measurement was estimated to be 0.00003 g·cm−3. The uncertainty in the excess

(15)

Excess properties can be modeled using a Redlich−Kister13 expansion. For binary systems, the expansion is given by: N

∑ ωpM,12x1x2(x1 − x2)p p=0

literature P/kPa

38.5

101.3

The excess entropy, SE, can be calculated from the excess property relation:

ME =

this work P/kPa

343.15

u(T) = 0.05 K (k = 2), u(P) = 0.1 kPa (k = 2), and u(ρ) = 0.00002 (k = 2).

SE =

T/K 333.15

0.749224 0.749 67925 0.749 0126 0.749 2527 0.738824

0.749 23

(16)

E

where M is the excess property for the binary system, N refers to the total number of Redlich−Kister binary fitting parameters, ωM p,12, where the subscript (p,12) denotes fitting parameter p between components 1 and 2. The value of p + 2 gives the order of the Redlich−Kister expansion, and xi is the component mole fraction of the mixture. The ωM p, 12 parameters have different units depending on the property (M) being modeled. 2.5. Thermodynamic Consistency Tests. Because the vapor−liquid equilibrium can be characterized by fixing any three of the parameters (pressure, temperature, liquid composition, and vapor composition), it is possible to calculate any one of the four parameters from a data set if the other three parameters are known. These methods are termed thermodynamic consistency testing and impose that the Gibbs−Duhem relation is satisfied. Some of the most-common and most-useful consistency tests are the area13 and point tests.18

3. MATERIALS AND METHODS 3.1. Materials. The alcohols used were reagent-grade (>0.99 mass fraction), and purities were confirmed by gas chromatography using a thermal conductivity detector. A Shimadzu GC C



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Table 3. Experimental and Calculated Densities for Propan-2-ol (1) + 2-Methyl-propan-1-ol (2) at 0.101 MPaa density (g·cm3) composition

experimental

correlation (eq 1)

T/K

T/K

x1

333.15

343.15

353.15

333.15

343.15

353.15

0.0000 0.0420 0.1428 0.1913 0.2906 0.3911 0.4444 0.4993 0.5485 0.5940 0.6911 0.7445 0.8481 0.8925 0.9491 1.0000

0.769 49 0.768 80 0.767 10 0.766 26 0.764 49 0.762 62 0.761 60 0.760 52 0.759 52 0.758 58 0.756 50 0.755 31 0.752 91 0.751 85 0.750 48 0.749 23

0.760 79 0.760 07 0.758 28 0.757 39 0.755 53 0.753 57 0.752 49 0.751 36 0.750 32 0.749 33 0.747 14 0.745 88 0.743 36 0.742 24 0.740 78 0.739 46

0.751 86 0.751 10 0.749 19 0.748 25 0.746 26 0.744 18 0.743 03 0.741 83 0.740 72 0.739 66 0.737 33 0.735 99 0.733 30 0.732 10 0.730 53 0.729 10

0.769 53 0.768 86 0.767 21 0.766 37 0.764 60 0.762 72 0.761 68 0.760 59 0.759 58 0.758 64 0.756 55 0.755 36 0.752 99 0.751 94 0.750 58 0.749 33

0.760 71 0.760 02 0.758 28 0.757 41 0.755 55 0.753 57 0.752 48 0.751 33 0.750 27 0.749 27 0.747 07 0.745 82 0.743 32 0.742 21 0.740 78 0.739 46

0.751 90 0.751 16 0.749 31 0.748 39 0.746 41 0.744 30 0.743 14 0.741 92 0.740 79 0.739 72 0.737 38 0.736 04 0.733 37 0.732 19 0.730 65 0.729 24

a Standard uncertainty (u) in pressure is u(P) = 0.0003 MPa. Standard uncertainty in density is u(ρ) = 0.00003 g·cm−3. Standard uncertainty in composition is u(x1) = 0.0005. Standard uncertainty in temperature is u(T) = 0.05 K.

Figure 1. (a) Experimental density for the system propan-2-ol (1) + 2-methyl-propan-1-ol (2) at 333.15 (▲), 343.15 (⧫), and 353.15 K (●). Literature data at 333.15 (Δ) is from Kermanpour et al.,27 and (○) Toropov.34 (b) Deviations between literature data and densities calculated by eq 1 (Δ, deviation from Kermanpour et al.)27 and ○ (deviation from Toropov).34

used. The overall standard uncertainty in composition was estimated to be 0.005 mole fraction from calibration. A MettlerToledo (model AB204-S) mass balance with a supplier uncertainty of 0.0001 g was used to prepare the standard samples. All uncertainties were determined using the guidelines of Taylor and Kuyatt.23

molar volume derived from density measurements was estimated to be 0.0002 cm3·mol−1. Vapor−liquid Equilibrium Measurements. The VLE measurements were conducted using a dynamic-analytical glass apparatus available in our laboratories. The equipment is a replica of that presented by Joseph et al.;20,21 however, temperature is controlled manually and has been used in our group for many years. Temperature was measured using a Pt-100 temperature probe. The overall standard uncertainty in temperature for VLE measurements was 0.05 K, determined by calibration using a WIKA CTB 9100 and WIKA CTH 6500 calibration kit. A WIKA P-10 0-100 kPa absolute transducer was used for the pressure measurements. The transducer was calibrated using a WIKA CPH 6000 unit. The overall standard uncertainty in pressure was 0.1 kPa. Phase samples were analyzed using a Shimadzu GC 2014 Plus with a 4 m × 1/8 in. stainless steel CRS Porapak Q packed column and helium as the carrier gas. The area-ratio method described by Raal and Muhlbauer22 was used for the calibration of the thermal conductivity detector

4. RESULTS AND DISCUSSION The pure component density and vapor pressures for the components considered in this work are presented in Table 2. It can be seen that there is a close correlation between the literature data and those measured in this work. The binary mixture density data for the propan-2-ol (1) + 2-methyl-propan-1-ol (2) measured in this work are presented in Table 3 and in Figure 1a, along with literature data that was measured at 333.15 K. An excellent correlation between the literature mixture density data at 313.2 K and the data measured in this work is evident. The density data was correlated with eq 1. The correlation parameters are presented in Table 4 along with RMSD between the D



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Table 4. Regressed Parameters for Density and Excess Volume Correlations density correlation (eq 1)

excess volume correlation (eq 16) T = 333.15 K T = 343.15 K T = 353.15 K

β1 −4.100 00 × 10−07 β5 8.298 61 × 10−04 ω1,12

β2 2.448 83 × 10−04 β6 −1.439 11 × 10−01 ω2,12

β3 4.066 43 × 10−02 β7 −8.815 00 × 10−04 ω3,12

−1.011 208 × 10−01 −1.237 287 × 10−01 −1.517 659 × 10−01

−9.306 656 × 10−03 −2.121 252 × 10−02 −3.983 122 × 10−02

4.186 262 × 10−02 3.840 507 × 10−02 3.408 428 × 10−02

β4 −1.335 00 × 10−06 β8 1.063 20 × 1000

RMSD 9.037 × 10−05

RMSD 1.918 × 10−03 2.275 × 10−03 1.970 × 10−03

Figure 2. (a) Excess volume for the system propan-2-ol (1) + 2-methyl-propan-1-ol (2) at 333.15 (▲), 343.15 (⧫), and 353.15 K (●). Literature data at 333.15 K (Δ, Kermanpour et al.27; ○, Toropov).34 (b) Deviations between literature data and excess volumes calculated by eqs 1 and 11 (Δ, deviation from Kermanpour et al.;27 ○, deviation from Toropov).34

Table 5. Experimental Vapor−Liquid Equilibrium Data Propan-2-ol (1) and 2-Methyl-propan-1-ol (2) at Various Temperaturesa T = 333.15 K

T = 343.15 K

T = 353.15 K

P (kPa)

x1

y1

γ1

γ2

P (kPa)

x1

y1

γ1

γ2

12.3 14.1 16.6 17.8 19.3 20.5 21.9 23.0 23.9 25.7 28.5 31.6 33.5 34.6 35.5 37.0 38.5

0.0000 0.0515 0.1299 0.1698 0.2192 0.2598 0.3117 0.3546 0.3895 0.4605 0.5803 0.7187 0.7909 0.8390 0.8731 0.9380 1.0000

0.0000 0.1695 0.3521 0.4235 0.4992 0.5499 0.6073 0.6470 0.6773 0.7319 0.8061 0.8794 0.9130 0.9341 0.9484 0.9752 1.0000

− 1.2066 1.1699 1.1543 1.1428 1.1282 1.1094 1.0911 1.0806 1.0621 1.0294 1.0053 1.0055 1.0016 1.0026 1.0002 1.0000

1.0000 1.0021 1.0033 1.0033 1.0048 1.0118 1.0142 1.0211 1.0254 1.0366 1.0687 1.0996 1.1314 1.1495 1.1717 1.2013 −

21.0 23.7 27.8 30.6 33.0 34.8 35.9 37.3 40.1 43.4 47.8 50.0 52.5 54.5 57.1 59.4 61.1

0.0000 0.0494 0.1298 0.1873 0.2370 0.2803 0.3087 0.3485 0.4145 0.5098 0.6350 0.6991 0.7638 0.8175 0.8870 0.9507 1.0000

0.0000 0.1589 0.3420 0.4414 0.5121 0.5623 0.5902 0.6268 0.6864 0.7546 0.8281 0.8600 0.8920 0.9178 0.9503 0.9785 1.0000

− 1.2470 1.1982 1.1811 1.1653 1.1418 1.1225 1.0982 1.0868 1.0500 1.0200 1.0060 1.0040 1.0020 1.0015 1.0010 1.0000

1.0000 1.0011 1.0031 1.0051 1.0061 1.0101 1.0152 1.0204 1.0256 1.0362 1.0749 1.1100 1.1469 1.1725 1.1989 1.2400 −

P (kPa)

x1

y1

γ1

γ2

32.7 38.1 45.4 49.0 53.7 56.3 59.5 61.0 68.5 74.3 79.9 83.4 86.4 88.7 90.5 92.3

0.0000 0.0571 0.1481 0.1958 0.2678 0.3099 0.3610 0.3944 0.5470 0.6403 0.7389 0.8162 0.8733 0.9187 0.9578 1.0000

0.0000 0.1867 0.3820 0.4571 0.5483 0.5903 0.6372 0.6612 0.7661 0.8192 0.8705 0.9083 0.9358 0.9578 0.9779 1.0000

− 1.3497 1.2687 1.2393 1.1912 1.1619 1.1378 1.1080 1.0394 1.0299 1.0198 1.0055 1.0031 1.0019 1.0011 1.0000

1.0000 1.0050 1.0072 1.0116 1.0131 1.0221 1.0331 1.0436 1.0816 1.1421 1.2119 1.2725 1.3388 1.4080 1.4494 −

a

Standard uncertainty (u) in pressure is u(P) = 0.0001 MPa. Standard uncertainty in composition is u(x1) = 0.005. Standard uncertainty in temperature is u(T) = 0.05 K.

experimental and correlated densities. Deviations between literature data and those calculated by eq 1 are shown in Figure 1b. The excess volumes calculated according to eq 11 are presented in Figure 2a. It can be seen that the calculated excess volume at 313.15 K corresponds well with data from the literature, as shown in Figure 2b. The mixture volume is less than the ideal volume in the temperature range considered here, and

the excess volume tends to increase with increasing temperature, with a minimum value at approximately x1 = 0.55. This implies that the molecules of the mixture occupy less volume than the weighted sum of the pure components. This result is expected and is common for hydrogen-bonding and -associating molecules. The excess volumes were correlated using a Redlich−Kister expansion. These fitting parameters are presented in Table 4. E



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The vapor−liquid equilibrium data for the propan-2-ol (1) + 2-methyl-propan-1-ol (2) system at 333.15, 343.15, and 353.15 K are presented in Table 5 and in Figure 3. This data was modeled

Figure 4. Excess Gibbs energy for the system consisting of propan-2-ol (1) + 2-methyl-propan-1-ol (2) at 333.15 (), 343.15 (····), and 353.15 K (- - - -). Figure 3. Vapor−liquid equilibrium data for the system propan-2-ol (1) + 2-methyl-propan-1-ol (2). (P-x1, P-y1) at 333.15 K (▲ and Δ), 343.15 K (⧫ and ◊), and 353.15 K (● and ○). NRTL model correlation (P-x1, P-y1) at: 333.15 K ( and − − − in black), 343.15 K (··· and -·-·- in black), and 353.15 K (- - - - and -··-··- in black). UNIFAC model prediction (P-x1, P-y1) at 333.15 K ( and − − − in red), 343.15 K (··· and -·-·- in red), and 353.15 K (- - - and -··-··- in red). Data from Oracz35 (P-x1, P-y1, calculated based on the assumption of ideal liquid) at 313.15 K (+, × ).

with the NRTL model in combination with the Hayden and O’Connell15 correlation. The calculated model parameters are presented in Table 6. The area and point thermodynamic Table 6. Regressed NRTL Model Parameters

a

parameter

system

a12 a21 b12 /K b21/K α12 RMSD/kPa δy1a

propan-2-ol (1) + 2-methyl-propan-1-ol (2) 0.13507 0.12813 −7.9984 −10.1584 −3.2200 0.4716 0.0033

Figure 5. Excess enthalpy (expressed as HE/T2) for the system consisting of propan-2-ol (1) + 2-methyl-propan-1-ol (2) at 333.15 (), 343.15 (····), and 353.15 K (- - - -). Literature data for the system consisting of ethanol (1) + propan-2-ol (2) at 298.15 K (○, Nagata et al.).33

calc Average absolute deviation: δy1 = abs(yexp 1 − y1 )/N.

consistency tests were applied to the measured data, and the data were found to be thermodynamically consistent. The system exhibits a small positive deviation from Raoult’s law. This is consistent with the fact that the two components considered here are very similar in chemical nature. UNIFAC model predictions were also carried out and show that there is a significant difference between the predicted and experimental data. Also presented in Figure 3 is the isothermal VLE data or Oracz35 for the propan-2-ol (1) + 2-methyl-propan-1-ol (2) system at 313.15 K for comparison of the data trend with temperature. The data measured here conform to this trend. The excess Gibbs energy, excess enthalpy, and excess entropy were calculated from the experimental data using eqs 13−15. These results are presented in Figures 4−6. The Gibbs excess energy is positive for the entire composition range. It can be seen in Figure 5 that the calculated excess enthalpy is negative, indicating a lower mixture enthalpy than the idealmixture enthalpy. The excess entropy is also negative. This type of behavior is categorized by Smith et al.,14 as is typical for

Figure 6. Excess entropy (expressed as TSE) for the system consisting of propan-2-ol (1) + 2-methyl-propan-1-ol (2) at 333.15 (), 343.15 (····), and 353.15 K (- - - -).

mixtures of two associating components, such as the alcohol− alcohol mixture considered here. Experimental excess enthalpy measurements via calorimetry were not available in the literature for the studied system; however, measurements for the system ethanol (1) + propan-2ol (2) was found in the literature.33 Because the ethanol (1) + propan-2-ol (2) system is also a low-molecular-weight alcohol− alcohol system and was measured in reasonably close temperature range to this work, it is expected that the behavior of the F



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Propanol-Propanol, and 2-Propanol-2-Butyl Alcohol Systems. Ind. Eng. Chem. 1952, 44, 2450−2453. (11) Wang, J.; Bao, Z. Investigation on Vapor−liquid Equilibrium for 2-propanol+1-butanol+1-Pentanol at 101.3 kPa. Fluid Phase Equilib. 2013, 341, 30−34. (12) Tamir, A.; Wisniak, J. Vapor-Liquid Equilibriums of IsobutanolN-Butanol and Isopropanol-Sec-Butanol Systems. J. Chem. Eng. Data 1975, 20, 391−392. (13) Redlich, O.; Kister, a. T. Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345−348. (14) Smith, J. M.; Van Ness, H. C.; Abbott, M. M. Introduction to Chemical Engineering Thermodynamics; McGraw-Hill: New York, 2005. (15) Hayden, J. G.; O’Connell, J. P. A Generalized Method for Predicting Second Virial Coefficients. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 209−216. (16) Renon, H.; Prausnitz, J. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135−144. (17) Walas, S. M. Phase Equilibria in Chemical Engineering; Butterworth: Boston, 1985. (18) Van Ness, H. C.; Byer, S. M.; Gibbs, R. E. Vapor-Liquid Equilibrium: Part I. An Appraisal of Data Reduction Methods. AIChE J. 1973, 19, 238−244. (19) Lide, D. R. CRC Handbook of Chemistry and Physics 86TH ed. 2005−2006; CRC Press: Boca Raton, FL, 2005. (20) Joseph, M.; Raal, J.; Ramjugernath, D. Phase Equilibrium Properties of Binary Systems with Diacetyl from a Computer Controlled Vapour−liquid Equilibrium Still. Fluid Phase Equilib. 2001, 182, 157− 176. (21) Joseph, M. A.; Ramjugernath, D.; Raal, J. D. Computer-Aided Measurement of Vapour-Liquid Equilibria in a Dynamic Still at SubAtmospheric Pressures. Dev. Chem. Eng. Miner. Process. 2002, 10, 615− 637. (22) Raal, J. D.; Mühlbauer, A. L. Phase Equilibria: Measurement and Computation; Taylor and Francis, Bristol, England, 1998. (23) Taylor, B. N.; Kuyatt, C. E. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results. Technology 1994, 1297, 2. (24) Alaoui, F. E. M.; Montero, E. A.; Bazile, J.-P.; Aguilar, F.; Boned, C. Liquid Density of Oxygenated Additive 2-Propanol at Pressures up to 140 MPa and from 293.15K to 403.15K. J. Chem. Thermodyn. 2012, 54, 358−365. (25) Yang, F.; Wang, X.; Wang, W.; Liu, Z. Densities and Excess Properties of Primary Amines in Alcoholic Solutions. J. Chem. Eng. Data 2013, 58, 785−791. (26) Coquelet, C.; Valtz, A.; Richon, D.; de la Fuente, J. C. Volumetric Properties of the Boldine + Alcohol Mixtures at Atmospheric Pressure from 283. 15 to 333. 15 K A New Method for the Determination of the Density of Pure Boldine. Fluid Phase Equilib. 2007, 259, 33−38. (27) Kermanpour, F.; Niakan, H. Z.; Sharifi, T. Density and Viscosity Measurements of Binary Alkanol Mixtures from (293.15 to 333.15) K at Atmospheric Pressure. J. Chem. Eng. Data 2013, 58, 1086−1091. (28) DDBST. Software and Separation Technology GmbH; Dortmund Data Bank (DDB): Oldenburg, Germany, 2012. (29) Biddiscombe, D. P.; Collerson, R. R.; Handley, R.; Herington, E. F. G.; Martin, J. F.; Sprake, C. H. S. 364. Thermodynamic Properties of Organic Oxygen Compounds. Part VIII. Purification and Vapour Pressures of the Propyl and Butyl Alcohols. J. Chem. Soc. 1963, 1954. (30) Fukuchi, K.; Ogiwara, K.; Tashima, Y.; Yonezawa, S.; Arai, Y. Measurement and Correlation of Densities for Liquids and Their Mixtures. Ube Kogyo Koto Senmon Gakko Kenkyu Hokoku 1983, 29, 93− 111. (31) Iglesias-Silva, G. A.; Bravo-Sánchez, M.; Estrada-Baltazar, A.; Bouchot, C.; Hall, K. R. P − ρ− T Data for 1-Butanol and Isobutyl Alcohol from (283.15 to 363.15) K at Pressures up to 66 MPa. J. Chem. Eng. Data 2015, 60, 1076−1090. (32) Bravo-Sánchez, M. G.; Iglesias-Silva, G. A.; Estrada-Baltazar, A.; Hall, K. R. Densities and Viscosities of Binary Mixtures of N -Butanol

excess enthalpy for the propan-2-ol (1) + 2-methyl-propan-1-ol (2) mixture would be similar to the ethanol (1) + propan-2-ol (2) system. This was found to be the case, as was also presented in Figure 5.

5. CONCLUSIONS Essential thermodynamic excess properties were derived from experimental vapor−liquid equilibrium and mixture density data for the potential biofuels propan-2-ol and 2-methyl-1-propanol at 333.15, 343.15, and 353.15 K. The excess volume was found to be negative in the temperature range considered. The vapor−liquid mixture tended to deviate slightly from Raoult’s law (positive deviation) and was found to be thermodynamically consistent. The excess Gibbs energy was found to be positive in the temperature range considered here. The excess enthalpy and entropy were derived from the experimental VLE data and were found to be negative for the temperature range considered here. This excess property behavior is typical for mixtures of two associating components.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +27-31-907-7378. ORCID

Caleb Narasigadu: 0000-0001-9224-136X Funding

This work is based on research supported by Sasol R&D Ltd. Notes

The authors declare no competing financial interest.

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REFERENCES

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Excess Properties and Phase Equilibria for the Potential Biofuel

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