Volumetric Study of the Mixtures n-Hexane + Isomeric Chlorobutane

Article pubs.acs.org/JPCB

Volumetric Study of the Mixtures n‑Hexane + Isomeric Chlorobutane: Experimental Characterization and Volume Translated Peng− Robinson Predictions Hernando Guerrero, Pilar Cea, Ignacio Gascón, Félix M. Royo, and Carlos Lafuente* Departamento de Química Física, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain S Supporting Information *

ABSTRACT: The pρTx behavior of the binary mixtures nhexane + isomeric chlorobutane has been studied over the whole composition range at temperatures between 283.15 and 323.15 K and pressures from 0.1 to 65.0 MPa. Experimental densities have been used to obtain different excess properties: excess molar volume, excess isobaric expansibility, excess isothermal compressibility, and excess internal pressure. These excess properties have been analyzed in terms of molecular interactions and structural effects. Finally, experimental densities of the binary mixtures have been compared with the predictions of the volume translated Peng−Robinson (VTPR) model. The overall average deviation between experimental and calculated densities is 0.00427 g·cm−3, which can be considered reasonably good predictions.

1. INTRODUCTION The study of the volumetric behavior of pure liquids and liquid mixtures at different pressures and temperatures provides experimental information of great interest. Among other thermodynamic data, density and derived properties are essential for an accurate design of industrial plants and pumping systems; however, the experimental measurement of these properties over a wide range of pressures and temperatures is not always feasible due to the economic and time-consuming costs. Consequently, the development of equations of state and theoretical models that allow the correct prediction of these properties is needed for process design. In this sense, the measurement of new experimental data allows the evaluation of predictive models. Here, we report the pρTx behavior of the binary mixtures formed by n-hexane and each one of the isomers of chlorobutane. Moreover, experimental densities have been compared with the predictions obtained with the volume translated Peng−Robinson group contribution equation of state (VTPR model),1−3 which combines the volume-translated Peng−Robinson equation of state4,5 with the UNIFAC group contribution model.6,7 Over the last years we have studied the volumetric and acoustic behavior8 and viscosity9 of the binary mixtures nhexane + isomeric chlorobutane at atmospheric pressure and three temperatures T = (283.15, 298.15, and 313.15) K. We also have analyzed the volumetric properties of the isomers of chlorobutane in the temperature range 283.15−328.15 K and pressures between 0.1 and 65.0 MPa.10 In this work, we extended our study to the pρT behavior of the pure n-hexane and the binary mixtures n-hexane + isomeric chlorobutane. © 2013 American Chemical Society

Densities of the pure n-hexane have been measured in the same range of pressures and temperatures as isomers of chlorobutane and have been correlated with temperature and pressure using the well-known Tait equation.11 Densities of the four binary mixtures were measured over the whole composition range at temperatures between 283.15 and 323.15 K and pressures from 0.1 to 65.0 MPa. Experimental densities of the binary mixtures and their pure components have been used to calculate excess molar volumes, excess isobaric expansibilities, excess isothermal compressibilities, and excess internal pressures. These excess properties have been analyzed in terms of molecular interactions and structural effects in the mixtures. The literature revision on these systems has provided several works involving densities at atmospheric pressure of the mixture n-hexane + 1-chlorobutane12−15 but only one reference for pVTx measurements. The work of Gołdon et al.16 presents the densities and excess volumes of the system n-hexane + 1chlorobutane at several temperatures and pressures up to 35.0 MPa.

2. EXPERIMENTAL SECTION The following liquids used in this study were obtained from Aldrich: n-hexane, 1-chlorobutane, 2-chlorobutane, and 2chloro-2-methylpropane (>0.99 in mass fraction). On the other hand, 1-chloro-2-methylpropane (>0.99 in mass fraction) Received: July 24, 2013 Revised: August 7, 2013 Published: August 9, 2013 10284

dx.doi.org/10.1021/jp407380a | J. Phys. Chem. B 2013, 117, 10284−10292

The Journal of Physical Chemistry B

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Table 1. Parameters of the Tait Equation and Standard Deviations, σ(ρ), for all the Compounds Studied A0/g·cm−3

compound n-hexane 1-chlorobutane 2-chlorobutane 1-chloro-2-methylpropane 2-chloro-2-methylpropane

0.84219 1.15393 1.14034 1.15932 1.14432

A1/g·cm−3·K−1

A2/g·cm−3·K−2

−4

−7

−3.435 −7.176 −6.963 −7.832 −8.329

× × × × ×

10 10−4 10−4 10−4 10−4

−9.5 −6.65 −7.35 −6.08 −6.65

× × × × ×

10 10−7 10−7 10−7 10−7

C

B0/MPa

B1/MPa·K−1

B2/MPa·K−2

σ(ρ)/g·cm−3

0.09123 0.0887 0.0885 0.0874 0.0883

302.80 388.38 361.41 401.61 403.37

−1.1905 −1.5257 −1.4305 −1.6878 −1.8340

0.0011800 0.0015551 0.0014601 0.0018730 0.0022015

0.00023 0.00009 0.00015 0.00027 0.00027

where n is the number of experimental data and p the number of parameters used. The number of these parameters was chosen to minimize the standard deviations. The fitted parameters along with the standard deviation for n-hexane and for isomers of chlorobutane10 have been collected in Table 1. The standard deviation obtained is 0.00023 g·cm−3, and the deviations between experimental and correlated densities are close to the uncertainty of the experimental densities and randomly distributed. In this table, the corresponding information for the isomeric chlorobutanes has been also included. Experimental n-hexane densities together with correlated values using the Tait equation are shown in Figure 1.

was provided by Fluka. All the liquids were used without further purification. The mixtures were prepared by mass using a Sartorious semimicrobalance CP225-D with a precision of ±1 × 10−5 g. The maximum estimated error in the mole fraction is ±1 × 10−4. Densities of the pure n-hexane and the four binary mixtures n-hexane + isomeric chlorobutane were measured using a highpressure, high-temperature Anton Paar DMA HP cell connected to an evaluation unit Anton Paar DMA 5000. The density is determined by measuring the oscillation period of the U-shaped tube made from Hastelloy C-276 gold. The cell temperature is controlled to ±1 × 10−3 K by means of an integrated Peltier thermostat. The required pressure was created by a hand pump 750.1100 from Sitec, Switzerland, and measured by a pressure transducer US181 from Measuring Specialties, USA. The uncertainty in the pressure measurement is ±5 kPa. For evacuating the whole apparatus a vacuum pump was employed. Details of the calibration and procedure have been reported in a previous paper,17 and the estimated uncertainty of our density measurements is ±1 × 10−4 g·cm−3.

3. RESULTS AND DISCUSSION The densities of pure n-hexane were measured in the temperature range 283.15−328.15 K (in 5 K steps) and pressures between 0.1 and 65.0 MPa and can be found in the Supporting Information. Density values were correlated with temperature and pressure using the Tait equation ρ=

ρ0 (T , p0 ) ⎛ B(T ) + p ⎞ 1 − C·ln⎜ B(T ) + p ⎟ ⎝ 0⎠

Figure 1. Density, ρ, as a function of temperature and pressure for nhexane: (●) experimental densities, () values calculated with the Tait equation.

(1)

where the reference pressure used in this work is p0 = 0.1 MPa. The ρ0 and B parameters were assumed to be dependent on temperature in the form of a power expansion

Thermophysical properties for n-hexane, including density, have been extensively reported; Cibulka and Hnedkovsky18 published a critical evaluation of experimental data of liquid densities at elevated pressures of n-alkanes and also gave the parameters of the corresponding Tait equations. We have compared our experimental values with the correlated values in terms of the relative root-mean square deviation, RMSDr:

n

ρ0 (T , p0 ) =

∑ Ai ·T i i=0

(2)

n

B (T ) =

∑ Bi ·T i i=0

(3)

⎛ 1 RMSDr = 100 × ⎜⎜ n ⎝

Ai parameters in eq 2 can be simultaneously fitted to temperature-dependent experimental density data at atmospheric pressure (p0 = 0.1 MPa). Finally, the parameter C in eq 1 was treated as temperature independent. The standard deviations, σ(ρ), between experimental and correlated density values were used as statistical values for the Tait fits

i=1

1/2

(5)

where n is the number of experimental data. The obtained RMSDr is 0.125%, so we can conclude that there is a good agreement among our experimental density values and the previously reported ones. The effect of temperature and pressure on density is well described by isobaric expansibility, αp, isothermal compressibility, κT, and internal pressure, pi, which are defined as

n

σ(ρ) = (∑ (ρi ,exp − ρi ,corr )2 /(n − p))1/2

2 ⎛ρ − ρi ,exp ⎞ ⎞ i ,corr ⎟⎟ ∑ ⎜⎜ ⎟⎟ ρ ⎠⎠ i ,corr i ⎝

(4) 10285


The Journal of Physical Chemistry B αp =

1 ⎛⎜ ∂V ⎞⎟ 1 ⎛ ∂ρ ⎞ =− ⎜ ⎟ ρ ⎝ ∂T ⎠ p V ⎝ ∂T ⎠ p

1 ⎛ ∂V ⎞ 1 ⎛ ∂ρ ⎞ κT = − ⎜ ⎟ = ⎜ ⎟ V ⎝ ∂p ⎠ ρ ⎝ ∂p ⎠

T

T

pi =

⎛ ∂U ⎞ α ⎜ ⎟ = T −p ⎝ ∂V ⎠T κT

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Table 2. Parameters, aii, for Fitting the Excess Volumes and Standard Deviations, σ(VE)

(6)

a00

a01

a02

a03

a10

a11

a12

a13

(7)

a20

a21

a22

a23

(8)

0.559 0.273 −0.109

In these equations the temperature and pressure derivatives of density have been evaluated using the Tait equation. The values of these properties in all the ranges of pressure and temperature studied can be found in the Supporting Information. The densities of the four binary mixtures were measured over the whole composition range at temperatures between 283.15 and 323.15 K and pressures from 0.1 to 65.0 MPa. These densities were correlated with temperature, pressure, and composition of the mixture using the following equation ρ(T , p , xi) =

0.902 0.378 −0.253 1.006 0.328 −0.294 1.777 0.104 −0.357

∑i Mixi ∑i

Mixi ρi (T , p)

+ V E(T , p , xi)

(9)

where Mi and ρi are the molar mass and density of the component i, respectively, and VE is the excess volume of the mixture, which has been correlated by means of a Redlich− Kister19 polynomial expansion with temperature- and pressuredependent parameters [a0(p , T ) + a1(p , T ) ·(2x1 − 1) + a 2(p , T ) ·(2x1 − 1)2 ] (10)

ai(p , T )/cm 3·mol−1 = aio + ai1· (p − 0.1) + ai2 ·(T − 283.15) + ai3·(p − 0.1) ·(T − 283.15) (11)

The adjustable parameters, aii, were determined by the method of least-squares. In Table 2 these parameters are collected together with the corresponding standard deviations. From volumetric measurements we have calculated excess molar volume, VE, excess isobaric expansibility, αEp , excess isothermal compressibility, κET, and excess internal pressure, pEi , through the expressions20−22

∑ xiVi i

αpE = α −

∑ ϕα i p,i i

κTE = κT −

∑ ϕκi T ,i i

piE = pi −

∑ ψipi ,i i

(12)

(13)

(14)

(15)

where ϕi is the volume fraction of component i in the mixture referred to the unmixed state and ψi is the compression factor of component i in the mixture, which is defined as

ψi =

xiKT , i ∑i xiKT , i

0.007

0.008

0.009

0.015

in this equation KT,i is the molar isothermal compressibility or compression of component i. The experimental density data together with calculated excess volumes for the four binary mixtures can be found in the Supporting Information. Our density data for the system n-hexane + 1-chlorobutane are in good agreement with those reported by Gołdon et al.,16 with the relative root-mean-square deviation between both sets of results equal to 0.136%. Figure 2 shows the temperature effect on the excess properties at p = 30 MPa. Since all the properties at the other pressures studied show a similar trend, for reasons of simplicity only the data at 30 MPa have been plotted. For the same reason, the pressure effect on the same properties at T = 298.15 K is illustrated in Figure 3. The volumetric behavior of the isomers of chlorobutane depends mainly on the strength of dipole−dipole interactions, as we have shown in a recent study.8 These interactions are stronger in primary (1-chlorobutane or 1-chloro-2-methylpropane) than in secondary (2-chlorobutane) or tertiary (2-chloro2-methylpropane) chlorinated isomers, as could be expected. Additionally, it should be considered that linear compounds present lower free volume than their branched analogues. n-Hexane is significantly less dense than isomers of chlorobutane because it does not show any specific selfinteraction; consequently, its molar volume is about 30% bigger than molar volumes of chlorobutanes. Furthermore, n-hexane shows bigger isothermal compressibility and lower internal pressure in all the ranges of pressures and temperatures than chlorobutane isomers. The excess molar volumes of the four binary mixtures are positive in the full range of composition. VE curves are slightly asymmetric, and maximum values for this property are shifted toward the zone rich in n-hexane. An increment in temperature makes the VE increase in all the systems studied, whereas VE values become smaller when pressure rises. VE values of the binary mixtures follow the sequence: 2-chloro-2-methylpropane > 1-chloro-2-methylpropane > 2-chlorobutane > 1-chlorobutane, although it should be underlined that the values for the

V E/cm 3·mol−1 = x1·(1 − x1) ·

VE = V −

n-Hexane + 1-Chlorobutane −0.000225 0.002714 0 −0.002146 0.00254 −0.000011 −0.001453 0.002143 0.000001 n-Hexane + 2-Chlorobutane −0.004098 0.005147 −0.000055 −0.003381 0.003567 −0.000008 0.000141 0.001332 0.000036 n-Hexane + 1-Chloro-2-methylpropane −0.004378 0.003906 −0.000035 −0.002383 0.003678 0.000021 −0.000386 −0.001797 0.000003 n-Hexane + 2-Chloro-2-methylpropane −0.010475 0.003913 −0.000081 −0.001603 0.003299 −0.000021 0.002306 0.007902 −0.000131

σ(VE)

(16) 10286



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Figure 2. Excess properties at p = 30 MPa and at different temperatures for the systems n-hexane + isomeric chlorobutane: (black line) 1chlorobutane; (red line) 2-chlorobutane; (blue line) 1-chloro-2-methylpropane; (green line) 2-chloro-2-methylpropane.

maximum values shifted toward the zone rich in n-hexane. The system containing 1-chloro-2-methylpropane shows values of αEp changing from negative to positive when the mole fraction of n-hexane increases in the mixture. Finally, in the system n-hexane + 2-chloro-2-methylpropane, αEp values vary

mixtures containing 2-chlorobutane or 2-methyl-1-chloropropane are just slightly different. Mixtures of n-hexane with 1-chlorobutane or 2-chlorobutane show positive values of αEp in the whole range of compositions. Therefore, curves of this property are asymmetric, with 10287



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Figure 3. Excess properties at T = 298.15 K MPa and at different pressures for the systems n-hexane + isomeric chlorobutane: (black line) 1chlorobutane; (red line) 2-chlorobutane; (blue line) 1-chloro-2-methylpropane; (green line) 2-chloro-2-methylpropane.

significantly with pressure; αEp values are positive at low pressures and negative at high pressures. Except for the binary system n-hexane + 1-chlorobutane, values of excess isothermal compressibility are negative over the whole composition range, and minimum values of this property

are shifted toward the region rich in n-hexane. An increment in temperature leads to more negative κET values, while the pressure increment makes the κET values become less negative. Finally, excess internal pressures are positive in the whole composition range for all the binary systems, and maximum 10288



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Table 3. Properties of the Pure Compounds: Critical Data, Acentric Factor, Translation Parameter, and PR-Twu α Function Parameters compound

Pc/kPa

Tc/K

Vc/cm3·mol−1

ω

c/cm3·mol−1

L

M

N

n-hexane 1-chlorobutane 2-chlorobutane 1-chloro-2-methylpropane 2-chloro-2-methylpropane

3025 3688.23 3951.67 3989 3951.68

507.6 542 520.6 527.05 507

443.5 312 305 305 295

0.523 0.218 0.3 0.2895 0.19

−1.3 7.8901 −6.6453 −4.2832 −10.2783

0.96506 0.988925 0.947079 0.859223 0.109132

0.94250 0.75593 1.06718 1.00272 0.890767

0.81637 0.654863 0.870236 0.878194 3.52574

Table 4. VTPR Group Interaction Parameters

a

na

m

anm/K

bnm

cnm/K−1

amn/K

bmn

cmn/K−1

1

2

439.8547

−0.46183

0

−87.8717

−0.10659

0

1: ‘CH2’. 2: ‘CCl’.

values of this property are also shifted toward the n-hexane-rich region. We can also underline that the pressure effect is, in general, more noticeable in all the systems and properties than the temperature effect. The values of the excess properties obtained can be explained considering the breaking or weakening of the dipole−dipole interactions that occurs when isomers of chlorobutane are mixed with n-hexane and the variation of free volume due to the differences in size and shape among these compounds. Positive values for excess molar volumes in the four binary systems at all temperatures and pressures indicate that the positive contribution to VE, due to the rupture of the dipole− dipole interactions, is more important than the negative contribution associated with the fitting between unlike components. The same factors contribute to the rest of the properties analyzed, although the relevance of each effect changes among the different properties: small absolute values obtained for αEp and pEi point to a balance between these two contributions of opposite sign, while negative values of κET reveal that the fitting effect contributes more significantly to this property.

bi = 0.0778

pC, i

(19)

i i αi(T ) = Tr,Nii(Mi − 1) exp[Li(1 − Tr,NM i )]

(20)

where Tr is the reduced temperature and L, M, and N are pure compound parameters. In the VTPR model, the following mixing rules for the parameters a and b, suggested by Chen et al.,25 are used a = b

∑ xi

aii GE + res bi A

(21)

where A = −0.53087 and is calculated using the residual part of the UNIFAC method. GEres

b=

∑ ∑ xixjbij i

bij3/4 =

(22)

j

(bi3/4 + bj3/4) 2

(23)

With respect to the translation parameter of the mixture, c, a linear mixing rule is employed c=

∑ xici i

(24)

Properties of the pure compounds taken directly from the Dortmund Data Bank26 and group interaction parameters27 used in the VTPR calculations are collected in Tables 3 and 4, respectively. In Figures 4 and 5 the predicted densities over the whole composition range at some selected temperatures and pressures together with the experimental densities for the systems studied here are graphically shown. We have tested the accuracy of the VTPR predictions by comparing the densities obtained experimentally with the corresponding calculated values. In Table 5 the average deviations in density, Δρ, and the relative root-mean-square deviations are shown. The overall Δρ is 0.00427 g·cm−3, and the corresponding RMSDr is 0.666%. The density predictions obtained with the VTPR model can be considered satisfactory especially due to the difficulties in predicting the liquid densities.

where the translation parameter, c, is defined as the difference between the volume calculated with the Peng−Robinson EoS and the experimental volume at a reduced temperature, Tr = 0.7.23 The pure component parameters, attractive parameter, aii, and covolume, bi, can be calculated from the critical temperature and pressure, using the following equations R2TC,2 i

pC, i

The temperature dependence of the attractive parameter, given by the α(T) function, can be obtained in the VTPR model using the expression proposed by Twu at al.24

4. VTPR MODEL PREDICTIONS The VTPR model combines the VTPR-EoS with the UNIFAC group contribution method, and it can be used to predict both the volumetric behavior and the phase equilibrium of a mixture. In this paper we have checked the reliability of the density predictions of the model by comparing our experimental results with the VTPR-predicted ones. The VTPR equation of state is RT p= (V + c − b) a(T ) − (V + c)(V + c + b) + b(V + c − b) (17)

aii(T ) = 0.45724

RTC, i

·αi(T ) (18) 10289



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Figure 4. Experimental and VTPR predicted densities at p = 30 MPa and at different temperatures for the systems n-hexane + isomeric chlorobutane: (black line) 1-chlorobutane; (red line) 2-chlorobutane; (blue line) 1-chloro-2-methylpropane; (green line) 2-chloro-2-methylpropane.

pane the predictions are more accurate at low temperatures, while for 2-chlorobutane and 2-chloro-2-methylpropane the results are more satisfactory at high temperatures.

The density predictions are more accurate in the alkane-rich region, probably due to the fact that the VTPR predictions for the pure n-hexane are better than for the pure isomers of chlorobutane. The best results are obtained for the mixture containing 1-chloro-2-methylpropane with an average Δρ of 0.00268 g·cm−3, while the less accurate predictions correspond to the mixture with 2-chlorobutane with an average Δρ of 0.00614 g·cm−3. This difference among the mixtures containing the isomers of chlorobutane is also related with the goodness of the VTPR predictions of the pure chloroalkanes. It can also be outlined that, in general terms, the predictions are better at low pressures. On the other hand, the temperature behavior of the predictions depends on the isomeric chlorobutane: for 1-chlorobutane and 1-chloro-2-methylpro-

5. CONCLUSIONS Following our study about thermophysical properties of the binary mixtures n-hexane + isomeric chlorobutane, in this contribution we have reported densities of these systems in a wide range of pressures and temperatures. Moreover, densities of the pure n-hexane have also been measured and correlated with the Tait equation. From experimental pρTx data we have obtained the following excess properties: excess molar volumes, excess isobaric expansibilities, excess isothermal compressibilities, and excess internal pressures. Excess molar volumes have 10290



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Figure 5. Experimental and VTPR predicted densities at T = 298.15 K and at different pressures for the systems n-hexane + isomeric chlorobutane: (black line) 1-chlorobutane; (red line) 2-chlorobutane; (blue line) 1-chloro-2-methylpropane; (green line) 2-chloro-2-methylpropane.

Table 5. Average Deviation in Density, Δρ, and Relative Root-Mean-Square Deviations, RMSDr, Between Experimental Data and VTPR Model Predictions system n-hexane n-hexane n-hexane n-hexane overall

+ + + +

1-chlorobutane 2-chlorobutane 1-chloro-2-methylpropane 2-chloro-2-methylpropane

Δρ/g·cm−3

RMSDr/%

0.00455 0.00614 0.00268 0.00372 0.00427

0.674 0.949 0.426 0.614 0.666

volumetric behavior of the binary mixtures is determined by two main contributions: the breaking or weakening of the dipole−dipole interactions of chlorobutane isomers and the fitting between unlike components due to their different size and shape. Finally, experimental densities have been compared with the predictions of the VTPR model, which combines the VTPREoS with the UNIFAC group contribution method. These predictions can be considered reasonably correct for all the systems. The best results are obtained for the mixture containing 1-chloro-2-methylpropane with an average deviation in density of 0.00268 g·cm−3, while the less accurate predictions correspond to the mixture with 2-chlorobutane (average deviation in density 0.00614 g·cm−3).

been correlated by means of a Redlich−Kister polynomial expansion with temperature- and pressure-dependent parameters. The values of the excess properties reveal that the 10291



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(14) Domínguez, M.; Artigas, H.; Santafé, J.; Mainar, A.; Urieta, J. S. Densities and Excess Molar Volumes of the Ternary Mixture (1Butanol + n-Hexane + 1-Chlorobutane) at 298.15 and 313.15 K. Application of the ERAS Model. Fluid Phase Equilib. 1998, 145, 115− 128. (15) Kovács, É. E.; Aim, K.; Linek, J. Excess Molar Volumes of (an Alkane + 1-Chloroalkane) at T 298.15 K. J. Chem. Thermodyn. 2001, 33, 33−45. (16) Gołdon, A.; Malka, I.; Hofman, T. Densities and Excess Volumes of the 1-Chlorobutane + n-Hexane System at Temperatures from (283.15 to 333.15) K and Pressures from (0.1 to 35) MPa. J. Chem. Eng. Data 2008, 53, 1039−1045. (17) Guerrero, H.; Lafuente, C.; Royo, F.; Lomba, L.; Giner, B. PrhoT Behavior of Several Chemicals from Biomass. Energy Fuels 2011, 25, 3009−3013. (18) Cibulka, I.; Hnedkovsky, L. Liquid Densities at Elevated Pressures of n-Alkanes from C-5 to C-16: A Critical Evaluation of Experimental Data. J. Chem. Eng. Data 1996, 41, 657−668. (19) Redlich, O.; Kister, A. T. Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345−348. (20) Benson, G. C.; Kiyohara, O. Evaluation of Excess Isentropic Compressibilities and Isochoric Heat-Capacities. J. Chem. Thermodyn. 1979, 11, 1061−1064. (21) Reis, J. C. R.; Blandamer, M. J.; Davis, M. I.; Douhéret, G. The Concepts of non-Gibbsian and non-Lewisian Properties in Chemical Thermodynamics. Phys. Chem. Chem. Phys. 2001, 3, 1465−1470. (22) Marczak, W. Internal Pressure of a Thermodynamically Ideal Mixture and the Excess Internal Pressure. Phys. Chem. Chem. Phys. 2002, 4, 1889−1890. (23) Ahlers, J.; Yamaguchi, T.; Gmehling, J. Development of a Universal Group Contribution Equation of State. 5. Prediction of the Solubility of High-Boiling Compounds in Supercritical Gases with the Group Contribution Equation of State Volume-Translated Peng− Robinson. Ind. Eng. Chem. Res. 2004, 43, 6569−6576. (24) Twu, C. H.; Coon, J. E.; Cunningham, J. R.; Gmehling, J. A New Generalized Alpha-Function for a Cubic Equation of State 0.1. PengRobinson Equation. Fluid Phase Equilib. 1995, 105, 49−59. (25) Chen, J.; Fischer, K.; Gmehling, J. Modification of PSRK Mixing Rules and Results for Vapor-Liquid Equilibria, Enthalpy of Mixing and Activity Coefficients at Infinite Dilution. Fluid Phase Equilib. 2002, 200, 411−429. (26) http://www.ddbst.de. (27) Schmid, B.; Gmehling, J. Revised Parameters and Typical Results of the VTPR Group Contribution Equation of State. Fluid Phase Equilib. 2012, 317, 110−126.

ASSOCIATED CONTENT

S Supporting Information *

The values of density of pure n-hexane together with isobaric expansibility, αp, isothermal compressibility, κT, and internal pressure, pi, in all the ranges of pressure and temperature studied. The experimental density data for the four binary mixtures along with calculated excess volumes are collected. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +34976762295. Fax: +34976761202. E-mail: celadi@ unizar.es. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Authors gratefully acknowledge financial support from Diputación General de Aragón and Fondo Social Europeo “Construyendo Europa desde Aragón”.

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REFERENCES

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Volumetric Study of the Mixtures n-Hexane + Isomeric Chlorobutane

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