Experimental Determination and Modelling Thermophysical Properties

Article Cite This: Ind. Eng. Chem. Res. 2018, 57, 5142−5150

pubs.acs.org/IECR

Experimental Determination and Modeling Thermophysical Properties of 1‑Chlorononane in a Wide Range of Conditions: Is It Possible To Predict a Contribution of Chlorine Atom? Vyacheslav V. Melent’ev,† Eugene B. Postnikov,‡ and Ilya Polishuk*,§ †

Laboratory of Molecular Acoustics and ‡Department of Theoretical Physics, Kursk State University, Radishcheva st., 33, 305000 Kursk, Russia § Department of Chemical Engineering, Biotechnology and Materials, Ariel University, 40700 Ariel, Israel S Supporting Information *

ABSTRACT: This study reports the experimental density and speed of sound data of 1-chlorononane along seven isotherms from 293.15 to 413.15 K at pressures from saturation up to 196.1 MPa. The pertinent isothermal compressibility and isobaric coefficient of expansion data have been obtained by numerical differentiating of densities. In addition, the saturated liquid densities have been measured from 253.15 to 443.15 K, isobaric heat capacities from 248.15 to 448.15 K, and speeds of sound from 246.88 to 457.25 K. These results have been interpolated by polynomials to obtain the saturated liquid isobaric coefficient of expansion, adiabatic and isothermal compressibility, isochoric heat capacity, and internal pressure data. Performances of three predictive approaches having different degrees of complexity, namely the Critical Point-based Perturbed Chain Statistical Association Fluid Theory, the Statistical Association Fluid Theory of Variable Range Mie Potential parametrized by a Corresponding States approach of Mejiá et al. (Ind. Eng. Chem. Res. 2014, 53, 4131), and the fluctuation theory-based Tait-like equation of state have been examined. The latter model has a superiority in estimating of the high-pressure data; however, unlike both statistical association fluid theory approaches, it utilizes the saturated liquid data. It has also been demonstrated that all the models successfully predict various phenomena related with replacement of hydrogen by chlorine in n-nonane molecule.

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fluctuation theory-based Tait-like equation of state (FT-EoS).14 This model requires as an input the saturation liquid phase data in order predict the pertinent properties at high pressures. Currently, implementation of FT-EoS is restricted to the pure compound liquid phases away from the critical temperatures. The more sophisticated models considered here are the Critical Point-based Perturbed Chain Statistical Association Fluid Theory (CP-PC-SAFT)15 and the Statistical Association Fluid Theory of Variable Range and Mie Potential16 parametrized by a Corresponding States approach of Mejiá et al. (CS-SAFT-VRMie).17 These models require a much more significant calculation efforts in comparison with FT-EoS, while their implementation for predicting thermodynamic properties often implies some nontrivial symbolic algebra. At the same time, these predictive versions of SAFT necessitate a much smaller input of experimental data, namely critical temperatures and pressures in the case of CP-PC-SAFT and critical temperatures

INTRODUCTION Chlorinated alkanes are widely used as solvents, lubricants, intermediates, etc. in various processes.1 Therefore, reliable data on their thermophysical properties in broad range of conditions along with appropriate interpretations and accurate predictions are important for chemical technology. Previously,2−4 speeds of sound and densities of 1-chloropropane, 1chlorohexane, and 1-iodohexane have been measured at temperatures from 293.15 to 413.15 K and pressures up to 200 MPa. Current investigation continues this series of studies, yet considering another chloroalkane molecule, namely 1chlorononane. So far, several references have reported densities,5−11 speeds of sound,6,12,13 and isobaric heat capacities6 of this compound at the atmospheric pressure. To the best of our knowledge, thermodynamic properties of 1chlorononane at high pressures have so far not been considered in literature. Consequently, their predictions present a challenging reliability test for the general thermodynamic models that do not consider a specific contribution of chlorine or fitting to the entire set of experimental data. In this study, we examine three predictive approaches having different degrees of complexity and requiring dissimilar amounts of input experimental data. The simplest one is the © 2018 American Chemical Society

Received: Revised: Accepted: Published: 5142

January 13, 2018 March 27, 2018 March 28, 2018 March 28, 2018 DOI: 10.1021/acs.iecr.8b00174 Ind. Eng. Chem. Res. 2018, 57, 5142−5150

Article

Industrial & Engineering Chemistry Research

the platinum resistance thermometer whose absolute error is ±0.01 K. The pertinent corrections respectively to the temperature and pressure dependence of the acoustic path have been performed as well. Additional details on the experimental setup and methodology can be found elsewhere.3,19 The densities at high pressures have been measured by the acoustical piezometer with the relative uncertainty not exceeding ±0.3%. Tables 2 and 3 report the densities and speeds of sound under high pressures, respectively. The atmospheric pressure data (see Table 1) have been n interpolated by the polynomials ∑i = 0 Ai T i whose coefficients and average absolute deviations are listed in Table S1 of the Supporting Information. Table S2 of the Supporting Information compares the available literature data with the values yielded by these polynomials. As seen, a particularly small number of references report the data in significant temperature intervals, while most of them have been published by the Laboratory of Molecular Acoustics (Kursk State University).6,12,13 Since in these references principally the same experimental equipment has been used, their deviations from the current results are very small. In view of the above, the data reported by other laboratories are particularly important for validation of our results. Among those references, only Vogel5 has reported the atmospheric pressure density data for several temperatures. Table S2 demonstrates that this source along with another one-point datum7 deviates from our results nearly twice less than the experimental uncertainty, that is, they can be considered as coinciding. This mutual data agreement is also supported by the nearly identical purity of samples: the refraction indices are nD = 1.43405 and nD = 1.4360,7 which deviate less than 0.08% from the value determined for our sample (nD = 1.4349). Remarkably, the latter data sources have been used for generating the Landolt-Börnstein recommended reference values20 that exhibit the same deviations from the current data. The latter is valid also for the values generated by an empirical expression for saturated liquid densities of the Yaws database21 (see Table S2). At the same time, the data of Nekrasova9−11 exhibit significant deviations from our data and previously20 it has already been recognized as unreliable. The latter should most probably be related to the unsatisfactory sample purity (nD = 1.4402).11 A somewhat better, but still insufficient, purity of sample (nD = 1.43682) might explain an intermediate deviation of the remaining datum.8 The polynomial interpolations with coefficients listed by Table S1 have also been implemented for calculating some additional thermodynamic properties at atmospheric pressure, namely the isothermal coefficient of expansion:

and acentric factors for CS-SAFT-VR-Mie. In addition, each of the models requires one saturated liquid density datum. Accuracy of the models under consideration in estimating a contribution of the chlorine atom is examined by comparing their predictions for 1-chlorononane with n-nonane and ndodecane. The latter compound has been selected due to the proximity of its molecular weight, saturated liquid speeds of sound, and viscosities to 1-chlorononane.

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EXPERIMENTAL METHOD AND RESULTS Liquid 1-chlorononane was purchased from SIGMA-Aldrich (>98% mole fraction) and used without further purification. Its purity has been verified by measuring the refraction index by optical refractometer IRF-22 at 293.15 K. The resulting value of nD = 1.4349 (the standard uncertainty u(nD) = 0.002) was in good agreement with the reference datum provided by the producer (SIGMA-Aldrich). The atmospheric pressure densities have been measured pycnometrically with the relative uncertainty not exceeding ±0.5%. The atmospheric pressure isobaric heat capacities have been obtained in the industrial dynamical calorimeter ITCp400. Estimations of the pertinent relative errors indicate that they do not exceed ±5% in the entire considered temperature range. The speeds of sound were measured by the pulse-phase echo method using the experimental setup described by Bolotnikov and Neruchev18 within the dispersionless frequency range of 1−5 MHz and the relative uncertainty of ±0.1%. The experimental data on densities, isobaric heat capacities, and speeds of sound at atmospheric pressure are listed in Table 1. The liquid 1-chlorononane was pressurized by the deadweight pressure gauge MP-2500 with the steps of ∼10 MPa, whose relative error is ±0.02%. The samples were placed into the thermostat where the absolute error of temperature stabilization is ±0.05 K. The temperatures were measured by Table 1. Experimental Densities, Isobaric Heat Capacities, and Speeds of Sound of 1-Chlorononane at Atmospheric Pressure (P0 = 0.101 MPa)a T (K)

ρ (kg m−3)

T (K)

Cp (J kg−1 K−1)

T (K)

c (m s−1)

253.15 263.15 273.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15

904.3 895.9 887.5 879.3 871.2 863.0 855.2 846.1 838.6 830.1 822.4 813.5 805.9 796.8 788.5 780.0 771.7 763.1 755.3 746.5

248.15 273.15 298.15 323.15 348.15 373.15 398.15 423.15 448.15

1708 1758 1822 1888 1956 2026 2098 2173 2249

246.88 251.15 258.37 261.01 267.50 275.40 284.96 285.04 289.64 303.22 316.70 348.52 367.07 378.99 400.66 410.14 415.79 437.94 457.25

1472.6 1458.4 1428.8 1418.8 1390.1 1362.9 1327.6 1325.0 1309.1 1258.8 1209.7 1096.7 1035.3 995.9 929.61 897.6 881.38 809.48 751.1

αP = −ρ−1(∂ρ /∂T )T

(1)

the adiabatic compressibility, expressed from the density ρ and the speed of sound c:

κs = 1/(ρc 2)

(2)

the isothermal compressibility: κT =

TαP2 1 + 2 ρCP ρc

the isochoric heat capacity: κ CV = CP T κS

a

Standard uncertainty ur(T) = 0.05 K, relative standard uncertainties: ur(P0) = 0.02%; ur(ρ) = 0.3 %; ur(CP) = 5%; ur(c) = 0.1%. 5143

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(4) DOI: 10.1021/acs.iecr.8b00174 Ind. Eng. Chem. Res. 2018, 57, 5142−5150

Article

Industrial & Engineering Chemistry Research Table 2. Experimental Densities of 1-Chlorononane (kg m−3)a T (κ)

a

P (MPa)

293.15

313.15

333.15

353.15

373.15

393.15

413.15

0.1 4.9 9.81 19.61 29.42 39.23 49.03 58.84 68.65 78.45 88.26 98.07 107.9 117.7 127.5 137.3 147.1 156.9 166.7 176.5 186.3 196.1

871.4 875.0 878.5 885.3 891.3 897.1 902.5 907.7 912.5 917.2 921.6 925.8 929.8 933.7 937.4 940.9 944.4 947.7 950.9 954.0 957.0 959.9

855.0 859.0 862.9 870.2 877.0 883.3 889.2 894.7 900.0 904.9 909.6 914.1 918.4 922.5 926.4 930.2 933.8 937.2 940.6 943.8 946.9 950.0

838.6 843.5 847.4 855.4 862.8 869.7 876.1 882.1 887.7 893.0 898.0 902.8 907.3 911.6 915.8 919.7 923.5 927.2 930.7 934.0 937.3 940.4

822.0 827.1 831.8 840.7 848.8 856.3 863.2 869.7 875.7 881.4 886.7 891.8 896.5 901.1 905.4 909.6 913.6 917.4 921.0 924.5 927.9 931.2

805.4 810.9 816.3 826.2 835.1 843.2 850.7 857.6 864.1 870.1 875.8 881.1 886.1 890.9 895.5 899.8 904.0 908.0 911.8 915.4 918.9 922.3

788.7 795.3 800.9 811.8 821.6 830.4 838.5 845.9 852.8 859.2 865.2 870.9 876.2 881.2 886.0 890.5 894.9 899.0 903.0 906.8 910.4 913.9

771.9 779.0 785.7 797.8 808.5 818.1 826.8 834.8 842.1 849.0 855.3 861.3 866.9 872.1 877.1 881.9 886.4 890.7 894.8 898.7 902.5 906.1

Relative standard uncertainties: ur(T) = 0.1%; ur(P) = 0.02%; ur(ρ) = 0.3%.

Table 3. Experimental Speeds of Sound in 1-Chlorononane (m s−1)a T (κ)

a

P (MPa)

293.15

313.15

333.15

353.15

373.15

393.15

413.15

0.1 4.9 9.81 19.61 29.42 39.23 49.03 58.84 68.65 78.45 88.26 98.07 107.9 117.7 127.5 137.3 147.1 156.9 166.7 176.5 186.3 196.1

1295.5 1319.1 1341.8 1387.7 1428.8 1466.8 1501.4 1536.1 1569.7 1599.3 1630.6 1659.0 1688.3 1716.3 1744.1 1771.4 1797.1 1823.3 1848.3 1870.8 1890.3 1908.9

1220.8 1245.8 1270.3 1316.9 1360.6 1401.7 1440.6 1477.4 1512.1 1544.7 1575.0 1602.8 1634.8 1662.2 1692.4 1718.6 1744.0 1769.5 1799.3 1822.9 1844.9 1864.6

1150.5 1177.5 1204.0 1254.0 1300.5 1343.9 1384.6 1422.9 1459.0 1493.4 1526.2 1557.6 1587.9 1617.2 1645.7 1673.3 1700.3 1726.6 1752.3 1777.3 1801.5 1824.2

1081.5 1110.7 1139.3 1193.2 1243.0 1289.2 1332.3 1372.6 1410.6 1446.5 1480.6 1513.2 1544.4 1574.4 1603.4 1631.4 1658.4 1684.5 1709.6 1733.6 1756.4 1777.8

1014.0 1046.4 1077.7 1135.7 1188.4 1236.6 1281.1 1322.6 1361.7 1398.6 1433.9 1467.7 1500.2 1531.3 1561.0 1589.1 1615.3 1639.2 1668.1 1692.2 1715.1 1735.6

949.2 983.6 1016.9 1078.8 1135.0 1186.1 1233.3 1276.7 1317.1 1355.5 1391.6 1426.1 1459.2 1490.7 1521.4 1550.4 1578.0 1604.8 1629.7 1652.8 1673.9 1693.9

884.5 922.0 958.3 1024.9 1084.7 1138.8 1188.0 1233.2 1275.2 1314.5 1351.7 1387.0 1420.9 1453.4 1484.6 1514.5 1542.9 1569.5 1593.9 1615.6 1635.0 1652.8

Standard uncertainty u(T) = 0.1 K; relative standard uncertainties: ur(P) = 0.02%; ur(c) = 0.1%.

the heat capacity ratio:

γ = CP /CV and the internal pressure: α Pi = T P − P κT

The pertinent results can be found in Table S3 of the Supporting Information. In addition, a numerical differentiation of the density data listed by Table 2 yields in the isothermal compressibility and the isobaric coefficient of expansion at high pressures (see Tables S4 and S5 of the Supporting Information).

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DOI: 10.1021/acs.iecr.8b00174 Ind. Eng. Chem. Res. 2018, 57, 5142−5150

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MODELING AND DISCUSSION FT-EoS14 is a very simple and effective tool for predicting thermodynamic properties at high pressures based on the liquid saturated pressure data. According to this model, the densities are given as −1

0

ρ = ρ0 + k ln[kρ0 κT (P − P0) + 1]

The pressure-explicit EoS expression is obtained as

P=

(7)

where ρ0 and κT are the densities and the isothermal compressibilities at normal pressure, respectively, and k is the local slope of the tangent to the function ln(ρκT), whose derivation is explained in details elsewhere.2,22 Here we only mention that it follows from the almost exponential dependence of the inverse reduced density fluctuation parameter on density at the saturation conditions: Mw 1 = e kρ0 − b RT ρ0 κT 0

(8)

where Mw and R are the molecular weight and the gas constant, respectively, while b is the substance-specific constant defined through the saturated density conditions at which ν = 1, that is, when the actual density fluctuations are equal to their values at the equivalent ideal gas state with the same density and the temperature. Note that values of the constant b and the Mw are not required for predictive calculations of the density and the speed of sound under high pressures. On the other hand, for convenience of the calculations mentioned above, the logarithm of isothermal compressibility and the parameter k have been calculated on the base of the data listed in Table 1 and represented as cubic polynomials, whose coefficients can be found in Table S6 of the Supporting Information. According to the FT approach, the isothermal compressibilities and the isobaric coefficients of expansion at high pressures are given as κT =

⎛ ∂P 2 ⎞ ⎛ ∂P ⎞ ⎜ ⎟ =⎜ 2 ⎟ =0 ⎝ ∂v ⎠Tc ⎝ ∂ v ⎠ Tc

αP = κT

Pi 0 + P T

(9)

(10)

while the speeds of sound are yielded by the following simple expression:23 c = c0 +

⎤ 1 ⎡k k2 ⎢ (ρ − ρ0 ) + (ρ − ρ0 )2 ⎥ ρκT ⎣ 2 8 ⎦

(11)

The CP-PC-SAFT15 is a development of the original PCSAFT24 aiming at replacing the vague fitting of its substancedependent molecular parameters by their standardized and transparent Cubic EoS-style solution. Its details and implementations to various systems have been described in great detail in the previous studies.25−34 In addition to the entirely transparent numerical procedure for solving the model parameters, this revision aims at addressing two other issues, namely allowing simultaneous prediction of critical and subcritical data and removal of the numerical problems affecting the original version of PC-SAFT.35−41 In the cases of nonassociating and nonpolar compounds, PC-SAFT expresses the residual Helmholtz energy as a sum of hard-sphere, chain, and dispersion contributions: Ares = AHS + Achain + Adisp

vc , EoS = δvc

(14,15)

Pc , EOS = Pc

(16)

ρL , EoS = ρL,experimental |273.15K

(17)

The pertinent solutions for 1-chlorononane and three additional 1-bromoalkanes are listed in Table S7 of the Supporting Information. The SAFT-VR-Mie16 approach comprises chains of bonded homonuclear spherical segments with individual segments that interact according to the Mie potentials. This model is attached by an additional flexibility in describing the softness and hardness of the interactions by the substance-specific adjustable parameters representing the repulsive and attractive exponents of the segment−segment interactions. The Mie potential is obtained according to the Barker-Henderson high-temperature perturbation expansion up to the third order. Generally speaking, this model is more complex and sophisticated in comparison with PC-SAFT. At the same time, unlike CP-PCSAFT, parametrization procedure of CS-SAFT-VR-Mie17 does not involve numerical solutions. Instead of that, the parameter values are obtained through generalized expressions defined for several values of the effective chain length m (from 1 to 6) in certain intervals of the Pitzer’s acentric factor ω. On one hand, the latter simplifies implementation of the model. However, on the other hand, these intervals are particularly wide. According to this method, 1-chlorononane (ω = 0.505) falls in the intervals defined for all the values of m from 2 until 6, including. It has been found that the best results for the densities and the speeds of sound have been obtained with m = 3 and m = 4, respectively. The input data required by both SAFT models for 1-chlorononane have been taken from the Yaws database,21 while the necessary density points (at 273.15 K for CP-PCSAFT and Tr = 0.7 for CS-SAFT-VR-Mie) have been obtained from the expression for the saturated liquid densities. Table 4 lists the average absolute deviations of the predictions yielded by considered models from the data listed in Tables 2, 3, S4, and S5. As seen, FT-EoS has a clear superiority over both SAFT models. The latter can be explained by the fact that unlike them, FT-EoS utilizes the saturated

ρ0 κT 0 kρ0 κT 0(P − P0) + 1

(13)

As discussed above, CP-PC-SAFT can be characterized by an advanced predictive capacity thanks to the substantial reduce of the required experimental data. It applies a standardized numerical solution of the substance-dependent parameters at the critical points. In addition, this model requires one lowtemperature liquid density point datum. Typically, such datum is obtained at the triple point. However, to the best of our knowledge, the pertinent densities of 1-chlorononane and several other haloalkanes has not been measured so far. Thus, following the previous study,26 the datum at 273.15 K has been selected. The values of m (the effective number of segments), σ (the segment diameter, Å), ε/k (segment energy parameter divided by Boltzmann’s constant, K), and δ (the critical volume displacement) are obtained by solving the following system of equations:

0

ν(ρ0 ) =

⎛ ∂Ares ⎞ RT ⎟ −⎜ ⎝ ∂v ⎠T v

(12) 5145


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positive and at the higher ones, negative. This phenomenon has been related by Randzio42,43 to a change of the intermolecular potential shape at the rising pressures, and, as seen, it is accurately predicted by FT-EoS. Although CP-PC-SAFT yields smaller absolute average deviation from the αp data than CSSAFT-VR-Mie, unlike the latter, this model fails in predicting its isotherms cross. At the same time, the predictions of CSSAFT-VR-Mie with m = 3 are more accurate than with m = 4. In an attempt to address a question asked in the title of this investigation, Figure S2 of the Supporting Information and Figure 1 compare the predictions of the models under consideration for densities and speeds of sound of 1chlorononane, n-nonane and n-dodecane for at 313.15 and 413.15 K. The figures demonstrate that FT-EoS has an overall superiority over both SAFT models as well in predicting the properties of both n-alkanes. They also reveal that in addition to the higher densities, 1-chlorononane exhibits another remarkable phenomenon, namely the smaller dependence of its speed of sound on pressure in comparison to n-alkanes. As

Table 4. Average Absolute Deviations (AAD%) in Predicting Densities, Speeds of Sound, Isothermal Compressibilities, and Isothermal Coefficients of Expansion of 1Chlorononane property

ρ

c

κT

αP

FT-EOS CP-PC-SAFT CS-SAFT-VR-Mie with m = 3 CS-SAFT-VR-Mie with m = 4

0.077 0.254 0.935 2.371

0.985 1.223 3.459 2.019

0.856 5.112 2.900 8.946

0.778 10.326 11.954 14.360

experimental data for the specific isotherms. In addition, the overall accuracy of CP-PC-SAFT is slightly better comparing to CS-SAFT-VR-Mie with both m = 3 and 4. In this respect, the special interest presents the results for the isobaric coefficient of expansion depicted by Figure S1 of the Supporting Information. A remarkable feature of this property is the intersection of isotherms around 300 bar. The latter means that at the lower pressures the temperature derivative of αp is

Figure 1. Speeds of sound in n-nonane, n-dodecane, and 1-chlorononane at 313.15 and 413.15 K. Points, experimental data obtained from Table 3 and Melikhov.44 Solid lines, predictions of FT-EoS, CP-PC-SAFT, and CS-SAFT-VR-Mie with m = 3. Dashed lines, CS-SAFT-VR-Mie with m = 4. 5146


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which, in turn, is directly determined by the energy of intermolecular interactions.45 This conclusion can be verified by the well-known interrelation between the strength of intermolecular interactions and the cohesive energy density46,47 determined by the molar enthalpy of vaporization. The latter allows estimating the internal pressure in nonassociating liquids according to

seen, although at low pressures the speed of sound in 1chlorononane is higher than in n-nonane, at the pressures above 800 bar it becomes lower, which is reasonable well estimated by the models. Although the overall accuracy of CP-PC-SAFT is unfavorable in comparison to FT-EoS, it predicts this phenomenon in a somewhat better-pronounced manner. The latter can be concluded also in the case of CS-SAFT-VR-Mie with m = 4. Nevertheless, FT-EoS can explain some consequences of inserting the chlorine atom on the intermolecular interactions. As indicated previously, implementation of this model is based on the fact the inverse reduced density fluctuation parameters of various liquids at saturation conditions ν(ρ0) exhibit the nearly exponential dependences on density (see eq 8). Consequently, ln(ν(ρ0)) turn into the almost straight lines, whose slopes are k and shifts, b. Figure 2 depicts the ln(ν(ρ0))

Δ vapH m =

− ρ0 dependences of the compounds under consideration in the temperature range 293.15−433.15 K. As seen, a slope of the 1-chlorononane’s fluctuation line is slightly reduced in comparison to two n-alkanes, which means that the pertinent value of k is somewhat smaller. Expectation of eq 11 reveals that the dependence of speed of sound on density is defined by this value. Consequently, such observation can explain the weaker dependence of speed of sound in 1-chlorononane on pressure as being determined by the differences between k values: similar elevations of the density result in smaller increment of the speed of sound. It can also be seen that the line corresponding to n-nonane is located below the lines corresponding to 1-chlorononane and n-dodecane, which means that the amplitude of the inverse reduced fluctuations in n-nonane deviates from two other substances. Using eq 6 and neglecting the saturation pressure, which is far smaller than the internal pressure away from the critical point, eq 8 can be rewritten as M wPi 0 RT2ραP 0

(19)

Substituting eq 19 into eq 18 while obtaining the experimental data on ΔvapHm of 1-chlorononane from Bolotnikov and Neruchev46 yields the line labeled on Figure 2 as 1-chlorononane (H). As seen, it is situated in the near vicinity to the pertinent line obtained from eq 8. At the same time, it has been demonstrated46 that ΔvapHm can be accurately estimated by a model considering the overall mean energy constants of attractive forces in liquid chlorinated alkanes as a weighted combination of energies of the pairwise interactions between hydrogen and chlorine atoms. According to this approach, the weight is dependent on the ratio between hydrogen and chlorine atoms in this “mixture” and on the ratio between the constants of the pair potential of their dispersion forces. Consequently, the ratio between the constants of the pair potential of dispersion forces for n-nonane and n-dodecane is also dependent on the number of hydrogen atoms. Thus, the current data analysis reveals that considering the ratios between constants, atomic fractions, densities, and molecular weights, a contribution of one chlorine atom is approximately equivalent to six additional hydrogen atoms of pure n-alkane. Nevertheless, the latter analysis is not valid for the heat capacities. Figure 3 depicts the saturated liquid CP and CV for the compounds under consideration in the molar units. As seen, these data for n-nonane and 1-chlorononane do not exhibit significant deviations, while the heat capacities of ndodecane are much higher. The latter might evidence that the bigger molecular weight of chlorine atom, apparently resulting in increase of the interatomic distance and molecular asymmetry, does not cause a noteworthy intensification of molecular vibrations, while the pertinent contribution of the propyl group is much significant. As seen, both CP-PC-SAFT and CS-SAFT-VR-Mie are capable of predicting these phenomena in a qualitative manner. Both models tend to overestimate the heat capacities of 1-chlorononane, while the overall accuracy of CP-PC-SAFT is somewhat higher. Remarkable, similar results are predicted by CP-PC-SAFT and CS-SAFT-VR-Mie for the saturated liquid phase data of 1bromoalkanes (see Figure S3 of the Supporting Information). Although the overall mean energy constants of attractive forces seem insignificant in the case of heat capacities, the above ΔvapHm analysis can be relevant for interpretation of viscosity data. Specifically, Figure 4 demonstrates that the saturated liquid viscosities of 1-chlorononane and n-dodecane are nearly identical and they are noteworthy higher in comparison to n-nonane. In this respect, it should be noticed that an accurate estimation of these viscosity inter-relations in the entirely predictive manner is a particularly challenging test for the density-based viscosity models since the densities of 1chlorononane and n-dodecane are dissimilar. Nevertheless, it can be seen that the recently proposed55 modeling framework comprising CP-PC-SAFT and the modified Yarranton−Satyro correlation (MYS) generalized by the CP-PC-SAFT molecular

Figure 2. Fluctuation lines in the temperature range 293.15−433.15 K derived from Table 2 for 1-chlorononane and from NIST webbook48 for n-nonane and n-dodecane as well as the values calculated from the molar enthalpy of vaporization (1-chlorononane (H)).

ν(ρ0 ) =

M wPi 0 ρ

(18)

Pi0

Since the combination of all factors excepting is close to each other for all the liquids, we can conclude that the “key player” influencing the shift between fluctuation lines of nnonane and 1-chlornonane/n-dodecane is the internal pressure, 5147


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capacities from 248.15 to 448.15 K, and speeds of sound from 246.88 to 457.25 K. These results have been interpolated by polynomials to obtain the saturated liquid isothermal coefficient of expansion, adiabatic compressibility, isothermal compressibility, isochoric heat capacity, and the internal pressure data. Experimental data reveal that replacing hydrogen by a chlorine atom in n-nonane molecule results in increase of densities by ∼20% and even more significant upsurge of viscosities. Although the densities of 1-chlorononane are still significantly higher in comparison to n-dodecane, their viscosities are nearly equal. This phenomenon matches the suppositions reached by relating the overall mean energy constants of attractive forces in liquid chlorinated alkanes as a weighted combination of energies of the pairwise interactions between hydrogen and chlorine atoms, namely the approximate equivalence of a chlorine atom to six hydrogen atoms. An accurate prediction of these viscosity data by the modeling framework comprising CP-PC-SAFT and MYS might evidence that the reliable predictive viscosity models should not be based solely on certain thermodynamic property such as density, but consider some additional molecular information, as accomplished by MYS. At the same time, while the heat capacities of 1-chloronoane and n-nonane expressed in molar units are comparable, they are significantly smaller in comparison to n-dodecane. This effect is estimated by CP-PC-SAFT and CS-SAFT-VR-Mie in qualitatively accurate manner. Another remarkable phenomenon, namely the smaller dependence of speeds of sound in 1chlorononane on pressure in comparison to n-alkanes, can be explained by the fluctuation theory and it is successfully predicted by both SAFT models. Although FT-EoS exhibits a clear overall superiority over these models in estimating the high-pressure data, it should be kept in mind that, unlike them, it utilizes the saturated liquid data for specific isotherms. Even so, due to its noteworthy simplicity, FT-EoS should be considered as a particularly effective tool for predicting thermodynamic properties at elevated pressures. Although the current overall outcomes of CP-PC-SAFT are slightly advantageous in comparison to CSSAFT-VR-Mie, the robustness of the latter model can be confirmed by its capability to estimate the high-pressure intersection of αp isotherms. Unfortunately, CP-PC-SAFT fails in predicting this effect.

Figure 3. Saturated liquid isochoric and isobaric heat capacities. Points, literature data for 1-chlorononane obtained from Tables 1 and S3; for n-nonane and n-dodecane, from Melikhov44 and Bessières et al.49 Solid lines, predictions of CP-PC-SAFT; dashed lines, CS-SAFTVR-Mie with m = 3; dotted lines, CS-SAFT-VR-Mie with m = 4.

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ASSOCIATED CONTENT

S Supporting Information *

Figure 4. Viscosities of saturated liquid n-nonane, n-dodecane, and 1chlorononane. Points, experimental data.50−54 Lines, data predicted by the modeling framework comprising CP-PC-SAFT and MYS.55

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.8b00174. Coefficients for polynomial interpolations of experimental data; comparison of current data with available literature sources on 1-chlorononane; derivative thermodynamic properties of 1-chlorononane at atmospheric pressure; values of isothermal compressibility at high pressures; values of isobaric coefficient of expansion at high pressures; coefficients for polynomial interpolations of logarithm of isothermal compressibility and parameter k in eq 7; values of CP-PC-SAFT parameters; predictions of isobaric coefficient of expansion of 1-chlorononane at high pressures; results for densities of 1-chlorononane at high pressures; comparison of accuracies of CP-PCSAFT and CS-SAFT-VR-Mie in predicting thermody-

parameters passes this test successfully. This approach is even capable of capturing the fact that the viscosities of 1chlorononane are a little higher than viscosities of n-dodecane.

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CONCLUSIONS This study reports the experimental density and speed of sound data of 1-chlorononane along seven isotherms from 293.15 to 413.15 K at pressures from saturation up to 196.1 MPa. The pertinent isothermal compressibility and the isobaric coefficient of expansion data have been obtained by numerical differentiating of densities. In addition, the saturated liquid densities have been measured from 253.15 to 443.15 K, isobaric heat 5148


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Perturbed Chain-Statistical Association Fluid Theory Equation of State Revisited. Ind. Eng. Chem. Res. 2014, 53, 14127. (16) Lafitte, T.; Apostolakou, A.; Avendaño, C.; Galindo, A.; Adjiman, C. S.; Müller, E. A.; Jackson, G. Accurate Statistical Associating Fluid Theory for Chain Molecules Formed from Mie Segments. J. Chem. Phys. 2013, 139, 154504. (17) Mejía, A.; Herdes, C.; Müller, E. A. Force Fields for CoarseGrained Molecular Simulations from a Corresponding States Correlation. Ind. Eng. Chem. Res. 2014, 53, 4131. (18) Bolotnikov, M. F.; Neruchev, Y. A. Speed of Sound of Hexane +1-Chlorohexane, Hexane+1-Iiodohexane, and 1-Chlorohexane+1Iodohexane at Saturation Condition. J. Chem. Eng. Data 2003, 48, 411. (19) Bolotnikov, M. F.; Verveyko, V. N.; Verveyko, M. V. (2004). Speeds of Sound, Densities, and Isentropic Compressibilities of Poly (propylene glycol)-425 at Temperatures from (293.15 to 373.15) K and Pressures up to 100 MPa. J. Chem. Eng. Data 2004, 49, 631. (20) Frenkel, M.; Hong, X.; Dong, Q.; Yan, X.; Chirico, R. D. Densities of Halohydrocarbons, 2.2.4 C7-C22. In Landolt-Börnstein Group IV Physical Chemistry 8J M; Springer-Verlag: Berlin, 2003. (21) Yaws, C. L. Yaws’ Critical Property Data for Chemical Engineers and Chemists; Knovel, 2014. (22) Chorążewski, M.; Postnikov, E. B.; Jasiok, B.; Nedyalkov, Y. V.; Jacquemin, J. A Fluctuation Equation of State for Prediction of HighPressure Densities of Ionic Liquids. Sci. Rep. 2017, 7, 5563. (23) Postnikov, E. B.; Goncharov, A. L.; Cohen, N.; Polishuk, I. Estimating the Liquid Properties of 1-Alkanols from C5 to C12 by FTEoS and CP-PC-SAFT: Simplicity Versus Complexity. J. Supercrit. Fluids 2015, 104, 193. (24) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: an Equation of State based on a Perturbation Theory for chain molecules. Ind. Eng. Chem. Res. 2001, 40, 1244. (25) Lubarsky, H.; Polishuk, I. Implementation of the Critical PointBased Revised PC-SAFT for Modeling Thermodynamic Properties of Aromatic and Haloaromatic Compounds. J. Supercrit. Fluids 2015, 97, 133. (26) Chorążewski, M.; Aim, K.; Wichterle, I.; Jacquemin, J.; Polishuk, I. High-Pressure Phase Equilibrium in the {Carbon Dioxide (1) + 1Chloropropane (2)} Binary System. J. Chem. Thermodyn. 2015, 91, 165. (27) Chorążewski, M.; Postnikov, E. B.; Oster, K.; Polishuk, I. Thermodynamic Properties of 1,2-Dichloroethane and 1,2-Dibromoethane under Elevated Pressures: Experimental Results and Predictions of a Novel DIPPR-Based Version of FT-EoS, PC-SAFT, and CP-PC-SAFT. Ind. Eng. Chem. Res. 2015, 54, 9645. (28) Lubarsky, H.; Polishuk, I.; Nguyen-Huynh, D. The Group Contribution Method (GC) Versus the Critical Point-Based Approach (CP): Predicting Thermodynamic Properties of Weakly-and NonAssociated Oxygenated Compounds by GC-PPC-SAFT and CP-PCSAFT. J. Supercrit. Fluids 2016, 110, 11. (29) Lubarsky, H.; Polishuk, I.; Nguyen-Huynh, D. Implementation of GC-PPC-SAFT and CP-PC-SAFT for Predicting Thermodynamic Properties of Mixtures of Weakly-and Non-Associated Oxygenated Compounds. J. Supercrit. Fluids 2016, 115, 65. (30) Polishuk, I.; Nakonechny, F.; Brauner, N. Predicting Phase Behavior of Metallic Mercury in Liquid and Compressed Gaseous Hydrocarbons. Fuel 2016, 174, 197. (31) Polishuk, I.; Vilk, A.; Chorążewski, M. Predicting Phase Behavior of Metallic Mercury in Liquid and Compressed Gaseous Hydrocarbons II: Further Examination of CP-PC-SAFT in the Light of New Data. Fuel 2017, 203, 686. (32) Polishuk, I. Implementation of CP-PC-SAFT for Predicting Thermodynamic Properties and Gas Solubility in 1-Alkyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide Ionic Liquids Without Fitting Binary Parameters. Ind. Eng. Chem. Res. 2017, 56, 7845. (33) Polishuk, I.; Sidik, Y.; NguyenHuynh, D. Predicting Phase Behavior in Aqueous Systems Without Fitting Binary Parameters I: CP-PC-SAFT EOS, Aromatic Compounds. AIChE J. 2017, 63, 4124.

namic properties of saturated liquid 1-bromobutane, 1bromohepatane, and 1-bromododecane (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone +972-3-9066346. Fax +972-3-9066323. ORCID

Eugene B. Postnikov: 0000-0001-7904-1881 Ilya Polishuk: 0000-0002-1153-3748 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS V.V.M. and E.B.P. are supported by RFBR, Research Project ́ No. 16-08-01203. We would like to thank Prof. José Matias Garrido, Universidad de Concepción, Chile, for a kind sharing of a code for the CS-SAFT-VR-Mie EoS.

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Experimental Determination and Modelling Thermophysical Properties

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