Thermodynamic Properties of Dichloromethane, Bromochloromethane

Article pubs.acs.org/IECR

Thermodynamic Properties of Dichloromethane, Bromochloromethane, and Dibromomethane under Elevated Pressure: Experimental Results and SAFT-VR Mie Predictions Mirosław Chorązė wski,*,† Jacobo Troncoso,*,‡ and Johan Jacquemin§ †

Institute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice, Poland Departamento de Fisica Aplicada, Universidad de Vigo, Campus de As Lagoas, 32004 Ourense, Spain § CenTACat, School of Chemistry and Chemical Engineering, Queen’s University of Belfast, Stranmillis Road, Belfast BT9 5AG, United Kingdom ‡

S Supporting Information *

ABSTRACT: The speeds of sound in dibromomethane, bromochloromethane, and dichloromethane have been measured in the temperature range from 293.15 to 313.15 K and at pressures up to 100 MPa. Densities and isobaric heat capacities at atmospheric pressure have been also determined. Experimental results were used to calculate the densities and isobaric heat capacities as the function of temperature and pressure by means of a numerical integration technique. Moreover, experimental data at atmospheric pressure were then used to determine the SAFT-VR Mie molecular parameters for these liquids. The accuracy of the model has been then evaluated using a comparison of derived experimental high-pressure data with those predicted using SAFT. It was found that the model provide the possibility to predict also the isobaric heat capacity of all selected haloalkanes within an error up to 6%.

1. INTRODUCTION The acoustic method is a very suitable device for the precise determination of the thermodynamic properties of compressed liquids based on the accurate measurements of their speed of sound.1,2 A prior knowledge of the thermodynamic properties of liquids like halogenoalkanes is of high interest due to their wide usage in science and in various industrial processes. For examples, halogenated methane may act as a one-carbon source in some organic synthesis,3−6 while dichloromethane plays also an important role as a convenient solvent for low temperature work, as it is used in industry as a cleaning agent and paint remover, due to its low freezing temperature. It is also very well-known that dichloromethane is used in extraction operation as a solvent for removal of caffeine from coffee beans, for example.7 Additionally, halomethanes are often used in the synthesis of several pharmaceuticals, herbicides, and pesticides, but they are also applied as fumigants and fire extinguishing media.8 It is interesting to mention also that bromochloromethane was used as a fire suppression agent by the German Luftwaffe during the World War II.9 In spite of such wide range of applications and utilizations, there are still gaps in the thermodynamic data sets for haloalkanes under high pressure available, to date, in the open literature. For example, to the best of our knowledge only one data set on the speed of sound in dichloromethane under elevated pressures is available into the literature,10 while several data sets are available for this property at 0.1 MPa for each investigated liquid.11−20 However, in the case of dichloromethane and dibromomethane, density data and derived properties are also well described at atmospheric pressure,11−17,19−51 as well as under high pressure as 1252−63 and 460,64−66 data sets are reported into the literature for pressure © 2014 American Chemical Society

up to 51.1 and 70.0 MPa, respectively. Additionally, available experimental data up to 2001 on the compressed liquid density were critically evaluated and fitted by the Tait equation by Cibulka et al.67 while very recently Gonçalves et al.55 reported new density data for dichloromethane under elevated pressures by using a vibrating tube densitometer, for example. However, published data for bromochloromethane on the compressedliquid densities and related quantities are very limited even at 0.1 MPa,20,47−49,68,69 and only three high-pressure data sets,64−66 reported only at 298.15 K, for pressure up to 20 MPa are available in the literature. Similarly, heat capacity data of these liquids even at atmospheric pressure are very limited in the open literature,19,70−75 as no data is so far published in the case of the bromochloromethane, for example. Based on this lack of experimental data and to further understand the relationship between the thermodynamic properties of dibromomethane, bromochloromethane, and dichloromethane, we decided to report herein a temperature−pressure study on selected liquid haloalkanes by means of the acoustic method.76 First, the speeds of sound in selected halide-substituted methane derivatives were determined as a function of pressure up to 100 MPa and the temperature from 293.15 to 313.15 K in order to provide accurate experimental data. Second, experimental density data of the dibromomethane, bromochloromethane, or dichloromethane have been also measured using a vibrating tube densitometer over the temperature range from 273.15 to 363.15, 273.15 to 333.15, or Received: Revised: Accepted: Published: 720

October 1, 2014 December 22, 2014 December 24, 2014 December 24, 2014 DOI: 10.1021/ie5038903 Ind. Eng. Chem. Res. 2015, 54, 720−730

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Industrial & Engineering Chemistry Research

Table 1. Comparison with Selected Literature Data at T = 298.15 K: Density ρ, Molar Heat Capacity at Constant Pressure CP, Speed of Sound u, Isobaric Expansivity αP, Isentropic Compressibility κS, Isothermal Compressibility κT, of the Investigated Liquids this work ρ/(kg·m−3)

1315.34

CP/(J·K−1·mol−1) u/(m·s−1) 103αP/K−1 1012κS/Pa−1 1012κT/Pa−1

98.58 1069.48 1.402 664.68 1048.8

ρ/(kg·m−3) CP/(J·K−1·mol−1) u/(m·s−1) 103αP/K−1 1012κS/Pa−1 1012κT/Pa−1

1923.67 104.14 984.08 1.202 536.80 814.9

ρ/(kg·m−3)

2482.75

CP/(J·K−1·mol−1)

104.88 [19] 947.14 1.053 448.99 669.7

u/(m·s−1) 103αP/K−1 1012κS/Pa−1 1012κT/Pa−1

literature dichloromethane 1314.20 [35]; 1315.10 [36]; 1315.20 [40]; 1316.00 [43]; 1316.10 [30]; 1316.16 [67]; 1316.20 [11, 14, 28]; 1316.30 [12, 29, 41]; 1316.48 [15]; 1316.50 [21−23, 25, 27]; 1316.58 [33]; 1316.78 [44, 55]; 1316.98 [24]; 1319.10 [38, 56]; 1325.64 [32]; 1326.40 [34] 95.61 [74]; 97.97 [74]; 100.9 [70]; 101.07 [75]; 102.70 [73]; 129.20 [71] 1035.00 [12]; 1071.30 [11, 14]; 1072.20 [15]; 1100.00 [17] 1.370 [61]; 1.391 [34, 35]; 1.450 [55] 660.75 [15]; 662.00 [11, 14]; 709.19 [12] 1020.0 [61]; 1026.0 [35, 56]; 1032.0 [67]; 1070.15 [55]; 1080.0 [46] bromochloromethane 1921.71 [20]; 1922.42 [48]; 1922.46 [65]; 1922.49 [68]; 1923.00 [47]; 1924.55 [49]; 1924.88 [64, 66]; 1931.30 [69] 986.10 [20] 1.174 [66]; 1.195 [64]; 1.369 [65] 535.14 [20] 749.0 [64, 66]; 823.0 [65] dibromomethane 2477.80 [50]; 2478.36 [49]; 2478.37 [66]; 2478.56 [64]; 2478.61 [20]; 2480.83 [48, 65]; 2481.50 [43]; 2482.97 [19]; 2483.97 [51]; 2484.09 [67]; 2484.20 [47] 104.10 [70]; 104.47 [72]; 127.19 [71] 943.00 [17]; 947.15 [19]; 949.20 [20] 0.9845 [66]; 1.047 [64]; 1.053 [19]; 1.211 [65] 447.79 [20]; 448.94 [19] 561.0 [64, 66]; 664.0 [65]; 669.6 [19]

of water, determined by the Karl Fischer titration method, was less than 4 × 10−5 for all investigated compounds. 2.2. Experimental Methods. Speed of Sound Measurements. The speeds of sound at the frequency of 2 MHz were measured under atmospheric and elevated pressures by the use of two measuring equipment setups with measuring vessels of the same acoustic path and construction based on a single transmitting-receiving ceramic transducer and an acoustic mirror. Both apparatuses operate on the principle of the pulse-echo-overlap method. Both instruments were first calibrated with doubly distilled water using recommended data published by Marczak at atmospheric pressure.79 The measurements uncertainty is close to ±0.5 m·s−1 at atmospheric pressure, while the precision is an order of magnitude better.80 The standard values of the speed of sound in water at elevated pressures were taken from the Kell and Whalley polynomial.81 The uncertainty of the measurements under elevated pressure was then estimated to be better than ±1 m·s−1. The pressure was measured using Hottinger Baldwin System P3MD within an uncertainty better than ±0.15% full scale. The temperature was measured using an Ertco Hart 850 platinum resistance thermometer certified by NIST with an uncertainty of ±0.05 K and a resolution of 0.001 K. During the measurements, the stability of ±0.01 K was maintained. Details of each apparatus, experimental procedure, and calibration can be found elsewhere.82,83 Density Measurements. Experimental densities at atmospheric pressure were measured using an Anton Paar DMA 5000 digital vibrating tube with an uncertainty better than ±5 × 10−2 kg·m−3 and repeatability better than ±5 × 10−3 kg·m−3. The instrument was calibrated with dry air and redistilled and degassed water. Before performing the appropriate measurements, the apparatus was also tested with the density of known

273.15 to 308.15 K at atmospheric pressure, respectively. Third, for each selected haloalkane, its SAFT-VR Mie molecular fitting parameters were then determined using only volumetric data at atmospheric pressure (i.e., dependence on the density as a function of temperature, calculated isobaric thermal expansivity, and isentropic compressibility at 298.15 K and 0.1 MPa), along with its vaporization enthalpy at 298.15 K reported in the literature.77,78 Additionally, a differential scanning calorimeter has been used to determine the temperature dependences on the isobaric heat capacity data of the bromochloromethane from 293.15 to 323.15 K and of the dichloromethane from 284.15 to 308.15 K at atmospheric pressure. Finally, calculated volumetric data as a function of temperature and pressure, experimental heat capacity data at atmospheric pressure, and literature VLE diagrams were then compared with those predicted using the SAFT-VR Mie equation to further evaluate the predictability of reported molecular fitting parameters.

2. EXPERIMENTAL SECTION 2.1. Chemicals Used. The dibromomethane, dichloromethane, and bromochloromethane used in this study were purchased from Alfa Aesar (molar basis purity >99%), from Lancaster (molar basis purity >99%), and from Avocado (molar basis purity close to 99.5%), respectively. Prior to use, all compounds were further purified by fractional distillation. In each case, only the middle fractions were then collected, resulting in a liquid sample with purity, determined by GLC analysis, greater than 99%. Additionally, all investigated liquids were dried with molecular sieve (Lancaster, type 3 Å, beads) and stored in dark glass flasks stored in a desiccator. The samples were finally degassed in an ultrasonic cleaner just before each measurement. After purification, the mass fraction 721

DOI: 10.1021/ie5038903 Ind. Eng. Chem. Res. 2015, 54, 720−730

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conditions using our experimental data is in excellent agreement (i.e., relative absolute average deviation close to 0.1%). This comparison can be used to estimate the accuracy of speed of sound data under elevated pressure reported in Table S1 of the Supporting Information. The following polynomial function (eq 1) was used to describe the temperature dependences on the speed of sound, density, and specific heat capacity at atmospheric pressure:

molality of aqueous NaCl. More experimental and calibration details can be found in our previous papers.84−87 Heat Capacity Measurements. The isobaric heat capacities at atmospheric pressure were measured with a differential temperature-scanning microcalorimeter from Calpresdat. The uncertainty of these measurements was estimated to be ±1%. The experimental instrument details, applied procedures, and the calibration have been described previously.88

2

3. RESULTS AND PVT CALCULATIONS The speeds of sound in dibromomethane, bromochloromethane, and dichloromethane have been measured in the temperature range from 293.15 to 313.15 K and at pressures up to 100 MPa. The isobaric heat capacities of the bromochloromethane and dichloromethane have been measured from 293.15 to 323.15 and 284.15 to 308.15 K at atmospheric pressure, respectively. Density data of the dibromomethane, bromochloromethane, or dichloromethane have been measured as a function of the temperature from 273.15 to 363.15, 273.15 to 333.15, or 273.15 to 308.15 K and at atmospheric pressure, respectively. In the case of dichloromethane the temperature dependence on investigated properties was determined only up to 308.15 K due to its low boiling temperature at 0.1 MPa (i.e. 312.75 K).78 Density, molar heat capacity at constant pressure, and speed of sound data for the investigated liquids obtained during this work at 298.15 K and at atmospheric pressure are given in Table 1, as well as their derived isobaric expansivity, isentropic compressibility, and isothermal compressibility. According to Table 1, it appears that experimental speed of sound data for the investigated samples at atmospheric pressure are in excellent agreement with reported literature data except in the case of dichloromethane data reported by Aminabhavi et al.12 and by Sette,17 based on which relative deviations close to +3.3% and to −2.8% are observed at 298.15 K. Additionally, measured speeds of sound at pressures higher than atmospheric are tabulated in Table S1 of the Supporting Information, while measured experimental values of speed of sound, density and heat capacity under atmospheric pressure are listed in Table S2 of the Supporting Information. As shown in Figure 1, the comparison between the speed of sound in the dichloromethane data reported by Niepmann et al.10 for pressures up to 60 MPa at 300 K with those interpolated under the same

y=

∑ aiT i

(1)

i=0

where y is the speed of sound, u0, density, ρ, or specific heat capacity, Cp, at atmospheric pressure p0; ai are the polynomial coefficients (ai = ui for the speed of sound, ai = ρi for the density, and ai = ci for the heat capacity) listed in Table 2. Table 2. Coefficients of Polynomial (Equation 1) for the Speed of Sound, Density, and Specific Heat Capacity under Atmospheric Pressure and Mean Deviations from the Regression Line Dichloromethane u0 m·s−1 +2248.943 ρ0 kg·m−3 +1753.743 c0 J·kg−1 K−1 +1455.261

u1 u2 m·s−1·K−1 m·s−1·K−2 −3.955927 0 ρ1 103ρ2 −3 −1 kg·m ·K kg·m−3·K−2 −1.096164 −1.255238 c1 103c2 −1 −2 J·kg K J·kg−1 K−3 −2.535259 +5.189285 Bromochloromethane

δu0 m·s−1 0.02 δρ kg·m−3 0.01 δCp J·kg−1 K−1 0.05

u0 m·s−1 +1996.571 ρ0 kg·m−3 +2508.597 c0 J·kg−1 K−1 +1275.05

u1 103u2 m·s−1·K−1 m·s−1·K−2 −3.738455 +1.148521 ρ1 103ρ2 −3 −1 kg·m ·K kg·m−3·K−2 −1.611688 −1.174488 c1 103c2 −1 −2 J·kg K J·kg−1 K−3 −3.22788 +5.537559 Dibromomethane


u0 m·s−1 +1790.831 ρ0 kg·m−3 +3173.003 c0 J·kg−1 K−1 +737.651

u1 m·s−1·K−1 −3.111798 ρ1 kg·m−3·K−1 −2.016145 c1 J·kg−1 K−2 −0.98778

103u2 m·s−1·K−2 +0.94598 103ρ2 kg·m−3·K−2 −1.002792 103c2 J·kg−1 K−3 +1.801954


The measured speeds of sound have been then correlated as a function of the temperature and pressure using the following double polynomial equation (eq 2) as suggested by Sun et al.89 m

p − p0 =

n

∑ ∑ aij(u − u0)i T j i=1 j=0

Figure 1. Comparison of the speed of sound in dichloromethane at elevated pressure reported herein with data reported by Niepmann et al.10 (●) for pressures up to 60 MPa at 300 K.

(2)

where aij are the polynomial coefficients, u is the speed of sound at p > 0.1 MPa, and u0 is the speed of sound calculated 722


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Industrial & Engineering Chemistry Research Table 3. Coefficients of Equation (Equation 2) and Mean Deviations from the Regression Line δu a1j

a2j

a3j

δu

(K−j·MPa·s·m−1)

(K−j·MPa·s2·m−2)

(K−j·MPa·s3·m−3)

(m·s−1)

Dichloromethane j 0 1 2

+7.018525 × 10−1 −1.616405 × 10−3

j 0 1 2 j 0 1 2

0.09 +3.043720 × 10−6 −5.819090 × 10−9 Bromochloromethane

−3.067007 × 10−10

+3.251524 × 10−3 −7.384836 × 10−6

+2.961767 × 10−2 −1.829024 × 10−4 +2.872223 × 10−7 Dibromomethane

−1.096549 × 10−4 +7.015191 × 10−7 −1.121889 × 10−9

+7.531698 × 10−1

+7.949514 × 10−4 −4.157432 × 10−12

κS, of the measuring liquids were calculated from the Laplace equation (eq 6)

from eq 1. Fitting coefficients aij as well as the mean deviations from regression lines are presented in Table 3. This polynomial equation was used to obtain the pρT properties of the liquids analyzed in this study. The calculations of density and heat capacity at constant pressure under elevated temperatures and pressures are performed in the way proposed by Sun et al.89 As previously described,76 the density (eq 3) and heat capacity at constant pressure (eq 4) data as a function of pressure can be computed by integration of the well-known thermodynamic relations: Δρ =

0.06

−3.772829 × 10−6

p2 ⎛ 1 α 2T ⎞ ⎜ + p ⎟d p ≈ ⎜ 2 Cp ⎟⎠ p1 ⎝ u

∫

∫p

1

p2

κS =

κT = κS +

2

αp T 1 dp + Δp 2 Cp u

1 ⎛ ∂ρ ⎞ ⎜ ⎟ ρ ⎝ ∂T ⎠ p

(6)

TVαp 2 Cp

(7)

The estimated overall uncertainties of the calculated αp, κS, and κT are expected to be close to ±1%, ± 0.15%, and ±0.3%, respectively.76,88 The computed values of density, isobaric heat capacity, isobaric coefficient of thermal expansion, isentropic compressibility, and isothermal compressibility under elevated temperature and pressure are presented in Tables S3−S7 of the Supporting Information. To analyze the accuracy of computed volumetric properties, calculated density data as the function of temperature and pressure were then compared with those available in the literature. Figures 2 and 3 show the comparison

(4)

In order to initiate the iterative procedure of solving the above set of first-order differential equations, a set of heat capacity data as a function of the temperature at a reference pressure must be known. The thermal expansivity, αp, is also obtained during this stage of calculation using eq 5. αp = −

1 ρu 2

Values of the isothermal compressibility, κT, were calculated from the following thermodynamic relationship (eq 7):

(3)

⎡ ⎤ ⎛ T ⎞⎢ 2 ⎛ ∂αp ⎞ ⎥ ΔCp = ⎜ ⎟ αp + ⎜ ⎟ dp ⎝ ρ ⎠⎢⎣ ⎝ ∂T ⎠ p⎥⎦

0.10

(5)

The initial values of density and heat capacity are obtained from the polynomial functions (eq 1). The requested data of the speed of sound and heat capacity of the dibromomethane as a function of the temperature at atmospheric pressure were taken from our earlier study.19 In this calculation, a small pressure step of 0.5 MPa is chosen in order to increase the precision of the numerical integration. Further details of the method of computation can be found elsewhere.76,89 The overall uncertainties (perturbation method and deviations between our results and those obtained by other laboratories) are estimated to be ±1% and ±0.5% for the isobaric heat capacity and density, respectively.76 Moreover, additional important thermodynamic properties, including the isentropic compressibility, isothermal compressibility have been then calculated. Isentropic compressibility data,

Figure 2. Comparison of the density of the dichloromethane at elevated pressure reported herein with data reported by (●) Lugo et al.;53 (■) Gonalves et al.;55 and (▽) Burkat et al.56 for pressures up to 30 MPa at 293.15 K. 723


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Figure 3. Comparison of the density of the dichloromethane at elevated pressure reported herein with data reported by (●) Kumagai et al.;54 (○) Gonçalves et al.;55 (■) Burkat et al.;56 (□) Bridgman;57 (▲) Newitt et al.;58 (△) Schamp et al.;59 (▼) Easteal et al.;61 and (▽) Baonza et al.62 for pressures up to 104 MPa at 298.15 K.

Figure 5. Comparison of the density of the dibromomethane at elevated pressure reported herein with data reported by (●) Giĺ nez et al.66 Hernández et al.;64 (■) Jarne et al.;65 and (▽) Garcia-Gimé for pressures up to 20 MPa at 298.15 K.

methane and dibromomethane, respectively. RAADs close to 0.03% or 0.22% and to 0.07% or 0.11% are observed by comparing computed density data using experimental speed of sound values in chlorobromomethane or in dibromomethane with values reported by Jarne et al.65 and by Gil-Hernández et al.,64 for example.

of computed dichloromethane density values with literature data as the function of pressure up to 100 MPa at 293.1553,55,56 and 298.15 K,54−59,61,62 respectively. Based on which, excellent agreement is generally observed since the maximum observed relative deviation is close to −0.3% demonstrating the good accuracy of the proposed method of computation. Interestingly, according to Figure 3, it appears that at 298.15 K, reported dichloromethane density data as a function of pressure are in excellent agreement with all reported density data sets54,55,57−59,61,62 with a relative absolute average deviation (RAAD) lower than 0.1% except with the data reported by Burkat et al.56 where an RAAD close to 0.3% is observed. Similarly, excellent agreements between computed dichloromethane density data as a function of pressure at 303.15 and 313.15 K are observed with the data reported by Lugo et al.53 with RAAD close to 0.08% and 0.07% at 303.15 and 313.15 K for pressures up to 25 MPa−by Schornack et al.52 (RAAD close to 0.30% for pressure up to 97.2 MPa) or by Diguet et al.63 for pressures up to 100 MPa at 303.2 K within a RAAD close to 0.20%. Similarly, as shown in Figures 4 and 5, excellent agreements are observed between calculated density data with reported values in the literature64−66 for both chlorobromo-

4. APPLICATION OF SAFT-VR MIE EQUATION Experimental data were used to fit the model parameters of the SAFT-VR Mie equation, recently proposed by Lafitte et al.90 This equation is based on the Wertheim theory91−96 applied to a fluid formed by Mie monomers. Herein, a brief description of the equation is outlined; a detailed explanation of this methodology can be found elsewhere.90 Since it was supposed that selected liquids do not present any association capability, the final value of the molar Helmholtz energy Am is the sum of three contributions, using eq 8: A m = RT (a i + a m + ac) i

m

(8)

c

where a , a , and a refer to the ideal, monomer, and chain contribution. am is obtained from perturbation theory by following the Barker and Henderson methodology.97,98 It consists of a high temperature expansion based on the hardsphere fluid, which was taken as reference. Three perturbation terms, a1, a2, and a3, are used. Therefore, am is given by eq 9: a m = a HS + βa1 + β 2a 2 + β 3a3

(9)

where β = 1/kBT, and a is the hard sphere fluid contribution obtained from the Carnahan−Starling equation (eq 10) as HS

a HS =

4η − 3η2 (1 − η)2

(10)

where η = πmsρd /6. ms is the segment number of the molecules, one of the model parameters which must be fitted to experimental data. It gives information about the length of the molecule. The parameter d is the diameter of the effective hard spheres corresponding to Mie segments. It is temperaturedependent and is given by eq 11: 3

Figure 4. Comparison of the density of the chlorobromomethane at elevated pressure reported herein with data reported by (●) Giĺ nez et al.66 Hernández et al.;64 (■) Jarne et al.;65 and (▽) Garcia-Gimé for pressures up to 20 MPa at 298.15 K.

d=

∫0

σ

(1 − e−βu(r))dr

(11)

u(r) is the Mie potential, defined as 724


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Industrial & Engineering Chemistry Research u(r ) =

λa / λ r − λa ⎛⎛ σ ⎞ λ r ⎛ σ ⎞ λ a ⎞ λr ⎛ λr ⎞ ε⎜⎜⎜ ⎟ − ⎜ ⎟ ⎟⎟ ⎜ ⎟ ⎝r⎠ ⎠ λr − λa ⎝ λa ⎠ ⎝⎝ r ⎠

⎛⎛ σ ⎞ λ r ⎛ σ ⎞ λ a ⎞ = Cε⎜⎜⎜ ⎟ − ⎜ ⎟ ⎟⎟ ⎝r⎠ ⎠ ⎝⎝ r ⎠

estimation process. The relative maximum deviations were 0.17, 2, and 3% for ρ, αp and κS, respectively. The obtained parameters for the studied compounds are listed in Table 4. It can be seen as expected, that the parameter Table 4. Fitting Parameters of the SAFT-VR Mie for the Studied Liquids

(12)

λr and λa are the repulsive and attractive exponents of the Mie potential, σ gives the distance at which the potential changes from repulsive to negative, and ε gives the strength of the interaction. All these quantities, except λa, fixed to 6, were then fitted by using experimental data presented herein. In order to calculate d, the integral given by eq 11 must be evaluated. This has been done using Gauss−Legendre quadrature with 20 points. The expressions for a1, a2, and a3 can be found elsewhere.90 The chain contribution is obtained from Wertheim theory. In order to calculate it, the prior knowledge of the radial distribution function, gm(σ) (eq 13), of the monomer model at r = σ is needed. Since no exact expression is available, it was also obtained as a perturbation expansion taking the hard sphere fluid as reference: g m(σ ) = g HS(σ )e(βεg1(σ )/ g

HS

(σ ) + β 2ε 2g2(σ )/ g HS(σ ))

ms σ/Å λa (ε/kB)/K

(13)

(14)

Therefore, five parameters are needed to fully characterize the system: ms, σ, λa, λr, and ε. In this work, λa was fixed to 6 since the attractive part of intermolecular potential of several systems like halogenoalkanes is accurately described by the London force, i.e. r−6, law can be applied. The other parameters were fitted using atmospheric pressure experimental data collected for each liquid during this work: density as a function of temperature, αp, and κS at 298.15 K. Moreover, vaporization enthalpy Δh of each liquid at 298.15 K, obtained from the literature,77,78 was also included during the fitting process. All these properties were used to determine the molar Helmholtz free energy form using well-known thermodynamic relationships reported above. The objective function (eq 15) to be minimized in the fitting process was f=

∑ wY (Ym − Ye)2

chlorobromomethane

dibromomethane

2.2714 3.3489 11.831 270.25

2.2511 3.4460 12.947 310.11

2.2165 3.5484 13.939 351.43

ms is almost the same in each liquid, as the number of segments for all studied molecules is almost the samei.e., there is no variation in the number of atoms for the selected compounds. On the other hand, it is found that σ increases by adding Br atoms, as it should be, since the Br atom is significantly larger than Cl one. This tendency is also observed for ε and λr, a fact which shows the higher the Br atom number, the stronger and harderi.e., more similar to a hard spherethe effective interaction potential is. Figures 6 and 7 give the results for density and κS versus temperature for several isobars. Moreover in order to see the tendency of curves to cross at high pressures, αp against pressure for several isotherms is also given in Figure 8. In each case, quite good results are obtained, by keeping in mind that only few data at atmospheric pressurefrom 4 to 6 points for density and only one for κS and αpwere used to fit the model parameters, thus calculations at high pressure are pure predictions. Figure 9 gives a comparison of the experimental vapor pressure data of selected liquids as the function of the temperature, when available, obtained from the literature,77,78 with those determined during this work using the SAFT-VR Mie equation. In spite of being a pure predictionas no vapor pressure value was used during the model parameters fitting processgood coherence was also obtained; in fact, critical temperature is predicted with an error under 10 K for all studied compounds. Finally, it must be highlighted that the isobaric heat capacity can be predicted with an error range from 4 to 6%, which although is much worse than the values obtained for the other thermodynamic properties, its deviations are of the same order as those found when experimental data from different sources are compared together showing again the good predictive capability of the SAFT-VR Mie equation on the thermodynamic properties of the selected halogenoalkanes.

where gHS(σ) is the radial distribution function of the hard sphere fluid at σ, and g1(σ) and g2(σ) are the first and second perturbation terms for gm at σ; their expressions can be found elsewhere.90 The chain contribution is then simply obtained using eq 14: ac = (1 − ms)ln(g m(σ ))

dichloromethane

(15)

5. CONCLUSION In this paper we have investigated the effect of temperature from 293.15 to 313.15 K and pressure up to 100 MPa on the speed of sound in three different haloalkanes namely the dichloromethane, chlorobromomethane and dibromomethane. Experimental speed of sound in dichloromethane data were then compared satisfactory with available literature data in order to show the accuracy of the selected methodology for pressure up to 60 MPa, which is close to 0.1%. Additionally, density and heat capacity measurements at atmospheric pressure have been also determined for these compounds as a function of the temperature to then be able to predict by using a numerical integration technique their volumetric properties and isobaric heat capacities as the function of temperature and pressure using experimental speed of sound

Where Y represents the physical property to be fitted, subscripts m and e denotes the model and experimental values, and, wY is the weight given to each property. We have chosen 10−3, 3 × 10−5, 103, and 109 for ρ, Δh, αp, and κS, respectively. Obviously, the parameters depend on the weights given to each property, but we have found that once the experimental data are correctly reproducedi.e., relative deviations are around a few percentchanges in weights induce only small variations in the parameter values. We have tried to include also heat capacity data at several temperatures to determine fitting model parameters, but only slight changes on them were observed. Additionally, in this case, a significant deterioration of the correlation of other properties was observed; therefore heat capacity data were removed from the model parameters 725


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Figure 6. Density as a function of temperature for several isobars: (●) 0.1; (■) 30; (◆) 50; and (▲) 100 MPa for (a) dichloromethane, (b) chlorobromomethane, and (c) dibromomethane. Solid lines represent SAFT predictions.

Figure 7. Isentropic compressibility as a function of temperature for several isobars: (●) 0.1; (■) 30; (◆) 50; and (▲) 100 MPa for (a) dichloromethane, (b) chlorobromomethane, and (c) dibromomethane. Solid lines represent SAFT predictions.

data. The accuracy of the proposed numerical technique, which was applied herein for all selected haloalkanes, was then checked by comparing calculated density with literature values as a function of temperature and pressure, based on which excellent agreements were observed within error lower than 0.3% in each case. Finally, selected experimental data at atmospheric pressure have been then used to determine the SAFT-VR Mie molecular fitting parameters for these liquids. The accuracy of calculated parameters has been then evaluated using a comparison of derived experimental high-pressure data with those predicted using this model. This comparison shows than fitting parameters provide the possibility to predict not only the volumetric properties but also the isobaric heat capacity of all selected haloalkanes within an error up to 6%, showing in fact the ability of the SAFT-VR Mie equation to

predict a wide range of physical properties of haloalkanes as a function of the temperature and pressure. Our results showed that the values of the thermal expansion coefficient for all investigated halomethanes decrease with increasing pressure. It is worth noting that the general observation of the pressure dependences of the thermal expansion coefficient for many liquids shows that the isotherms of αp present intersections in characteristic pressure range, in which (∂αP/∂T)P = 0. The lines of null dependence of αp against T divide the p−T plane into two regions where (∂αP/ ∂T)P > 0 and (∂αP/∂T)P < 0.99−101 It can be seen that for investigated liquids, dibromomethane, dichloromethane, and bromochloromethane, there are no crossings of thermal expansivities up to 100 MPa. One can see that the general 726


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Figure 8. Isobaric thermal expansivity as a function of pressure for several isotherms: (●) 293.15; (■) 298.15; (◆) 303.15; (▲) 308.15; (▼) 313.15; and (×) 318.15 K for (a) dichloromethane, (b) chlorobromomethane, and (c) dibromomethane. Solid lines represent SAFT predictions.

Figure 9. Vapor pressure against temperature for: (a) dichloromethane (b) chlorobromomethane, and (c) dibromomethane. Solid red lines are correlated experimental data and black ones represent SAFT predictions. Squares and circles represent the critical point coordinates for experimental and SAFT values.

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ASSOCIATED CONTENT

S Supporting Information *

behavior is very similar to that observed for alkanes, that is, thermal expansion coefficient decreases with increasing alkyl chain length and short-chain alkanes exhibit a positive temperature dependence in αp for a broader range of pressures than long-chain alkanes.99 Our present results, as well as those recently published on the thermal expansivities of α,ωdichloroalkanes,101 confirm these tendencies for liquid haloalkanes. Therefore, the crossings isobaric thermal expansivities for tested halomethanes could be observed above 100 MPa.

Experimental values of speeds of sound, densities, and molar heat capacities at atmospheric pressure and experimental speeds of sound and computed values of density, isobaric heat capacity, isobaric coefficient of thermal expansion, isentropic compressibility, and isothermal compressibility under elevated temperature and pressure presented in Tables S1−S7. This material is available free of charge via the Internet at http://pubs.acs.org

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (M.C.). 727


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Industrial & Engineering Chemistry Research *E-mail: [email protected] (J.T.).

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Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Many thanks are given for the assistance of Sylwia Jez̨ ȧ k during the measurements of the density at atmospheric pressure. J.T. thanks Xunta de Galicia for financial support under the project REGALIS (CN 2012/120).

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Thermodynamic Properties of Dichloromethane, Bromochloromethane

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