Vapor Pressures and Thermophysical Properties of Dimethyl

Article pubs.acs.org/jced

Vapor Pressures and Thermophysical Properties of Dimethyl Carbonate, Diethyl Carbonate, and Dipropyl Carbonate Václav Pokorný, Vojtěch Štejfa, Michal Fulem, Ctirad Č ervinka, and Květoslav Růzǐ čka* Department of Physical Chemistry, University of Chemistry and Technology, Prague, Technická 5, CZ-166 28 Prague 6, Czech Republic S Supporting Information *

ABSTRACT: In this work, a thermodynamic study of important industrial solvents, dimethyl carbonate (CAS RN: 616-38-6), diethyl carbonate (CAS RN: 105-58-8), and dipropyl carbonate (CAS RN: 623-96-1), is presented. The vapor pressure pressure measurements were performed using the static method in the temperature interval 238−308 K. Heat capacities of condensed phases were measured by Tian−Calvet calorimetry in the temperature interval 260−358 K. The phase behavior was investigated by DSC in the temperature interval 183− 300 K. The thermodynamic properties in the ideal gaseous state were calculated using the methods of statistical thermodynamics based on calculated fundamental vibrational frequencies and molecular structure data. Calculated ideal-gas heat capacities and experimental data on vapor pressures, condensed phase heat capacities, and vaporization enthalpies were treated simultaneously to obtain a consistent thermodynamic description.

1. INTRODUCTION This work is a continuation of our effort1,2 to establish reliable vapor pressures for industrial chemicals produced on a large scale. Despite their massive production and extensive use (e.g., as solvents or electrolytes in batteries), the vapor pressures of dimethyl carbonate, diethyl carbonate, and dipropyl carbonate at ambient temperatures are not known with sufficient accuracy; previously published values are scattered or in mutual disagreement in this temperature range. Reliable vapor pressure data are indispensable for processes involving phase equilibria and for phase equilibrium studies on systems containing these compounds. In this work, we first assessed all available literature vapor pressure data and examined their consistency with calorimetrically determined vaporization enthalpies and heat capacities of condensed phases and ideal gas. Literature review and consistency tests revealed that new vapor pressure data in the low pressure region and new heat capacities for all three compounds were needed. These data were experimentally determined in this work. Also, heat capacities and entropies in the ideal gaseous state for all of the studied compounds were calculated using the methods of statistical thermodynamics. Fundamental vibrational frequencies and other required molecular parameters were calculated using density functional theory (DFT) and compared with available experimental data from the literature. Consequently, recommended vapor pressure data for dimethyl carbonate, diethyl carbonate, and dipropyl carbonate were developed by the simultaneous correlation of selected vapor pressure and related thermal data (SimCor method, described previously3 and for reader’s convenience also in the Supporting Information). In the case of dimethyl © 2017 American Chemical Society

carbonate, the crystal heat capacities and enthalpy of fusion were measured and used for the establishing thermodynamically consistent sublimation pressures.

2. EXPERIMENTAL SECTION 2.1. Materials. All three compounds were obtained from Aldrich. The samples were stored over 4A molecular sieves for approximately 2 weeks. Sample characteristics are summarized in Table 1. Given the assessed purities, the compounds were studied without further purification. 2.2. Vapor Pressure Measurements. The vapor pressure measurements were performed using the static method with an apparatus internally denoted as STAT6. As this apparatus was previously described in detail in this journal,4 we present here only its operating pressure range (0.5−1333 Pa), temperature range (233−313 K), and the resulting combined expanded (0.95 level of confidence) uncertainty of vapor pressure measurements, which is adequately described by the expression Uc(p/Pa) = 0.005(p/Pa) + 0.05. 2.3. Heat Capacity Measurements. The Tian-Calvet calorimeter (SETARAM μDSC IIIa, France) was used for the heat capacity determination in the temperature range from 260 to 358 K (dimethyl carbonate was measured only up to 333 K due to its volatility). Heat capacities were obtained using a continuous method.5 A detailed description of the calorimeter and its calibration was published previously;6 the combined Received: March 27, 2017 Accepted: July 24, 2017 Published: August 9, 2017 3206

DOI: 10.1021/acs.jced.7b00295 J. Chem. Eng. Data 2017, 62, 3206−3215

Journal of Chemical & Engineering Data

Article

Table 1. Sample Descriptions compound

CAS No.

supplier

dimethyl carbonate diethyl carbonate dipropyl carbonate

616-38-6 105-58-8 623-96-1

Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich

mole fraction purity 0.999a 1.000a 0.996a

water mass fraction 2000 cm−1 and SF = 0.9980 − 1.55 × 10−5 ν for ν < 2000 cm−1. Energy barriers of methyl rotations were obtained from a relaxed scan for the lowest energy conformer. All relative energies of conformers are listed without zero point vibrational point energy corrections as they were found not to significantly improve the agreement between calculated and experimental energy barriers to internal rotations.43 The energy levels of hindered internal rotations were obtained by solving a one-dimensional Schrödinger equation using our code performing the FGH method.44 Throughout the whole work, the following abbreviations for dihedral angles are used to label various conformers (in accordance with our previous work45): trans (t) ≈ 180°, gauche (g) ≈ 60°, antigauche (g′) ≈ −60°, distorted gauche (d or d′) ≈ 95° or −95°, eclipsed (e or e′) ≈ 120° or −120°, and cis (c) ≈ 0°. In some conformations, the dihedral angle was ≈ 40° which was designated as narrowed gauche (n or n′). The labeling of dihedral angles describing the conformers proceeds along the longest chain. As the carbonates are symmetrical, up to four isomorphs can exist for each mentioned sequence. 3.5.1. Dimethyl Carbonate. Several spectroscopic works concerning dimethyl carbonate can be found in the liter3211



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of the studied compounds were found in the literature for comparison. Table 9 lists the ideal-gas thermodynamic properties of all carbonates calculated in this work.

Among the xnnx conformers, only the enne conformer was found to be stable at the B3LYP-D3/6-311+G(d,p) level of theory, while enne and nnnn conformers are stable at the B3LYPD3/6-311+G(2df,p) level of theory. All other conformations could not be optimized or possessed imaginary vibrational frequencies. The effect of the xnnx conformers on ideal gas properties is however negligible due to their high relative conformational energy exceeding 60 kJ·mol−1. 3.5.3. Dipropyl Carbonate. No spectroscopic data or theoretical conformational studies for dipropyl carbonate were found in the literature. The conformational analysis was performed based on the conclusions drawn for lower carbonates. Unlike diethyl carbonate, the lowest energy conformer is gttttg′, while the all-trans conformer has relative conformational energy of 2.77 kJ·mol−1. The 25 nonisomorphic xxttxx conformers have relative energies compared to gttttg′ conformation lower than 3.5 kJ·mol−1 and the energies of 41 nonisomorphic xxtcxx conformers lie in the interval 10.4−15.7 kJ·mol−1. The g angle in xxxxgx conformers with tt or tc configuration around the carbonyl group is distorted to a degree of about 80°, which leads to the instability of xxxxgd′ conformers and low energy of xxxxdg′ conformers compared to that expected for alkyl chain. Eight nonisomorphic xxnnex conformers were successfully optimized, all of them with relative energy higher than 55 kJ·mol−1. The conformers with nn configuration are stable only as xennex or xgnneg′, which indicates that the eclipsed dihedral angle must be stabilized, either with the opposite e or adjacent g′. The dispersion forces have stabilization effect on other high-energy structures; namely, three xnnnnx structures were found to be stable. These structures have relative energy higher than 65 kJ· mol−1 and may not contain nor g′ neither d′ angle due to the steric hindrance. 3.5.4. Summary of Calculations of Ideal-Gas Thermodynamic Properties. The results of conformational study are summarized in Table S3 in the Supporting Information, which lists stable conformers, their relative energies, symmetries, dipole moments, and products of inertia Icalc ABC. The most stable tt form of dimethyl carbonate can be characterized by the product of inertia −135 Icalc kg·m2, while the experimental value ABC = 12.32 × 10 exp amounts to IABC = 12.0684 × 10−135 kg·m2.55 The parameters of methyl rotations are listed in Table S4 in the Supporting Information. Relaxed scans were performed only for conformers with tt configuration around the carbonyl group, as the ct conformers have lower impact on the properties so the difference in barrier height plays a negligible role. The potential energy scans of methyl rotations for diethyl carbonate were performed for the conformers with terminal t and g dihedral angles as the different position from carbonyl plane was expected to affect the energy barrier. As the obtained barriers to methyl rotation were close to each other such treatment was not followed for dipropyl carbonate for which only the potential energy profile of methyl rotation for the most stable conformer gttttg’ was calculated and subsequently used in the calculation of contributions of methyl rotations to ideal-gas thermodynamic properties for each stable conformer. The final ideal-gas thermodynamic properties of the equilibrium mixture were determined using the relations for mixing terms for entropy, heat capacity, and enthalpy34,42 based on the individual contributions of all stable conformers. The temperature-dependent population of conformers was constructed using the Maxwell−Boltzmann distribution and molecular energies of the conformers. Neither experimental nor calculated data on ideal-gas thermodynamic properties of any

Table 9. Standard Molar Thermodynamic Functions (in J· K−1·mol−1) of Dimethyl Carbonate, Diethyl Carbonate, and Dipropyl Carbonate in the Ideal Gaseous State at p = 105 Pa Using B3LYP-D3/6-311+G(d,p) Calculationsa dimethyl carbonate

diethyl carbonate

dipropyl carbonate

T/K

Cg0 p,m

Sg0 m

Cg0 p,m

Sg0 m

Cg0 p,m

Sg0 m

100 150 200 250 273.15 298.15 300 400 500 600 700 800 900 1000

65.0 74.2 81.5 90.1 94.6 99.8 100.2 122.3 143.1 160.8 175.7 188.1 198.7 207.8

253.2 281.4 303.8 322.9 331.1 339.6 340.2 372.2 401.9 429.8 456.0 480.4 503.4 525.0

79.1 96.4 113.0 131.0 139.8 149.5 150.2 188.2 221.4 248.7 271.2 290.1 306.1 319.8

300.1 335.6 365.5 392.6 404.6 417.2 418.2 466.7 512.3 555.2 595.3 632.8 667.9 700.9

102.7 123.2 143.8 167.0 178.6 191.5 192.5 243.7 289.1 327.0 358.5 385.0 407.6 426.9

346.8 392.5 430.8 465.4 480.7 497.0 498.1 560.7 620.1 676.3 729.1 778.8 825.5 869.4

a

Calculated fundamental frequencies were scaled by a linear function SF1 = 0.9980−1.55 × 10−5 νi below 2000 cm−1 and by a constant SF2 = 0.961 above 2000 cm−1.42

3.6. Recommended Vapor Pressure Data Developed by the SimCor Method. First, obvious outliers that were distant from the rest of the vapor pressure data were rejected based on the arc representation for each compound as described in section 3.1. The remainder of the vapor pressure data sets was tested using the SimCor method for consistency (each data set separately). This refined the choice of vapor pressure data sets which were used for final correlation. The selected vapor pressure data (data given in bold in Table 3) were treated simultaneously with selected liquid heat capacities (data given in bold in Table 5), ideal-gas heat capacities (Table 9), and vaporization enthalpies (Table 7) using the SimCor method. The thermal data should be used in the temperature range in which the pVT correction in eqs S1 and S2 in the Supporting Information does not play a significant role in the SimCor method. In the case of dimethyl carbonate, the pVT correction is significant even at the triple point temperature Tt (278.16 K), and thermal data were given a low weight for the crystal phase and were not included in the SimCor for the liquid phase. It is believed that the high quality ebulliometric vapor pressures by Steele et al.11 combined with values obtained by Negadi et al.10 can be safely extrapolated to the triple point temperature Tt = 278.16 K. Recommended vapor pressure data are represented by the Cox equation56 ln

n ⎛ T 0/K ⎞ Ai (T /K)i ) = 1 − exp( ⎟ ⎜ ∑ T /K ⎠ p0 ⎝ i=0

p

(2) 0

0

where p is the vapor pressure, T is the temperature, T and p are the temperature and pressure of an arbitrarily chosen reference point, and Ai are correlation parameters. Parameters of eq 2 are given in Table 10. This table contains also parameters for crystalline dimethyl carbonate, which were obtained by a 3212



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Table 10. Parameters of the Cox Equation, eq 2 compound

phase

A0

A1 × 103

dimethyl carbonate dimethyl carbonate diethyl carbonate dipropyl carbonate

crystal liquid liquid liquid

3.200912 3.164781 2.918732 3.365923

−0.359423 −1.606787 −1.742267 −1.578683

A2 × 106

T0/K

p0/Pa

(Tmin − Tmax)/K

1.477391 1.422602 1.283409

278.16 278.16 400.00 308.00

2358 2358 103300 391.9

258−272 283−398 238−400 238−308

simultaneous treatment of vapor pressure and enthalpy of sublimation at the triple point temperature and the difference cr ΔgcrC0p,m = Cg0 p,m − Cp,m. The enthalpy of sublimation at the triple point temperature was obtained from the vaporization enthalpy at the same temperature (obtained from Cox equation, eq 2, with the parameters for the liquid phase from Table 10) and the calorimetrically determined enthalpy of fusion (see Table 8). For the crystalline phase with such limited input data, the Cox equation, eq 2, with two adjustable parameters was adequate. As a result, the parameters of the Cox equations for the crystalline and liquid phases provide consistent values of vapor pressure, enthalpy of sublimation, and vaporization at the triple point temperature. Figures 7−9 show the deviations of individual vapor pressure data points from the recommended values calculated by means of

Figure 8. Diethyl carbonate: relative deviations (p − pcalc)/pcalc of vapor pressures p from the recommended values pcalc calculated using the Cox equation, eq 2, with parameters listed in Table 10. Dark green △, Choi and Jonich15 (partially displayed); light green ×, Rodriguez et al.;16 blue ◇, Kozlova et al.;14 magenta ◁, Xing et al.;17 cyan ★, Marrufo et al.;18 red ■, this work; ···, absolute deviations. Data sets represented by filled symbols were used in the SimCor method.

Figure 7. Dimethyl carbonate: relative deviations (p − pcalc)/pcalc of vapor pressures p from the recommended values pcalc calculated using the Cox equation, eq 2, with parameters listed in Table 10. Olive ◁, Jiang and Zhang;57 cyan ▶, Negadi et al.;10 orange ●, Steele et al.;11 orange ○, Steele et al.11 (exluded); light green ×, Rodriguez et al.;12 dark green ▽, Fukano et al.;13 blue ◇, Kozlova et al.;14 red ■, this work; ···, absolute deviations. Data sets represented by filled symbols were used in the SimCor method. Figure 9. Dipropyl carbonate: relative deviations (p − pcalc)/pcalc of vapor pressures p from the recommended values pcalc calculated using the Cox equation, eq 2, with parameters listed in Table 10. Blue ◇, Kozlova et al.14 (partially displayed); red ■, this work; ···, absolute deviations. Data sets represented by filled symbols were used in the SimCor method.

the Cox equation, eq 2, with parameters from Table 10. As the calculation of enthalpies of vaporization via the Clapeyron equation requires an evaluation of the appropriate pVT correction and the estimation of uncertainties of vapor pressures resulting from the SimCor is not straightforward, the vapor pressures and vaporization enthalpies along with the associated uncertainties are tabulated in Tables S5−S7 in the Supporting Information for convenience.

fit extend the temperature range to ambient and subambient temperatures. New vapor pressure data and condensed phase heat capacities for all three compounds were determined in this work. The thermodynamic properties in the ideal gaseous state for all the studied compounds were calculated by the methods of statistical thermodynamics based on calculated fundamental frequencies, molecular parameters, and conformational energies

5. CONCLUSIONS Vapor pressure equations for dimethyl carbonate, diethyl carbonate, and dipropyl carbonate developed by a multiproperty 3213



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(9) Č enský, M.; Rohác,̌ V.; Růzǐ čka, K.; Fulem, M.; Aim, K. Vapor pressure of selected aliphatic alcohols by ebulliometry. Part 1. Fluid Phase Equilib. 2010, 298, 192−198. (10) Negadi, L.; Ghanem, G.; Ait-Kaci, A.; Jose, J. Static measurements of the total vapor pressure of binary mixtures of dimethyl carbonate with benzene or isopropylbenzene at temperatures between 273 and 373 K. ELDATA: Int. Electron. J. Phys.-Chem. Data 1997, 3, 53−62. (11) Steele, W. V.; Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A.; Smith, N. K. Thermodynamic properties and ideal-gas enthalpies of formation for dicyclohexyl sulfide, diethylenetriamine, di-n-octyl sulfide, dimethyl carbonate, piperazine, hexachloroprop-1-ene, tetrakis(dimethylamino)ethylene, N,N′-Bis-(2-hydroxyethyl)ethylenediamine, and 1,2,4triazolo[1,5-a]pyrimidine. J. Chem. Eng. Data 1997, 42, 1037−1052. (12) Rodríguez, A.; Canosa, J.; Domínguez, A.; Tojo, J. Isobaric vapour−liquid equilibria of dimethyl carbonate with alkanes and cyclohexane at 101.3 kPa. Fluid Phase Equilib. 2002, 198, 95−109. (13) Fukano, M.; Matsuda, H.; Kurihara, K.; Ochi, K. Ebulliometric determination of vapor−liquid equilibria for methanol + ethanol + dimethyl carbonate. J. Chem. Eng. Data 2006, 51, 1458−1463. (14) Kozlova, S. A.; Emel’yanenko, V. N.; Georgieva, M.; Verevkin, S. P.; Chernyak, Y.; Schäffner, B.; Börner, A. Vapour pressure and enthalpy of vaporization of aliphatic dialkyl carbonates. J. Chem. Thermodyn. 2008, 40, 1136−1140. (15) Choi, J. K.; Joncich, M. J. Heats of combustion, heats of formation, and vapor pressures of some organic carbonates. Estimation of carbonate group contribution to heat of formation. J. Chem. Eng. Data 1971, 16, 87−90. (16) Rodríguez, A.; Canosa, J.; Domínguez, A.; Tojo, J. Isobaric vapor−liquid equilibria of diethyl carbonate with four alkanes at 101.3 kPa. J. Chem. Eng. Data 2002, 47, 1098−1102. (17) Xing, Y.; Fang, W.; Li, D.; Guo, Y.; Lin, R. Density, viscosity, and vapor pressure for binary mixtures of tricyclo [5.2.1.02.6] decane and diethyl carbonate. J. Chem. Eng. Data 2009, 54, 1865−1870. (18) Marrufo, B.; Loras, S.; Lladosa, E. Phase equilibria involved in the extractive distillation of cyclohexane + cyclohexene using diethyl carbonate as an entrainer. J. Chem. Eng. Data 2011, 56, 4790−4796. (19) Pardo, J. M.; Tovar, C. A.; Cerdeiriña, C. A.; Carballo, E.; Romaní, L. Excess quantities of dialkyl carbonate + cyclohexane mixtures at a variable temperature. Fluid Phase Equilib. 2001, 179, 151−163. (20) Ding, M. S. Liquid−solid phase equilibria and thermodynamic modeling for binary organic carbonates. J. Chem. Eng. Data 2004, 49, 276−282. (21) Valencia, J. L.; Troncoso, J.; Peleteiro, J.; Carballo, E.; Romani, L. Isobaric molar heat capacities of the ternary system dimethyl carbonate + p-xylene + n-decane. Fluid Phase Equilib. 2005, 232, 207−213. (22) Comelli, F.; Francesconi, R.; Bigi, A.; Rubini, K. Excess molar enthalpies, molar heat capacities, densities, viscosities, and refractive indices of dimethyl sulfoxide + esters of carbonic acid at 308.15 K and atmospheric pressure. J. Chem. Eng. Data 2006, 51, 665−670. (23) Comelli, F.; Bigi, A.; Vitalini, D.; Rubini, K. Densities, viscosities, refractive indices, and heat capacities of poly(ethylene glycol-ranpropylene glycol) + esters of carbonic acid at (293.15 and 313.15) K and at atmospheric pressure. J. Chem. Eng. Data 2010, 55, 205−210. (24) Becker, L.; Gmehling, J. Measurement of heat capacities for 12 organic substances by Tian−Calvet calorimetry. J. Chem. Eng. Data 2001, 46, 1638−1642. (25) Zábranský, M.; Kolská, Z.; Růzǐ čka, V.; Domalski, E. S. Heat capacity of liquids. Critical review and recommended values: Supplement II. J. Phys. Chem. Ref. Data 2010, 39, 013103. (26) Louguinine, W. Study of the latent heats of vaporization of some liquids. Ann. Chim. Phys. 1898, 13, 289. (27) Mansson, M. Enthalpies of combustion and formation of ethyl propionate and diethyl carbonate. J. Chem. Thermodyn. 1972, 4, 865− 871. (28) Biltz, W.; Fischer, W.; Wunnenberg, E. Molecular and atomic volumes. XXV. The volume occupied by crystalline organic compounds at low temperatures. Z. Phys. Chem. 1930, 151, 13−55. (29) Wachter, P.; Schweiger, H.-G.; Wudy, F.; Gores, H. J. Efficient determination of crystallisation and melting points at low cooling and

obtained at the DFT B3LYP-D3/6-311+G(d,p) level of theory. To our knowledge, the thermodynamic properties in the ideal gaseous state for all of the studied compounds as well as the heat capacities and the temperature and enthalpy of fusion for dipropyl carbonate are reported for the first time.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00295. (i) Description of the SimCor method; (ii) graphical comparison of vaporization enthalpies; (iii) measurement of phase behavior and enthalpies of fusion (thermograms of DSC measurements); (iv) details on DFT calculations; (v) tables containing recommended sublimation and vapor pressures and enthalpies (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Michal Fulem: 0000-0002-5707-0670 Ctirad Č ervinka: 0000-0003-1498-6715 Květoslav Růzǐ čka: 0000-0001-9048-1036 Funding

The authors acknowledge financial support from from specific university research (MSMT no. 20-SVV/2017) and Czech Science Foundation (GACR no. 17-03875S). The access to computing and storage facilities owned by parties and projects contributing to the National Grid Infrastructure MetaCentrum, provided under the program “Projects of Large Infrastructure for Research, Development, and Innovations” (LM2010005) and the CERIT-SC under the program Centre CERIT Scientific Cloud, part of the Operational Program Research and Development for Innovations, Reg. No. CZ.1.05/3.2.00/08.0144, is highly appreciated. Notes

The authors declare no competing financial interest.

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REFERENCES

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Vapor Pressures and Thermophysical Properties of Dimethyl

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