ARTICLE pubs.acs.org/IECR
Experimental and Theoretical Study of Chemical Equilibria in the Reacting System of the di-Alkyl Carbonate Synthesis. Sergey P. Verevkin,* Vladimir N. Emel’yanenko, and Svetlana A. Kozlova Department of Physical Chemistry, University of Rostock, Dr.-Lorenz-Weg. 1, 18059 Rostock, Germany
Irina Smirnova† and Wolfgang Arlt Lehrstuhl f€ur Thermische Verfahrenstechnik der Universit€at Erlangen N€urnberg, Egerlandstr. 3, 91058 Erlangen, Germany
bS Supporting Information ABSTRACT: The chemical equilibrium of the reactive system (propylene carbonate + butanol = dibutyl carbonate +1,2propanediol) was studied in the temperature range (303 to 373) K in the liquid phase using the method of sealed ampules using K2CO3 as heterogeneous catalyst. This reactive system exhibits a strong nonideal behavior of the mixture compounds in the liquid phase. The knowledge of the activity coefficients is required in order to obtain the thermodynamic equilibrium constants K a. A well established procedure, COSMO-RS, has been used to assess activity coefficients of the reaction participants in the liquid phase. Enthalpies of reactions of the dialkyl carbonate synthesis reaction in the liquid phase were obtained from temperature dependences of the corresponding thermodynamic equilibrium constants. For the sake of comparison, high-level ab initio calculations of the reaction participants have been performed using the GAUSSIAN-03 program package. Absolute electronic energy values of the molecules have been obtained using G3MP2 level. Using these results calculated equilibrium constants and enthalpies of reaction of the dialkyl carbonates synthesis in the liquid phase based on the principles of statistical thermodynamics are found to be in acceptable agreement with the data obtained from the thermochemical measurements.
1. INTRODUCTION Transformation of carbone dioxide into useful organic compounds has attracted attention as a cheap and safe C1 building block in organic synthesis. On the other hand, CO 2 is a stable compound in the sense of thermodynamics. Thus in any case, energy has to be added for chemical reactions directly or in form of highly energetic compounds. One example for highly energetic compounds is the coupling reaction of CO2 with epoxides affording first the five-membered cyclic alkylene carbonatesethylene carbonate (EC), propylene carbonate (PC), or butylene carbonate1 (see Figure 1). The purpose of this paper is to explore the thermodynamical limits of such reactions in order to give a chance to compare this route with other routes of synthesis that avoid just the production of CO2. In the second step, the alkylene carbonate is transesterified with an alcohol to dialkyl carbonate and a corresponding glycol. The alkylene carbonates, as well as an open chained dialkyl carbonates (dimethyl carbonate, diethyl carbonate, dibutyl carbonate, etc.) are expected to experience a considerable expansion of their market in the coming years, due to their growing use in the chemical (as solvent and reagent), pharmaceutical (as intermediates), and polymer industry. Also the use of dimethyl carbonate (DMC) as an additive to gasoline is expected to increase 30Mt per year.2 DMC is a useful methylation and carbonylation agent and a precursor of polycarbonate resins. r 2011 American Chemical Society
Due to the negligible toxicity of DMC, it is promising as a substitute for phosgene.3 The industrialization of the synthesis of DMC from propylene carbonate by transesterification of PC with methanol according to the Figure 1 is aggravated by generation of 1,2-propanediol (PD) as a byproduct. However, according to a recent study the technology of the DMC synthesis (Figure 1) could be substantially improved by making PD convert back to PC by reaction of PD and CO2 over zinc acetate catalyst4 (see Figure 2). The transesterification reactions 13 (see below) of the alkylene carbonates with alcohol to dialkyl carbonate and the corresponding glycol are reversible in a technical application. Thus, for the optimization of the reaction conditions the knowledge of the thermodynamic data is required. However, in the current literature, main efforts have been focused on the kinetics and catalysis and only few investigations5,6 on the thermodynamics of the transesterification reactions have been done. For example, Knifton and Duranleau5 studied catalysis and equilibrium of the ethylene carbonate transesterification with methanol in the presence of exchange resins with amine and ammonium Received: April 2, 2011 Accepted: July 11, 2011 Revised: July 4, 2011 Published: July 11, 2011 9774
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Figure 1. Synthesis of cyclic alkylene carbonates and transesterification into dimethyl carbonate.
2. EXPERIMENTAL PROCEDURES
Figure 2. Reaction for cyclic carbonates sysnthesis from CO2 and 1,2alkanediols catalyzed by zinc acetate.
pendant groups, zirconium, titanium, and tin homogeneous catalysts:
Zhang et al.6 studied the equilibrium reaction conditions of the propylene carbonate transesterification with methanol using CH3ONa, NaOH, Na2CO3, and CH3COONa as catalysts:
As an extension of thermodynamic studies, we have performed in this work the investigation of the chemical equilibrium of the transesterification of propylene carbonate with butanol to 1,2propanediol (PD) and dibutyl carbonate using K2CO3 as a catalyst:
We report here experimental data on the reaction enthalpy, ΔrH°m (liq), derived from the temperature dependence of equilibrium constants measured in the reactive mixtures. In order to prove the validity of the procedure used, these data on ΔrH°m (liq) are compared with those calculated from differences of the experimental enthalpies of formation of the pure reaction participants. Further information for the systems studied in this work was obtained from high-level ab initio calculations of the reaction participants (carbonates, diols, and alcohols). A possibility of prediction of equilibrium yields and equilibrium constants with the help of ab initio calculations was studied by using of the G3MP2 method from the Gaussian 03 program package.
2.1. Materials. Samples of butanol-1, propylene carbonate, 1,2-propanediol, and dibutyl carbonate were of commercial origin (Aldrich). GC analyses of the as-purchased samples of these chemicals gave purities >99% in agreement with their specifications. The degree of purity was determined using a Hewlett-Packard gas chromatograph 5890 Series II equipped with a flame ionization detector and a Hewlett-Packard 3390A integrator. The carrier gas (nitrogen) flow was 7.2 dm3 3 h1. A capillary column HP-5 (stationary phase cross-linked 5% PH ME silicone) was used with a column length of 30 m, had an inside diameter of 0.32 mm, and a film thickness of 0.25 μm. The standard temperature program of the GC was T = 323 K for 180 s followed by a heating rate of 10 K 3 min1 to T = 523 K. 2.2. Chemical Equilibrium Study in the Liquid Phase. The chemical equilibrium of propylene carbonate with butanol-1 into 1,2-propanediol and dibutyl carbonate according to reaction 3 was studied in the temperature range 303373 K. A glass vial with a screwed cap was filled up with an initial liquid mixture of propylene carbonate and butanol-1. K2CO3 was added as a solid catalyst. The quantity of catalyst was approximately 20% weight of the mixture. The vial was thermostatted at a given temperature with an uncertainty of (0.1 K and periodically shaken. After definite time intervals the vial was cooled rapidly in ice and opened. A sample for GC analysis was taken from the liquid phase using a syringe. After thermostatting the vial at the original temperature the procedure was pursued and the samples were taken successively until no further change of the compositions was observed indicating that the chemical equilibrium was established. The compositions of the reaction mixtures were determined chromatographically. Response factors of all reagents were determined using calibration mixtures of the corresponding components prepared gravimetrically. The experimental equilibrium ratios Kx of reaction 3 in the liquid phase were determined as ratios of mole fractions xi of the reaction participants:
Kx ðeq3Þ ¼
xPD 3 xDBC x2BuOH 3 xPC
ð4Þ
Mole fractions xi at equilibrium in the liquid phase, and values of Kx are listed in Table 1. However, an equilibrium constant formulation in mole fractions assumes unrealistic ideal mixtures. This experimental finding has to be converted to formulations in activities or fugacities. We have chosen the concept of activities ai of the reaction participants. Taking into account that ai = γi 3 xi, the true thermodynamic constant Ka of 9775
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Table 1. System: Propylenecarbonate (PC) + Butanol-1 (BuOH) S 1,2-Propanediol (PD) + Dibutylcarbonate (DBC). a T/K 303.2 313.2
323.2
xPC
n
xBuOH
xPD
xDBC
γPCb
γBuOHb
γPDb
γDBCb
Kγ (eq 3) b
Kx(eq 3) c
Ka(eq 3) d 0.20
24
0.0624
0.7435
0.0955
0.0986
3.83
1.02
1.33
2.16
0.719
0.27 ( 0.04
16
0.0390
0.7814
0.1066
0.0730
4.20
1.01
1.30
2.32
0.704
0.33 ( 0.03
0.23
14
0.0680
0.7224
0.1082
0.1014
3.39
1.02
1.32
2.07
0.770
0.31 ( 0.04
0.24
8
0.0671
0.7542
0.0833
0.0954
3.46
1.02
1.33
2.05
0.755
0.21 ( 0.03
0.16
16
0.0613
0.7390
0.1047
0.0950
3.48
1.02
1.32
2.09
0.762
0.30 ( 0.03
0.23
26
0.0377
0.8002
0.0938
0.0683
3.85
1.01
1.30
2.21
0.735
0.26 ( 0.06
0.19
28
0.0446
0.7980
0.0847
0.0727
3.42
1.01
1.30
2.07
0.772
0.22 ( 0.04
0.17
23 8
0.0303 0.0593
0.8220 0.7664
0.0945 0.0894
0.0532 0.0849
3.60 3.24
1.01 1.01
1.28 1.31
2.17 2.01
0.765 0.788
0.25 ( 0.04 0.22 ( 0.03
0.19 0.17 0.24
25
0.0467
0.7718
0.1016
0.0799
3.06
1.01
1.29
1.97
0.816
0.29 ( 0.04
26
0.0499
0.7611
0.1144
0.0746
3.03
1.01
1.28
2.00
0.828
0.29 ( 0.04
0.24
343.2
19
0.0296
0.7886
0.1612
0.0206
2.96
1.01
1.20
2.19
0.874
0.18 ( 0.03
0.16
10
0.0310
0.8200
0.1130
0.0360
2.98
1.00
1.24
2.05
0.844
0.19 ( 0.04
0.16
353.2
32
0.0304
0.8231
0.0906
0.0559
2.74
1.00
1.27
1.86
0.854
0.22 ( 0.04
0.21
333.2
358.2
15
0.0380
0.8037
0.0981
0.0602
2.58
1.00
1.26
1.81
0.878
0.24 ( 0.04
0.21
363.2 373.2
33 20
0.0201 0.0384
0.8610 0.8185
0.0897 0.0910
0.0292 0.0521
2.63 2.32
1.00 1.00
1.24 1.25
1.85 1.71
0.871 0.907
0.18 ( 0.05 0.18 ( 0.07
0.15 0.17
27
0.0287
0.8337
0.0942
0.0434
2.37
1.00
1.24
1.73
0.901
0.20 ( 0.04
0.18
Experimentally determined composition of equilibrium mixtures and and Kxvalues in the liquid phase, calculated from the eq 4. (T is temperature of investigation; n is number of determinations of composition within the time of equilibrium study; xi is the mole fraction measured chromatographically). b γi and Kγ calculated by COSMO-RS c Uncertainty is the twice standard deviation. d Ka = Kx 3 Kγ (according to eq 5) with Kx from experiment and Kγ from COSMO-RS a
Table 2. System: Ethylenecarbonate (EC) + Methanol (MeOH) S 1,2-Ethanediol (ED) + Dibmethylcarbonate (DMC). a T/K
xEC
xMeOH
xED
xDMC
γECb
γMeOHb
γEDb
γDMCb
Kγ (eq 1) b
Kx(eq 1)
Ka(eq 1) c
373.2
0.0783
0.7435
0.0838
0.0944
1.92
1.02
1.01
1.70
0.875
0.136
0.119
383.2
0.1062
0.6637
0.1173
0.1129
1.70
1.03
1.03
1.57
0.926
0.188
0.174
393.2
0.1109
0.6811
0.1059
0.1021
1.62
1.03
1.03
1.53
0.941
0.143
0.135
398.2
0.1592
0.6027
0.1138
0.1243
1.46
1.05
1.06
1.43
0.986
0.147
0.145
403.2
0.0771
0.7561
0.0919
0.0749
1.66
1.01
1.00
1.56
0.927
0.118
0.109
403.2
0.1046
0.7128
0.0876
0.0950
1.57
1.02
1.02
1.49
0.946
0.112
0.106
403.2 413.2
0.0830 0.1057
0.7419 0.7039
0.0846 0.0897
0.0905 0.1007
1.62 1.49
1.02 1.02
1.01 1.02
1.52 1.44
0.930 0.961
0.124 0.121
0.115 0.116
423.2
0.1075
0.6967
0.0934
0.1024
1.43
1.02
1.02
1.40
0.975
0.128
0.125
423.2
0.0802
0.7475
0.0824
0.0899
1.49
1.01
1.00
1.43
0.954
0.124
0.118
Experimentally determined composition of equilibrium mixtures and and Kxvalues in the liquid phase (T is temperature of investigation; xi is the mole fraction measured chromatographically). b γi and Kγ calculated by COSMO-RS. c Ka = Kx 3 Kγ (according to eq 5) with Kx from experiment and Kγ from COSMO-RS a
the reaction 3 is expressed: Ka ðeq3Þ ¼
aPD 3 aDBC γ γ xPD xDBC ¼ 2PD 3 DBC 3 2 3 3 2 aBuOH 3 aPC γBuOH 3 γPC xBuOH 3 xPC
¼ Kγ 3
xPD 3 xDBC x2BuOH 3 xPC
ð5Þ
where the values of activity coefficients γi and their ratio Kγ were calculated using COSMO-RS.7 For the sake of comparison with own results we involved some data for similar reactions available in the literature.5,6 Experimental studies of dimethyl carbonate synthesis from ethylene carbonate and methanol over basic catalysts5 according to the eq 1 were performed in most cases in equilibrium conditions. We treated the primary data on equilibrium mole fractions from
Knifton and Duranleau5 (see Table 2) using eqs 4 and 5 like our own results. Unfortunatelly, the experimental results reported by Zhang et al.6 for the equilibrium of propylene carbonate transesterification with methanol according to eq 2 did not contain the primary data on equilibrium mole fractions. For this reason it was not possible to calculate the true thermodynamic equilibrium constant Ka of the reaction 2 using eq 5 as it has been done in the present work. 2.3. COSMO-RS Calculations. COSMO-RS model (Conductorlike Screening Model for Real Solvents)7 is based on quantum mechanics and allows an a priori prediction of thermodynamic properties such as activity coefficients based on the molecular structure only. This approach was introduced to chemical engineering by Arlt et al.8 In the COSMO model, the solute molecule is considered to be embedded in a cavity 9776
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Table 3. Comparison of the Thermodynamic Functions ΔrH°m and ΔrS°m of the Reactions in the Liquid Phase; lnKa = a + b 3 (T/K)1 a Reaction
a
b
K
ΔrH°m (equilibrium)
ΔrS°m
ΔrH°m (calorimetry)c
ΔrH°m(liq) (eq 9)d
kJ 3 mol1
J 3 mol1 3 K1
kJ 3 mol1
kJ 3 mol1
1
398
3.6
589.0
4.9 ( 7.8
29.4 ( 19.5
11.9 ( 1.4
7.8
2
317
7.1
833.6
6.9 ( 0.1b [6]
58.5 ( 0.5
11.7 ( 1.9
13.9
3 7
338 298
2.4
258.0
2.2 ( 3.0 31.1 ( 1.717e
20.2 ( 9.1
10.5 ( 2.9 34.0 ( 1.5
11.8 27.0
a The average temperature of the equilibrium study. It was assumed19 that the enthalpy of reaction changes on passing from the average temperature of the experimental range to T = 298 K are negligible within the boundaries of the uncertainties. b Derived from the temperature dependence of Kx. c Calculated from the enthalpies of formation of the reaction participants measured by combustion calorimetry at T = 298.15 K. d Calculated direct using H298 of the reaction participants obtained from G3MP2 according to eq 9. e Directly measured using the solution calorimetry.
Figure 3. Temperature dependence of equilibrium constants: 4, reaction 1, Kx; 2, reaction 1, Ka; 0, reaction 2, Kx; O, reaction 3, Kx; b, reaction 3, Ka.
surrounded by a virtual conductor. The COSMO-RS concept7 based on statistical thermodynamics provides the transfer from the state of the molecule embedded in a virtual conductor to a real solvent. The only information needed in calculations is the molecular structure. As known,9 the conformations of a substance has a remarkable influence on the quality of the prediction of physicochemical properties. In the present study, the conformational analysis of all solutes was carried out by the semiempirical PM3 method using the HyperChem program. First, an initial molecular structure is generated and visualized with the help of HyperChem Release 7.51 for Windows. Then, the obtained molecule placed in vacuum is subjected to a conformational analysis where the potential energies are calculated by the semiempirical PM3 method (HyperChem). Further, the geometry of each conformation obtained is optimized using DFT/COSMO by means of the Turbomole 5.7 program. The structures gained as a result of the conformational analysis and DFT/COSMO optimization (BP-TZVP) are used to calculate activity coefficients with the help of the COSMOtherm (Ver.2.1 Rev.01.04) program. The activity coefficients have been calculated for a substance as a mixture of definite composition of all stable conformers according to the conformation analysis.
These activity coefficients γi allow transforming the equilibrium constants in terms of mole fractions to the true thermodynamic constants according to eq 5. 2.4. Quantum Chemical Calculations. High level ab initio calculations have been performed on the basis of the G3MP2 to obtain ideal gas thermodynamic functions for the dialkyl carbonates synthesis reactions 13. Standard ab initio molecular orbital calculations were performed with the Gaussian 03 Rev.04 series of programs.10 Energies were obtained at the G3MP2 level of theory. G3 theory is a procedure for calculating energies of molecules containing atoms of the first and second row of the periodic chart based on ab initio molecular orbital theory. A modification of G3 theory that uses reduced orders of MollerPlesset perturbation theory is the G3MP2 theory.11 This method saves considerable computational time compared to the G3 theory with some loss in accuracy, but is much more accurate than G2MP2 theory. For all the species included in this study, full geometry optimizations were carried out at the HF/6-31G(d) level. The corresponding harmonic vibrational frequencies were evaluated at the same level of theory to confirm that the optimized structures found correspond to potential energy minima and to evaluate the corresponding zero-point vibrational energies, ZPE, and the thermal corrections at T = 298 K. ZPE values were scaled by the empirical factor 0.8929. All the minima found at the HF/6-31G(d) level were again fully reoptimized at the MP2(FULL)/6-31G(d) level. G3MP2 theory uses geometries from second-order perturbation theory and scaled zero-point energies from Hartry-Fock theory followed by a series of single-point energy calculations at the MP2/Full, QCISD(T) and MP2/ GTMP2Large levels of theory (for details see ref 11). The enthalpy values at T = 298 K were evaluated according to standard thermodynamic procedures.12
3. RESULTS AND DISCUSSION 3.1. Equilibrium Constants, Activity Coefficients and Reaction Enthalpies. The experimental results of the chemi-
cal equilibria study of the dibutyl carbonate synthesis according to the reaction 3 are listed in Table 1. The experimental values of Kx measured in this work as well as those for reactions 1 and 3 are hardly changed by the temperature (see Tables 1 and 2). The true thermodynamic constants Ka calculated for reactions 1 and 3 using the eq 5 and activity coefficients γi predicted by COSMO-RS are given in Tables 1 and 2. Analysis of activity coefficients of the reaction 9777
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Table 4. Thermodynamic Functions ΔrG°m, ΔrH°m and ΔrS°m of the reactions 13 at T = 298 K
reaction
a
ΔrG°m (G3MP2)a
ΔrH°m (G3MP2)a
ΔrS°m (G3MP2)a
kJ 3 mol1
kJ 3 mol1
J 3 mol1 3 K1
Kp (G3MP2)a
Ka (eq 8)a
Ka (exp)a
1
4.46
47.02
142.7
6.1
0.82
0.20
2
3.03
42.02
131.4
3.4
0.55
0.014
3
5.21
44.64
132.3
8.2
0.98
0.22
Calculated from the experimental dependences lnKa = a + b 3 (T/K)1 given in Table 3.
participants reveals that most of activity coefficients calculated for reactions 1 and 3 are distinctly larger than unity and they definitely diminish with the rising temperature. However, the ratios of activity coefficients Kγ increase only slightly with the rising temperature. Experimental values of Ka for reactions 2 and 3 were approximated as a function of temperature by the linear equation ln Ka ¼ a þ b 3 ðT=KÞ1
used to calculate independently ΔfH°m(calorimetry) of the dialkyl carbonate synthesis reactions in the liquid phase (see Table 3), for example, for reaction 1: Δr H°m ðliqÞðcalorimetryÞ ¼ Δf H°m ðliqÞðEDÞ þ 2 Δf H°m ðliqÞðMeOHÞ Δf H°m ðliqÞðEDÞ Δf H°m ðliqÞðDMCÞ ¼ ð11:9 ( 1:4ÞkJ 3 mol1
ð6Þ
using the method of least-squares. The slopes of these lines allow the calculation of the standard enthalpy of this reaction ΔrH°m. Numerical results are presented in Table 3. Because the experimental results reported by Zhang et al.6 for the reaction equilibrium of the propylene carbonate transesterification with methanol according to eq 2 did not contain the primary data on equilibrium mole fractions, only their experimental values of Kx for reaction 2 were approximated using eq 6. Following, the thermodynamic interpretation of the standard enthalpy of this reaction, ΔrH°m, (see Table 3) using only temperature dependence of Kx is not completely correct. However, the enthalpy of reaction 3, ΔrH°m (liq) = (5.3 ( 3.0) kJ 3 mol1, calculated from the slope of ln Kx = a + b 3 (T/K)1 was in agreement with ΔrH°m (liq) = (2.2 ( 3.0) kJ 3 mol1 calculated from ln Ka = a + b 3 (T/K)1 (see Table 3). The similar assumption is also valid for the transesterification reactions 1 according to comparison given in Figure 3. Following, for a quick appraisal of the enthalpy of transesterification reactions like 1-3, the experimental temperature dependence of Kx could be used. Values of Kx for such reactions are hardly changed with the temperature. Following, it is advantageous to performe synthesys at possibly low temperature, provided that effective catalysts allow the acceptable time to reach transesterification equilibrium. 3.2. Comparison of the Reaction Enthalpies Obtained from Equilibrium Studies and from Calorimetry. Reactions of alkylene carbonates transesterification (reactions 13) were studied in the temperature range of 293423 K and the standard enthalpies of these reactions in the liquid phase were derived indirectly from the slope of lnKa vs 1/T-plots or lnKx vs 1/T-plots (see Table 3). The validity of the reaction enthalpies obtained from the chemical equilibrium study can be verified by comparison with the values of the reaction enthalpies calculated from the formation enthalpies of the pure reactions participants according to the Hess’s law. Experimental data on ΔrH°m (liq) necessary for such a comparison are available in literature (see Table S1, Supporting Information): for methanol, 13 butanol-1,13 ethylene carbonate,14 propylene carbonate,14 dimethyl carbonate,15 dibutyl carbonate,15 and 1,2-ethanediol.16 These data were
Additionaly, in order to extend the validation of the data treatment procedure applied in the present work, we involved experimental data for a parent reaction of synthesis of dimethyl carbonate over hydrolysis of tetra-methoxy methane, where relaiable reaction enthalpy was directly measured using solution calorimetry:17
Experimental data on ΔfH°m (liq) for tetra-methoxymethane17 and water18 necessary for calculations using the Hesss law were available in the literature (see Table S1, Supporting Information). Comparison of equilibrium and calorimetric results of reactions 13 and 7 is given in the Table 3. Calculated values of the ΔrH°m(calorimetry) for the reaction 13 and 7 are in acceptable agreement (within the boundaries of experimental uncertainties) with those derived from the chemical equilibrium studies confirming their thermodynamic consistency. 3.3. Thermodynamic Functions and Equilibrium Constants of the Reactions Dialkyl Carbonates Synthesis from Ab Initio Calculations. In our recent work 14,15 we established a remarkable ability of the G3MP2 ab initio method to predict gaseous enthalpies of organic carbonates accurately. In general, chemical reactions of transesterification like 13 are thermodynamically controlled. Thus, a desired yield of goal products (diverse dialkyl carbonates) could be possibly predicted with the help of ab initio calculations. In order to validate this procedure, following thermodynamic functions: Gibbs energy Δ r G°m, reaction enthalpy, ΔrH°m, reaction entropy, ΔrS°m, and equilibrium constants in the ideal gas phase, KP, were calculated for the gas phase reactions 13 using G3MP2 method under assumption of the ideal gas behavior. Calculated values are given in Table 4, accounting for the conformers populations of of 1,2-ethanediol and 1,2-propanediol in equilibrium mixtures.19 Equilibrium constants for the chemical reactions of transesterification like 13 in the gaseous phase K P , 9778
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(derived from the ab initio calculations) and in the liquid phase K a (required to assess the yield) depend on each other
in the following simplified way (e.g., for the reaction according to eq 1):
2 PEC, 0 3 PMeOH, BMeOH 3 PMeOH, 0 þ BEC 3 PEC, 0 BED 3 PED, 0 BDMC 3 PDMC, 0 0 exp Ka ¼ KP 3 PED, 0 3 PDMC, 0 RT where P i,0 are the saturated vapor pressures of the pure components. Saturated vapor pressures for methanol, EC, ED, and DMC are available in literature2023 (see Table S1 in Supporting Information). The second virial coefficients B have been assesed using an approximative procedure given by Reid et al. 24 Using values of KP for the gaseous reactions 13 calculated with help G3MP2 (column 5, Table 4), the true thermodynamic constants Ka (according to eq 8 in the liquid phase were calculated (column 6, Table 4) and compared with experimental values (column 7, Table 4). As can be seen from Table 4, the ab initio calculated constants Ka (according to eq 8 are overestimated in comparison to the experimental values. However, for the reactions 1 and 3 our calculations are able to predict the general level of the equilibrium constants. Thus, the procedure developed in this work could be practically applied for assessment of yields of transesterification reactions like reactions 13 studied in this work. Analysis of the equilibrium constants listed in Table 4 has revealed an additional practical aspect for reactions 13. As can be seen from Table 4, the ab initio calculated constants K p in the gaseous phase (column 5, Table 4) are remarkably high in comparison to those in the liquid phase. Following, it is advantageous to perform reactions of synthesis of dialkylcarbonates according to eqs 13 at elevated temperatures and in the gaseous phase in order to rich high yields of products. 3.4. Comparison of the Reaction Enthalpies Obtained from Equilibrium Studies and from Ab Initio Calculations. An additional test to establish the validity of the experimental and calculation procedures presented in this paper provides the comparison of the reaction enthalpies of reactions 13 and 7 obtained from experimental studies and from ab initio calculations (similar as it has been done in Section 3.2. Using the G3MP2 procedure, the standard reaction enthalpies, ΔrHm°(g), of the reactions 13 in the ideal gaseous phase at 298.15 K were calculated (see Table 4). The values of ΔrH°m(g) are related to the standard reaction enthalpies, ΔrH°m(liq), in the liquid state by Δr Hmo ðliqÞ ¼ Δr Hmo ðgÞG3MP2
∑i νi Δgl Hmi
ð9Þ
where Δgl Hmi are the molar enthalpies of vaporization of the pure compounds i at the reference temperature. The latter values for compounds involved in the reactions 13 and 7 are well established and are available in the literature (see Table S2 in the Supporting Information. Enthalpies of reaction ΔrH°m(g)G3MP2 calculated directly from enthalpies of reaction participants using G3MP2 are given in the Table 4 (column 3). Enthalpies of reactions 13 and 7 ΔrH°m (liq)G3MP2 in the liquid phase calculated according to eq 9 are listed for comparison with experimental values in Table 3 (column 8). The calculated values of the ΔrH°m(liq)G3MP2 for the reaction 13 and 7 are in acceptable agreement with those derived from the chemical equilibrium studies
ð8Þ
(Table 3, column 5) and with those calculated according to the Hess’s law.
6. CONCLUSIONS Experimentally determined chemical equilibrium data of the chemical reactions involving organic carbonates in the liquid phase offer to test theoretical models such as COSMO-RS in the liquid phase and theoretical results obtained from ab initio calculations in the gaseous phase. In particular, the results obtained for the gaseous phase demonstrate that ab initio calculation methods available today allow predicting chemical equilibrium data in the liquid phase with good quality. The present work demonstrates the usefulness of ab initio calculations in predicting chemical equilibrium properties of reactions being of considerable technical importance. ’ ASSOCIATED CONTENT
bS
Supporting Information. thermodynamic data for comounds used in this work (Table S1); results of the conformational analysis for 1,2-ethanediol (Table S2); results of the conformational analysis for 1,2-propanediol (Table S3), total energies at 0 K and enthalpies at 298 K (in Hartree) of the molecules studied in this work (Table S4).This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Present Addresses †
TU HH-Harburg, Verfahrenstechnik II, Eissendorfer Str.38, 21073 Hamburg-Harburg.
’ ACKNOWLEDGMENT This work has been supported by Research Training Group 1213 “New Methods for Sustainability in Catalysis and Technique” (DFG). ’ REFERENCES (1) Wei, T.; Wang, M.; Wei, W.; Sun, Y.; Zhong, B. Synthesis of dimethyl carbonate by transesterification over CaO/carbon composites. Green Chem. 2003, 5, 343–346. (2) Aresta, M.; Dibendetto, A. In Carbon Dioxide: Recovery and Utilization; Aresta, M.; Ed.; Kluwer Academic Publishers: Dordrecht, Boston, London, 2003, p 211. (3) Tatsumi, T.; Watanabe, Y.; Koyano, K. A. Synthesis of Dimethyl Carbonate from Ethylene Carbonate and Methanol Using TS-1 as Solid Base Catalyst. Chem. Commun. 1996, 2281. (4) Zhao, X.; Sun, N.; Wang, S.; Li, F.; Wang, Y. Synthesis of Propylene Carbonate from Carbon Dioxide and 1,2-Propylene Glycol over Zinc Acetate Catalyst. Ind. Eng. Chem. Res. 2008, 47, 1365. 9779
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