Thermodynamic Properties of N-Methyl-Substituted Ethane-1, 2

Article pubs.acs.org/jced

Thermodynamic Properties of N‑Methyl-Substituted Ethane-1,2diamines: Experimental and Computational Study Sergey P. Verevkin,*,†,‡ Vladimir N. Emel′yanenko,‡ Vasiliy A. Pozdeev,†,§ Vladimir Diky,∥ Robert D. Chirico,∥ and Kenneth Kroenlein*,∥ †

Department of Physical Chemistry and Department of “Science and Technology of Life, Light, and Matter”, University of Rostock, Dr-Lorenz-Weg-1, 18059, Rostock, Germany ‡ Department of Physical Chemistry, Kazan Federal University, 420008 Kazan, Russia § Samara State Technical University, 443100 Samara, Russia ∥ Thermodynamics Research Center, Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305-3328, United States S Supporting Information *

ABSTRACT: Vapor pressures for four N-methyl-substituted ethane-1,2-diamines were measured using the transpiration method. Enthalpies of vaporization were derived from the temperature dependence of the vapor pressures. Consistency of the experimental data was assessed and confirmed with group-additivity (GA) and quantum-chemical (QC) methods. Further confirmation of the results is provided through combined assessment with properties reported in the literature for the parent compound ethane-1,2diamine and a group of alkyl-substituted alkane-1,2-diamines. The effective application of modern QC methods in critical evaluation of enthalpies of vaporization and enthalpies of formation is demonstrated.

1. INTRODUCTION Development of efficient strategies for curbing emission of greenhouse gases is an area of high research interest and active technical development. Indeed, Carbon Capture and Sequestration was the focus area selected for the recent ACS (American Chemical Society) Virtual Issue in which this journal participated.1 Many CO2 capture processes rely on the use of amine solvents to remove CO2 from flue gas, and the effectiveness of any particular amine depends on its structure and associated thermophysical and thermochemical properties. Unfortunately, the property data available in the literature for these compounds are generally restricted to simple amines and have unknown data quality. Critical evaluation through careful assessment of families for related compounds is required. The evaluated information can then be used as a basis for identification of materials with desired behavior. In the present work, we report new vapor-pressure measurements for four N-methyl-substituted ethane-1,2-diamines (Figure 1, boxed compounds 2 through 5). The parent compound ethane-1,2-diamine is compound 1 (Figure 1). Literature vapor pressures for N,N,N′,N′-tetramethylethane1,2-diamine (Figure 1, compound 6) are included in the analysis, as they provide insights into the effects of complete methyl-substitution on the two amino groups. All data are assessed in combination with vapor pressures and enthalpies of combustion for ethane-1,2-diamine (1) and a series of branched © XXXX American Chemical Society

alkane-1,2-diamines (compounds 7, 8, and 9 of Figure 1) to provide critically evaluated enthalpies of vaporization and enthalpies of formation for the liquid and gas phase for this important family of compounds. (Numbers following compound names in this article correspond to numbers given in Figure 1.) The described assessment procedures can be applied to a wide variety of compound families and demonstrate an effective use of modern computational tools in combination with experimental data for critical evaluation of thermodynamic properties. At present, there are two broadly used approaches for prediction of enthalpies of formation in the gas phase; groupadditivity (GA) methods and quantum chemical (QC) computation. In the empirical GA methods, a molecule is considered as a simple sum of building blocks (i.e., bonds, atoms, or groups of atoms), and schemes with various degrees of sophistication exist.2,3 This approach has proved successful over decades for prediction and validation of thermochemical properties, provided the molecules lack extensive branching or conjugation. The broad experimental base for this approach (cf. ref 3) has made it a core element of validation for new experimental measurements. A good indicator of possible Received: November 24, 2015 Accepted: March 22, 2016

A

DOI: 10.1021/acs.jced.5b01003 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

even more heavy atoms.7,8 Moreover, in contrast to GA methods, the degree of branching or conjugation in the molecule of interest represents no limitation for QC evaluations. Unfortunately, QC calculations are currently limited to the ideal-gas phase, while enthalpies of formation for the liquid phase ΔfHm° (l, 298.15 K) are of greatest importance in industrial process design, and in particular, for optimization of CO2 capture with liquid amines. To overcome this limitation, recent work8 suggests that the enthalpy of formation for the liquid phase ΔfHm ° (l, 298.15 K) can be obtained by the combination of computational and experimental methods through application of the thermodynamic relationship: Δf Hm° (l, 298.15 K) = Δf Hm° (g, 298.15 K) − Δ1g Hm° (298.15 K)

(1)

where ΔfHm ° (g, 298.15 K) is calculated with a suitable QC method, and the enthalpy of vaporization Δg1Hm ° (298.15 K) is derived from the temperature dependence of experimental vapor pressures, measured with an appropriate method (vapor transpiration, static manometry, mass loss with a quartz-crystal microbalance, comparative ebulliometry, inclined-piston gauge manometry, etc.). This approach provides an alternative to traditional combustion calorimetry in determination of the enthalpy of formation for the liquid phase ΔfHm ° (l, 298.15 K) for compounds that show technological promise, but lack direct measurements. In the context of a continued cooperation3,9 between the Thermodynamics Research Center of the National Institute of Standards and Technology (NIST) and the Thermochemistry of Advanced Materials Lab at the University of Rostock, an experimental and computational study of methyl-substituted ethane-1,2-diamines (Figure 1) was undertaken to further validate the combination of QC methods with experimental enthalpy-of-vaporization determinations as a tool in providing enthalpies of formation for the liquid phase of key materials. Additionally, GA group parameters are provided here for the prediction of vaporization and formation enthalpies of the industrially important polyamines. Experimental study of the long-chain polyamines was not possible due to complications arising from their thermal instability and sensitivity to CO2. Nonetheless, reliable thermochemical data for polyamines can be obtained through combination of computational, experimental, and empirical methods. The following measurement results and analysis demonstrate effective application of modern QC methods in critical evaluation of enthalpies of vaporization and enthalpies of formation.

Figure 1. Alkanediamines considered in this work: (1) ethane-1,2diamine [107-15-3]; (2) N-methylethane-1,2-diamine [109-81-9]; (3) N,N′-dimethylethane-1,2-diamine [110-70-3]; (4) N,N-dimethylethane-1,2-diamine [108-00-9]; (5) N,N,N′-trimethylethane-1,2-diamine; [142-25-6]; (6) N,N,N′,N′-tetramethylethane-1,2-diamine [11018-9], (7) propane-1,2-diamine [78-90-0]; (8) butane-1,2-diamine [4426-48-6]; (9) 2-methylpropane-1,2-diamine [811-93-8]. Compounds enclosed in the box are those for which new experimental vapor pressures are reported in this work. Bonds in bold type represent the alkyl substitutions on the parent compound (1).

experimental errors is a large discrepancy between experimental and GA-estimated values, particularly if closely related compounds show no such discrepancy.3 However, deviations can also indicate specific intramolecular interactions (e.g., strain, ortho-effects, hydrogen bonding, etc.) that are nonadditive. Addressing these interactions requires the addition of specific group contributions to represent these behaviors. If taken to the extreme, this approach would result in an extensive collection of new and complex nonadditive terms, which, in turn, could only be derived from precise measurements. Inevitably, GA methods fail to predict thermochemical properties for any molecule that is more complex than those in the fitting set. In quantum chemical (QC) calculations,4 enthalpies are calculated with a suitable method (G*, DFT, CBS-Q, etc.) for a molecule of interest, and then, converted to enthalpies of formation for the gas phase ΔfHm° (g, 298.15 K) using atomization, isodesmic, homodesmic, isogyric, or other type of reaction. In recent years, QC procedures, particularly highlevel composite methods,5,6 have been developed that provide ΔfHm ° (g, 298.15 K) values with uncertainties (∼5 kJ·mol−1) near those achievable by experiment for molecules with ten or

2. MATERIALS AND METHODS 2.1. Materials. Samples of the ethane-1,2-diamines were of commercial origin and were further purified by fractional

Table 1. Source and Purity of the Chemical Samples compoundsa c

N-methylethane-1,2-diamine (2) N,N′-dimethylethane-1,2-diamine (3) N,N-dimethylethane-1,2-diamine (4) N,N,N′-trimethylethane-1,2-diamine (5)

CAS RN

source

purification method

purityb

analysis method

[109-81-9] [110-70-3] [142-25-6] [108-00-9]

Alpha Aesar Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich

distilled distilled distilled distilled

0.999 0.999 0.999 0.999

GC GC GC GC

“Ethane-1,2-diamine” is abbreviated “ED” in Tables 3, 6, and 7. bPurity is expressed in mass fraction. cThe bracketed numbers correspond to the structures given in Figure 1.

a

B



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Table 2. Experimental Vapor Pressures p at Temperature T with Standard Uncertainties u(p), Determined with Sample Mass m, Volume of N2 Transfer Gas V(N2), Temperature of Soap-Bubble Meter Ta, and Gas Flow Rate F, plus Fitted Parameters for eq 3 Ta/K

mb/mg

V(N2)c/dm3

Tad/K

Fe/(dm3·h−1)

pf/Pa

u(p)g/Pa

N-Methylethane-1,2-diamine [109-81-9]

ln(p /Pa) =

284.12 R

−

272.2 274.3 275.4 278.0 278.6 279.4 280.2 281.3 282.3 283.1 284.1 284.9 286.3 287.8 289.3 290.6 292.2 294.6 296.2 298.1 300.2 302.2

ln(p /Pa) =

273.8 274.2 275.2 276.7 278.2 280.7 283.2 285.6 288.2 290.7 293.2 295.6 298.2 298.2 300.7 300.7

−

61.0 T/K ln 298.15 R

(

)

1.94 4.05 4.29 3.78 3.27 4.49 4.09 4.03 4.90 4.60 5.57 5.23 5.90 6.42 7.14 7.71 8.89 10.62 11.80 13.27 15.00 16.87 299.41 R

−

281.4 285.6 290.6 300.7 305.6 310.7 308.2 279.2 283.3 288.2 293.2 295.8 298.2 303.4

ln(p /Pa) =

66198.28 (R·T / K)

70750.94 (R·T / K)

−

65.9 T/K ln 298.15 R

(

−

57965.76 (R·T / K)

11.70 12.19 12.61 12.76 15.35 11.55 12.53 14.07 12.71 12.69 14.84 13.26 11.69 22.36 12.68 26.92

−

57.3 T/K ln 298.15 R

(

297.3 1.02 296.9 1.05 297.8 1.02 297.7 1.01 300.3 1.04 296.6 1.05 298.4 1.02 299.5 1.05 298.3 1.02 296.4 1.04 298.4 1.03 297.0 1.03 298.7 1.02 296.9 1.02 297.3 1.04 298.1 1.02 296.2 1.02 295.8 1.03 295.5 1.03 296.7 1.01 296.9 1.00 296.8 1.00 N,N′-Dimethylethane-1,2-diamine [110-70-3]

273.1 318.1 344.9 414.8 445.5 469.5 494.3 535.5 586.7 607.5 657.9 697.2 773.8 860.1 940.4 1034.3 1176.1 1394.1 1541.2 1761.8 2016.7 2275.2

6.9 8.0 8.6 10.4 11.2 11.8 12.4 13.4 14.7 15.2 16.5 17.5 19.4 21.5 23.5 25.9 29.4 34.9 38.6 44.1 50.4 56.9

0.308 0.322 0.280 0.279 0.278 0.279 0.279 0.324 0.307 0.285 0.298 0.335 0.280 0.288

293.6 1.12 293.6 1.12 294.0 1.12 294.0 1.12 294.0 1.11 294.0 1.12 294.1 1.12 294.1 1.11 294.0 1.12 294.0 1.12 294.0 1.12 294.0 1.12 294.0 1.12 294.0 1.12 N,N-Dimethylethane-1,2-diamine [108-00-9]

504.5 693.6 1022.9 2105.9 2892.0 3973.6 3408.4 425.8 585.1 857.9 1228.3 1498.0 1780.9 2477.1

12.6 17.4 25.6 52.7 72.3 99.4 85.2 10.7 14.7 21.5 30.7 37.5 44.5 62.0

739.7 752.6 808.0 886.9 968.7 1114.0 1309.1 1561.1 1820.9 2087.9 2391.5 2763.2 3185.5 3282.3 3755.1 3727.2

18.5 18.8 20.2 22.2 24.2 27.9 32.8 39.1 45.5 52.2 59.8 69.1 79.7 82.1 93.9 93.2

)

5.31 7.70 9.94 20.57 28.22 38.89 33.32 4.68 6.15 8.44 12.72 17.47 17.42 24.99 261.62 R

0.256 0.454 0.442 0.320 0.259 0.333 0.289 0.263 0.289 0.260 0.293 0.257 0.262 0.255 0.259 0.254 0.256 0.257 0.257 0.254 0.250 0.249

) 0.487 0.493 0.472 0.431 0.476 0.306 0.281 0.262 0.202 0.174 0.177 0.136 0.104 0.192 0.095 0.204

294.2 291.6 291.7 291.6 294.2 292.2 294.2 294.2 294.2 292.4 292.7 293.2 293.5 292.7 293.6 293.6 C

1.04 1.29 1.29 1.29 1.06 1.02 1.06 1.05 1.01 1.04 1.06 1.04 1.04 1.00 1.04 1.02



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Table 2. continued Ta/K

mb/mg

303.2 303.2

13.32 31.01

ln(p /Pa) =

288.49 R

274.2 276.7 281.8 286.8 291.0 296.3 298.2 301.0 303.2 304.1 305.4

−

66379.98 (R·T / K)

2.77 3.36 5.02 7.32 9.74 13.91 16.07 19.08 25.29 23.90 26.83

V(N2)c/dm3

−

62.2 T/K ln 298.15 R

(

Tad/K

Fe/(dm3·h−1)

pf/Pa

u(p)g/Pa

N,N-Dimethylethane-1,2-diamine [108-00-9] 0.087 293.6 1.04 0.204 294.2 1.02 N,N,N′-Trimethylethane-1,2-diamine [142-25-6]

4330.6 4290.6

108.3 107.3

0.142 0.141 0.141 0.142 0.141 0.141 0.143 0.142 0.161 0.142 0.147

502.1 605.0 885.8 1271.3 1685.6 2403.3 2732.9 3259.2 3811.1 4074.2 4402.0

12.6 15.2 22.2 31.8 42.2 60.1 68.3 81.5 95.3 101.9 110.1

) 294.9 294.9 294.9 294.9 294.9 294.9 294.9 294.9 295.1 294.9 294.9

1.06 1.06 1.06 1.06 1.06 1.06 1.07 1.06 1.07 1.06 1.06

a

u(T) = 0.1 K. bMass of transferred sample condensed at T = 243 K. cVolume of nitrogen V(N2) used to transfer m/g of the sample; u(V) = 0.005 dm3, and u(m) = 0.0001 g. dTa is the temperature of the soap bubble meter used for measurement of the gas flow. eFlow rate of the nitrogen gas. f Vapor pressure at temperature T, adjusted for the residual vapor pressure at T = 243 K by an iteration method. gExpanded uncertainty in p (0.95 level of confidence) calculated with U(p/Pa) = 0.05 + 0.05(p/Pa).

2.3. Computations. Ab initio molecular orbital calculations for conformers for all compounds considered (Figure 1) were performed with the Gaussian 09 series of programs.14 The initial search for stable conformers was performed with the force field MMFF94 method,15 and relative enthalpies and Gibbs energies for the stable conformers were computed with the mPW2PLYP(FC)/6-311+(d,p) method.16 Energies for the most stable isomers were calculated at the G4 level,6 and equilibrium populations were calculated with established procedures of statistical thermodynamics.17 All vibrations were assumed to be harmonic, and the default scaling factor of 1.0 was used.

distillation with a spinning-band column in vacuum. The degree of purity was determined with a gas chromatograph equipped with an HP-5 capillary column, column length of 30 m, inside diameter 0.32 mm, and film thickness 0.25 μm. No impurities greater than 0.001 mass fraction were detected in the samples used for the vapor pressure measurements. Provenance and purity of the compounds are given in Table 1. 2.2. Transpiration Method. Vapor pressures were measured with the transpiration method.10−12 Approximately 0.5 g of a sample was mixed with small glass beads and placed in a thermostated U-shaped saturator. A well-controlled nitrogen stream was passed through the saturator at a constant temperature (±0.1 K), and the transported material was collected in a cold trap. The amount of condensed sample was determined by GC analysis using nonane as an external standard. The vapor pressure p at each temperature T was calculated from the amount of product collected within a defined time period. By assuming the validity of Dalton’s law for the saturated nitrogen stream, values of p were calculated with the equation: p = mRTa /VM

3. RESULTS 3.1. Vapor Pressures and Enthalpies of Vaporization. Experimental vapor pressures pi measured in this research for the N-methyl-substituted ethane-1,2-diamines are listed in Table 2. The vapor pressures were fitted with the equation:18 ln(p /p°) =

(2)

Δgl C p°,m ⎛ T ⎞ a b + + ln⎜ ⎟ R RT R ⎝ T0 ⎠

(3)

Δg1C°p,m

where a and b are adjustable parameters and is the difference between the isobaric molar heat capacities of the gas and liquid. The reference pressure p° is 1 Pa, T0 is the selected reference temperature (298.15 K), and R is the molar gas constant. Required values of Δg1C°p,m were estimated with the procedure of Chickos and Acree,19 which requires the isobaric molar heat capacity of the liquid at T/K = 298.15 K. For the compounds studied here, experimental values for the heat capacities are absent in the literature, so they were estimated with the GA method developed by Chickos et al.,20 updated here with group parameters for secondary and tertiary sp3 nitrogen based on heat capacities of liquid amines from the literature (Supporting Information, Table S1).21−27 New group parameters were tested successfully with recent data on heat capacities for aliphatic diamines.28 Values of liquid heat capacity Cp,m ° (l, 298.15 K) and heat-capacity difference Δg1Cp,m ° , estimated in this work and used in eq 2, are given in Table 3.

where R = 8.3144598 J·K−1·mol−113; m and M are the mass and molar mass, respectively, of the compound sample of interest, V is the total volume of transported gas (sample + nitrogen), and Ta is the temperature of the soap-bubble meter used for measurement of the gas flow rate. The volume of the carrier gas VN2 was determined from the flow rate and the time measurement. The contribution of the sample volume to total volume of gas was not significant. Amines are sensitive to water and atmospheric CO2, thus requiring deactivation of all glassware. The glass beads and Ushaped traps were washed with 0.1 M NaOH to suppress possible acidity of the glass surface, and all glassware was dried at 383 K. All samples were maintained under a N2-stream in the saturator and cold trap, ensuring no contact with atmospheric CO2 or moisture. This treatment allowed for reproducible results. D



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Table 3. Enthalpies of Vaporization Δg1H°m Derived in This Research for Ethylene Diamines (EDs) and Quantities Used in Adjustment of Δg1H°m (Tmid) to the Temperature T = 298.15 Ka compound

methodb

Trangec/K

N-methyl-ED (2) N,N′-dimethyl-ED (3) N,N-dimethyl-ED (4) N,N,N′-trimethyl-ED (5) N,N,N′,N′-tetramethyl-ED (6)

T T T T S

272.2−302.2 279.2−310.7 273.8−303.2 274.2−305.4 273.1−365.0

Δg1 H°m(Tmid)

Δg1Cp,md

Cp,m(1)e

± ± ± ±

−59.3 −65.9 −57.3 −62.2

187.2 212.6 179.6 198.4

48.9 51.4 41.8 48.5

0.2 0.2 0.2 0.2

Δg1H°m (298.15 K)

source

± ± ± ± ±

this work this work this work this work literature

48.0 51.1 40.9 47.8 41.1

0.3 0.3 0.3 0.3 1.1f

a Units for enthalpies and heat capacities are kJ·mol−1 and J·K−1·mol−1, respectively. bMethods: T = transpiration; S = static method. cTrange is the temperature range of the vapor-pressure measurements used to derive Δg1H°m. Tmid is the midpoint temperature of Trange. dThe heat capacity difference between the liquid and gas phase at temperature T = 298.15 K estimated with the method of Chickos and Acree.19 eHeat capacities for the liquid phase at T = 298.15 K estimated with the method of Chickos et al.20 with updated group additivity values described in the text. fDerived with a fit of the Wagner eq (eq 5) to vapor pressures reported in the literature.30−33 Equation parameters derived as described in the text: A = −8.72067; B = 3.28183; C = −4.75095; D = 0, and pc = 3.2 MPa.

Enthalpies of vaporization Δg1Hm at temperature T were derived from the temperature dependence of vapor pressures using eq 3: Δgl Hm° = −b + Δ1g C °p ,mT

pressure (pc = 3.2 MPa) was estimated by application of Waring’s criterion36 to constrain the shape of the vapor− pressure curve at high temperatures, with a minimum at T/Tc = 0.86 for the function: R d(ln p)/d(1/T). The fitted parameters A, B, and C, and the derived enthalpy of vaporization for the temperature T = 298.15 K are given in footnote f and the body of Table 3, respectively.

(4)

Coefficients a and b of eq 3 are given in Table 2 for each compound, and values of Δg1Hm ° (298.15 K) are given in Table 3. Procedures for calculation of the standard uncertainties for Δg1H°m have been described12 and include uncertainties arising from the experimental conditions and vapor pressures. Vapor pressures and enthalpies of vaporization for N-methylethane1,2-diamine (2), N,N′-dimethylethane-1,2-diamine (3), N,Ndimethylethane-1,2-diamine (4), N,N,N′-trimethylethane-1,2diamine (5) are reported here for the first time. 3.2. Treatment of Literature Vapor Pressures for N,N,N′,N′-Tetramethylethane-1,2-diamine. Vapor pressures of N,N,N′,N′-tetramethylethane-1,2-diamine (6) have been measured by Levitas et al.29 with a mercury manometer and repeatedly over the last 18 years with static methods at the University of Lyon in France.30−33 Levitas et al.29 stated that the relative uncertainty for their vapor pressures was 2%, but inspection of the results for the compounds studied showed that that the expanded uncertainty (0.95 level of confidence) was, at least, 10%, based on the apparent repeatability. In addition, the temperature dependence of the vapor pressures from this source was unphysical at the lowest temperatures reported, where a plot of ln(p/po) against T−1 showed positive curvature. Consequently, these data were not considered further in the property analyses. Vapor pressures reported from the University of Lyon30−33 for N,N,N′,N′-tetramethylethane-1,2-diamine (6) were reported with uncertainties near 1%; however, consistency between the four data sets is nearer to 6%. In the fit described below, an expanded uncertainty of 6% (0.95 level of confidence) was assigned to the values. The Wagner equation34 was fit to the experimental vapor pressures measured at the University of Lyon.

4. DISCUSSION In interpreting the reliability of any new experimental data, checks for both internal consistency, as well as consistency with the relevant literature should be made. The values reported here (Table 3) for enthalpies of vaporization of N-methylsubstituted ethane-1,2-diamines are assessed with available results for monoamines and other diamines. To normalize data for disparate molecules, various empirical, semiempirical, and computational methods for evaluation are used and described below. 4.1. Validation of Enthalpies of Vaporization at T = 298.15 K with a Group-Additivity (GA) Method. GA methods are widely used in assessment and prediction of enthalpies of formation.2,3 In previous studies,37−41 the methodology of Benson2 was adapted successfully for prediction of enthalpies of vaporization for mono- and diamines. The group definitions and associated contributions or group-additivity values (GAVs), required to estimate Δg1H°m(298.15 K) of amines and diamines, are collected in Table 4. Table 5 shows successful application of these GAVs in estimation of enthalpies of vaporization for branched monoamines through comparison of the estimated values Δg1H°m(GA) with those based on experimental vapor pressures42−45 and enthalpies-of-vaporization Δg1H°m(exp).44,46 The application of the GA approach to assessment of the enthalpies of vaporization of the diamines follows. The aliphatic monoamines are well-known associating liquids,47 and the values of GAVs for estimation of Δg1Hm (298.15 K) are related to the intensity of these intermolecular interactions. Relative to the monoamines, the diamines studied in this work exhibit a significantly more extended threedimensional network with enhanced intermolecular interactions.48 To account for this, an additional contribution Γ (NH2−(CH2)2−NH2), for the specific interactions due to the close proximity of two amino groups, was included. For example, for ethane-1,2-diamine, the additional contribution {Γ (NH2−(CH2)2−NH2) = 3.8 kJ·mol−1} is calculated as the ° (298.15 K) value difference between the experimental Δg1Hm and the sum of the increments C−(N)(C)(H)2 and N−

ln(p /pc ) = (1/Tr){A(1 − Tr) + B(1 − Tr)1.5 + C(1 − Tr)2.5 + D(1 − Tr)5 }

(5)

where Tc and pc are the critical temperature and critical pressure and Tr = T/Tc. Because of the narrow temperature range for the available data (273 < (T/K) < 365), the equation was truncated to three adjustable parameters; A, B, and C, with D = 0. The critical temperature (Tc = 568 K) was estimated with a QSPR (quantitative structure−property relationship) method develop by Kazakov et al.35 at NIST. The critical E



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Table 4. Group-Additivity Values (GAVs) Γi for Calculation of Enthalpies of Vaporization Δg1H°m, and Enthalpies of Formation Δf Hm ° (g) of Alkanes, Amines, and Diamines at 298.15 Ka Γi/(kJ·mol−1)

group

Δg1 C−(C)(H)3 C−(C)2(H)2 C−(C)3(H) C−(C)4 six-ring C−(N)(C)(H)2 C−(N)(C)2(H) C−(N)(C)3 N−(C)(H)2 N−(C)2(H) N−(C)3 six-ring NH2−(CH2)2−NH2 NH2−(CH2)2−NH(R) NH2−(CH2)2−N(R)2 NH(R)−(CH2)2−N(R)

The sequential methylation of the amino groups in ethane1,2-diamine should perturb the H-bonded network in the liquid phase, and the measured enthalpies of vaporization should reflect this. In order to quantify the effect of each additional methyl group on the enthalpy of vaporization, we calculated the difference between the experimental Δg1Hm value and that predicted from the GAVs based solely on the monoalkylamines (Table 4). These differences are given in Table 6 (column 4, rows 5 through 9), for each compound. An interpretation of the observed differences in Δg1H°m can be made with the aid of Figure 2. In Figure 2, it is seen that, starting from ethane-1,2-diamine (1), the first methylation to form N-methylethane-1,2-diamine (2) slightly strengthens (+0.8 kJ·mol−1) the H-bond network in the liquid, as does methylation of the next amino-group (+1.6 kJ·mol−1) to form N,N′-dimethylethane-1,2-diamine (3). These small increases may be associated with the increase in isotropic polarizability seen with addition of each methyl group as computed with the B3LYP/6-31g(2df,p) level, as part of the G4 calculations. In contrast, double methylation of the aminogroup in N,N-dimethylethane-1,2-diamine (4) significantly reduces H-bonding, as evidenced by the −7.7 kJ·mol−1 difference. The effect of reduced H-bonding is also seen for the complete methylation of the amino groups in N,N,N′,N′tetramethylethane-1,2-diamine (6), where a difference of −7.3 kJ·mol−1 is seen relative to N,N,N′-trimethylethane-1,2-diamine (5). The correlation between the apparent degree of association in the liquid, as based on structural considerations, and the observed enthalpies of vaporization provides good evidence of consistency for the experimental values. 4.2. Quantum Chemical (QC) Calculations for Alkane1,2-Diamines. In a series of recent articles,7−9 enthalpies of formation ΔfH°m(g, 298.15 K) computed with (QC) methods for small- to midsized molecules (less than 10 non-hydrogen atoms) were shown to agree well with experimental gas-phase enthalpies of formation (within 4 kJ·mol−1). It was concluded that, when the condensed-phase enthalpy of formation is unavailable experimentally, this properties can be obtained through combination of the computed gas-phase enthalpy of formation with an experimental enthalpy of vaporization or sublimation.8 This approach was used to obtain enthalpies of formation in the liquid phase for the N-methyl-substituted ethane-1,2-diamines studied (compounds 2−6). The relevant thermodynamic relationship between the properties was given earlier (eq 1). The composite QC method G46 was used for calculation of the gas-phase enthalpies of formation ΔfHm ° (g, 298.15 K), and the enthalpies of vaporization were derived based on the temperature dependence of the vapor pressures reported in Table 2 (compounds 2−5) and in the literature (compound 6). Alkane-1,2-diamines are flexible molecules that exist as an equilibrium mixture of conformers in the gas phase. For example, a careful conformational analysis of the N,N,N′,N′tetramethylethane-1,2-diamine (6) using DFT (density functional theory) and composite methods49 revealed nine conformers; four with relative energies in the range 0−1.7 kJ· mol−1 and five in the range 5−25.5 kJ·mol−1, as determined at the G3(MP2)5 level. The four most stable (i.e., lower-energy) conformers were estimated to account for 83% of the total population.49 Conformational equilibrium must be considered ° (g, 298.15 K). In practice, only for correct calculation of ΔfHm the few most-stable conformers typically are essential for the

Γi/(kJ·mol−1) Δf Hm ° (gas)

Hm °

Alkanes 6.33 4.52 1.24 −2.69 5.9 Amines 2.9 −2.0 −7.7 18.0 12.6 4.9 5.9 Diamines 3.8 4.8 −2.9 6.4

−42.05 −21.46 −9.04 −1.26 5.4 −26.9 −20.0 −16.1 19.4 64.1 103.2 5.4 0 0 0 0

a

The group-additivity values were collected from evaluations in previous studies.37−41

Table 5. Comparison of Enthalpies of Vaporization Δg1Hm ° (T = 298.15 K) Estimated with the Group-Additivity Values of Table 4(GA) with Those Derived from Experimental Property Values from the Literature (exp)a compound isopropylamine (IPA) sec-butylamine (SBA) tert-butylamine (TBA) isobutylamine (IBA)

Δg1H°m(exp)b

Δg1H°m(GA)

Δc

± ± ± ±

28.7 32.9 29.3 33.7

0.3 −0.1 −0.4 0.0

28.4 33.0 29.7 33.7

0.2 0.2 0.2 0.2

Units are kJ·mol−1 for all values. bThese values were derived with experimental vapor pressures and enthalpies of vaporization from the literature. Fits of the Wagner eq (eq 5) to the literature vapor pressures p were in excellent accordance with the experimental values ° . Citations to the key experimental values for each compound of Δg1Hm follows. IPA {p, Osborn and Douslin (1968);42 Δg1H°m, Majer et al. ° , Majer et al. (1979)44}, SBA {p, Ahmed et al. (2012);43 Δg1Hm (1979),44 Wadso (1969)46}, TBA {p, Osborn and Douslin (1968);42 Δg1Hm ° , Wadso (1969)46}, IBA {p, Osborn and Douslin (1980),45 Majer et al. (1979);44 Δg1H°m, Majer et al. (1979),44 Wadso (1969)46}. Uncertainties represent the expanded uncertainty (0.95 level of confidence). cΔ = Δg1H°m(GA) − Δg1H°m(exp). a

(C)(H)2 from Table 4 and can be ascribed to the enhanced intermolecular interactions in the diamine relative to the monoamines. In our previous work,40 we studied a series of alkyl-substituted alkane-1,2-diamines (Figure 1, compounds 7− 9), where crowding of an amino group was shown to inhibit the intermolecular association in the liquid. As a consequence, the contribution Γ (NH2−(CH2)2−NH2) in the branched alkane1,2-diamines becomes noticeably smaller in comparison to those in ethane-1,2-diamine (1) (see column 4 of Table 6, rows 1 through 4). For the series of N-methyl-substituted ethane-1,2diamines studied in the current work (Figure 1, compounds 2− 6), the compounds were selected to accentuate this effect. F



Article

Table 6. Comparison of Experimental and Predicted Enthalpies of Vaporization Δg1H°m and Enthalpies of Formation for the Gas Phase ΔfH°m(g) at Temperature T = 298.15 Ka compound

Δg1 Hm(exp)

1

2

ethane-1,2-diamine (1)

45.8 ± 0.4h

propane-1,2-diamine (7) butane-1,2-diamine (8) 2-methylpropane-1,2-diamine (9)

45.8 ± 0.3h 48.5 ± 0.9h 45.2 ± 0.9h


48.0 51.1 40.9 47.8 41.1

± ± ± ± ±

0.3i 0.3i 0.3i 0.3i 1.1j

Δg1Hm(GA)b

Δc

Δf H°m(exp)d

3

4

5

41.8 4.0 −17.2 ± Branched Alkane 1,2-Diamines 43.2 2.6 −52.0 ± 47.7 0.8 −71.7 ± 43.9 1.3 −88.8 ± N-Methyl-Substituted Ethane-1,2-diamines 43.2 4.8 44.7 6.4 43.8 −2.9 45.3 2.5 45.9 −4.8

Δf H°m(QC)e

Δf H°m(GA)f

Δg

6

7

0.6

−15.0

−15.0

0.0

8

0.5 1.2 1.1

−52.1 −70.1 −88.6

−50.2 −71.6 −88.3

−1.9 −1.5 −0.3

−11.5 −7.7 −17.4 −14.8 −14.0

−12.4 −9.7 −15.3 −12.7 −15.6

0.9 2.0 −2.1 −2.1 1.6

Units are kJ·mol−1 for all values, and uncertainties are the expanded uncertainty with of 0.95 level of confidence. Numbers in brackets correspond to the compound numbers given in Figure 1. bPredicted with group-additivity values (GA) for alkanes and amines (not diamines) given in Table 4. c Difference between columns 2 and 3, which is the contribution Γ (alkanediamine) due to the specific intermolecular interactions in the 1,2° (g) were derived with enthalpies of combustion from the literature50 and the enthalpies of vaporization alkanediamines. dThese values of ΔfHm derived from the literature and given in column 2, as described in the text (end of section 4.2). eComputed with the composite quantum chemical (QC) method G4, as described in the text (section 4.2). fPredicted with the group-additivity (GA) values given in Table 4. Also, see section 4.3. g Difference between columns 6 and 7. hThese values were derived with vapor pressures,40,51,52 and enthalpies of vaporization46 from the literature, as described in the text (end of section 4.2). iValues derived from the vapor pressures measured in this research (see Tables 2 and 3). jDerived with literature vapor pressures as described in the text (section 3.2). a

where ΔGi° = G° − Gst° , and the Gibbs energy Gst° refers to the most stable conformer. Additionally, enthalpies H°298 were calculated with the high-level composite method G46 for the most stable conformers, which were further combined with the relative enthalpies from mPW2PLYP/6-311+(d,p) method to ° (g, 298.15 K) for the equilibrium mixture. calculate ΔfHm Computed values of H298, G298, the enthalpy and Gibbs energy relative to the most stable conformer, the estimated mole fraction in the equilibrium mixture, the enthalpy of formation for each conformer, and the weighted average for ΔfHm ° based on the populations, are given in the Supporting Information (Table S2). The computed enthalpies H298 were converted to enthalpies ° (g, 298.15 K) for the gas phase, using the of formation ΔfHm conventional atomization reaction for the diamines.

Figure 2. Interplay of specific intermolecular interactions in methylsubstituted ethane-1,2-diamines in terms of differences Γ (diamine) between experimental enthalpies of vaporization and the sum of increments for amines from Table 4. The number in the center of each structure corresponds to the compound numbers given in Figure 1 and in the text. Values of Γ (diamine) in kJ·mol−1 are given in brackets, as well as in column 4 of Table 6.

CaHbN2 → aC + bH + 2N

The computed values of ΔfHm ° (g, 298.15 K) for the nine alkane-1,2-diamines studied are given in Table 6 (column 6). Validation of the QC results specifically for the alkane-1,2diamines is provided through comparison of computed and experimental enthalpies of formation for the gas phase for ethane-1,2-diamine (1) and the three branched alkane-1,2diamines (compounds 7−9). Enthalpies of combustion and derived enthalpies of formation for the liquid phase were measured by Good and Moore in 1970.50 Vapor pressures were measured by Messerly et al.51 (compounds 1 and 7−9), Ahmed et al.52 (compounds 1 and 7), and Verevkin et al.40 (compounds 7 and 9). For 1,2-ethanediamine, vapor pressures have also been reported by Hieber and Woerner,53 Hirata et al.,54 and Daubert and Hutchison;55 however, these measurements have relatively large uncertainties, particularly in comparison with those of Messerly et al.51 The enthalpy of vaporization at temperature T = 298.15 K was measured by Wadso46 for 1,2-ethanediamine and 1,2-propanediamine. Enthalpies of vaporization were derived in this research with fits of the Wagner equation (eq 5) to the vapor pressures from

calculations. Conformers with relative energies more than ∼6 kJ·mol−1 are essentially not represented in the gas phase. In this work, the composition of the equilibrium mixture of conformers was evaluated for all diamines shown in Figure 1. A preliminary conformational analysis was performed using the force-field MMFF94 method.15 Distributions of dihedral angles were randomly sampled for each compound, and the resultant geometries were optimized. Atomic enthalpies H298 and Gibbs energies G298 were computed with the mPW2PLYP(FC)/6311+(d,p) method16 for the collection of stable conformers deduced in the preliminary analysis and were used to estimate the equilibrium population Pi for each conformer i at T = 298.15 K in the gas phase: Pi =

e−ΔGi / RT n 1 + ∑i = 1 e−ΔGi / RT

(7)

(6) G



Article

Table 7. Estimation of Enthalpies of Formation for the Liquid Phase ΔfH°m(l) at T = 298.15 K for Alkanediamines. (p° = 0.1 MPa)a compound

Δg1Hm(exp)

1 ethane-1,2-diamine (1)

2 45.8 ± 0.4f

propane-1,2-diamine (7) butane-1,2-diamine (8) 2-methylpropane-1,2-diamine (9)

45.8 ± 0.3f 48.5 ± 0.9f 45.2 ± 0.9f


48.0 51.1 40.9 47.8 41.1

± ± ± ± ±

0.3g 0.3g 0.3g 0.3g 1.1h

ΔfH°m(QC)b

ΔfH°m(l)

3 4 −15.0 −60.8 Branched Alkane-1,2-diamines −52.1 −97.9 −70.1 −118.6 −88.6 −133.8 N-Methyl-Substituted Ethane-1,2-diamines −11.5 −59.5 ± 3i −7.7 −58.8 ± 3i −17.4 −58.3 ± 3i −14.8 −62.6 ± 3i −14.0 −55.1 ± 3i

predictedc ΔfH°m(l)

experimentald Δe

5 −63.0 ± 0.5

6 −2.2

−97.8 ± 0.4 −120.2 ± 0.8 −134.0 ± 0.7

−0.1 −1.6 −0.2

a Units are kJ·mol−1 for all values, and uncertainties are the expanded uncertainty with of 0.95 level of confidence. bComputed with the composite quantum chemical (QC) method G4, as described in the text (section 4.2). cDifference between columns 3 and 2. dExperimental values reported by Good and Moore.50 eDifference between column 5 and 4. fThese values were derived with vapor pressures40,51,52 and enthalpies of vaporization46 from the literature, as described in the text (end of section 4.2). gValues derived from the vapor pressures measured in this research (Table 3). h Derived with literature vapor pressures as described in the text (section 3.2). iBased on results for the branched alkane-1,2-diamines (differences in column 6), a conservative estimate of the expanded uncertainty with 0.95 level of confidence is 3 kJ·mol−1 for the values of ΔfH°m(l) for the Nmethyl-substituted ethane-1,2-diamines.

the literature.40,51,52 The derived enthalpies of vaporization Δ1gHm° (298.15 K) were combined with the enthalpies of ° (l, 298.15 K) reported by formation for the liquids ΔfHm Good and Moore50 to calculate the enthalpies of formation in the gas phase ΔfH°m(g, 298.15 K). All values are listed in Table 6, where good agreement is seen between the experimental and ° (g, 298.15 K). QC values for ΔfHm 4.3. Validation of the Enthalpies of Formation for the Gas Phase with a Group-Additivity (GA) Method. As described above, use of a GA method in evaluation of enthalpies of vaporization is complicated by the presence liquid-phase association in alkanediamines. Such effects are greatly reduced in the gas phase, so application of GA methodology to the gas phase enthalpies of formation ΔfH°m(g, 298.15 K) should be successful. A system of GAVs for prediction of formation enthalpies of N-containing compounds (see Table 4) was developed previously,40,41 based on available data for the monoalkyl substituted amines. The GA values for ΔfH°m(g, 298.15 K) were calculated with the GAVs (Table 4) as the sum of the appropriate increments for each compound, and the results are listed in Table 6 (column 7). As shown in Table 6 (column 8), the differences between the GA and QC derived values of ΔfH°m(g, 298.15 K) do not exceed ∼2 kJ·mol−1 for the nine alkanediamines, thus demonstrating the mutual consistency of the results derived with the empirical (GA) and computational (QC) procedures. 4.4. Evaluation of Enthalpies of Formation for the Liquid Phase. Having established consistent sets of enthalpies of vaporization and enthalpies of formation for the gas (Table 6), these can be combined (eq 1) to derive the standard molar enthalpy of formation data in the liquid phase (see Table 7, column 4).

Generalization and implementation of these methods within the expert-system software NIST ThermoData Engine56−64 could provide a valuable mechanism for assessment of evaluated properties for extended families of related compounds.

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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.5b01003. Molar heat capacities Cp,m of liquid amines reported in the literature and used for evaluation of group-additivity values at temperature T = 298.15 K and details of conformational analysis and enthalpy of formation computations (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (vaporization/sublimation experiments (Rostock) and data evaluation). *E-mail: [email protected] (data evaluation (NIST)). Funding

This work has been partly (VNE) supported by the Russian Government Program of Competitive Growth of Kazan Federal University. One author (VAP) acknowledges gratefully a research scholarship from the DAAD (Deutscher Akademischer Austauschdienst). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This article is, in part, a contribution of NIST, and is not subject to copyright in the United States for the authors V.D., R.D.C., and K.K. Products or companies are named solely for descriptive clarity and this neither constitutes nor implies endorsement by NIST or by the U.S. government. Other products may be found to work as well or better.

5. CONCLUSION The combination of experimental, group-additivity, and quantum chemical methods is demonstrated, here, to be a useful tool in critical evaluation and prediction of thermodynamic properties for alkanediamines, with particular application to enthalpies of vaporization and enthalpies of formation. H



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