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Thermodynamic Study of N-methylformamide and N,N-Dimethyl-Formamide

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Abstract
An extensive thermodynamic study of N-methylformamide (CAS RN: 123-39-7) and N,N-dimethylformamide (CAS RN: 68-12-2), is presented in this work. The liquid heat capacities of N-methylformamide were measured by Tian–Calvet calorimetry in the temperature interval (250 – 300) K. The vapor pressures for N-methylformamide and N,N-dimethylformamide were measured using static method in the temperature range 238 K to 308 K. The ideal-gas thermo-dynamic properties were calculated using a combination of the density functional theory (DFT) and statistical thermodynamics. A consistent thermodynamic description was developed using the method of simultaneous correlation, where the experimental and selected titerature data for vapor pressures, vaporization enthalpies, and liquid phase heat capacities and calculated ide-al-gas heat capacities are treated together to ensure overall thermodynamic consistency of the results. Resulting vapor pressure equation is valid from the triple point to the normal boiling point temperature.
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Subject: Chemistry and Materials Science  -   Physical Chemistry

1. Introduction

This work represents a continuation of our efforts to provide reliable thermodynamic data for biogenic compounds, including α,ω-diamines [1], acetamides [2], proteinogenic α-amino acids [3,4], and their N-acetyl amides [5]. It reports new thermodynamic data for N-methylformamide (NMF) and N,N-dimethylformamide (DMF).
NMF and DMF are (given their low molar mass) high boiling compounds, having normal boiling temperatures (Tnbp) of approximately 472 K and 426 K, respectively. The disparity in Tnbp is attributed to hydrogen bonds in NMF (H-bonds are reported only in mixtures containing DMF, not in pure DMF [6], which is aprotic).The difference in normal temperatures of fusion is even higher (270.6 K for NMF [7] and 212.86 K for DMF [8]).
NMF contains (–CO) and (–NH) groups, interconnected in the same manner as a peptide bond, playing a central role in biochemistry. The aqueous solution of DMF serves as a model solvent for the interior of proteins [9].
Amides, due to their similarity to proteins, generally serve as model substances for basic research as the investigation of protein conformation, hydration and stability. Both NMF and DMF are commonly used solvents in peptide synthesis, and they play similar roles in facilitating the chemical reactions involved in building peptide bonds.
Beyond biological applications, NMF and DMF are used on an industrial scale as reactants [10,11] and as excellent solvents for both organic compounds and inorganic electrolytes [12], because of their chemical bifunctionality and high polarity. They find extensive use in the manufacture of e.g., pharmaceuticals, pesticides, fibers, adhesives, and coatings. Their unlimited miscibility in water and many organic solvents (including alcohols, esters, ethers, ketones and aromatic hydrocarbons) contrasts with their immiscibility with aliphatic hydrocarbons, which is utilized for separating aromatics from aliphatic components in petroleum refinement [12,13].
The prevailing use of DMF is attributed to its superior thermal stability; NMF undergoes chemical transformations at higher temperatures, especially when in contact with residual water [13]. Solutions of salts in DMF serve as fillers for electrolytic capacitors and batteries owing to the high dielectric constant of DMF [12].
As NMF and DMF serve as model substances for studying interactions in biological systems, they were extensively studied both experimentally [6,14,15,16,17] and computationally [18,19,20,21]. Both compounds could be used in parametrizing molecular dynamics force fields (FF) for an accurate representation of peptide bond behavior, or for FF verification. The ability of an FF to correctly capture the energetics and dynamics of peptide bonds is essential for simulating larger and more complex peptide structures.
In addition to quantities describing properties of a single molecule (e.g., bond lengths and orientation, spatial arrangement, charge distribution), macroscopic physico-chemical quantities, such as excess properties of mixtures containing NMF or DMF, and, in particular, densities and vaporization enthalpies of pure compounds, are necessary for the parameterization of FFs (and/or for their validation). While liquid densities can be readily obtained for NMF and DMF using, for example, vibrating tube densitometers, the accurate determination of vaporization enthalpies for high boiling substances is challenging, especially near the room temperature, i.e., in the low-pressure region. At the same time, enthalpies of vaporization (when combined with enthalpies of solution at infinite dilution) can yield enthalpies of solvation, especially hydration. These quantities are decisive for understanding the nature of solute-solvent interaction, both in water and organic solvents [22].
Therefore, both NMF and DMF deserve new vapor pressure measurements near room temperature (enabling to calculate vaporization enthalpies) and a more complex processing of related thermodynamic properties, leading to consistent data with low uncertainties. Densities and vapor pressures are essential also for parametrization of equations of state (e.g., SAFT family EOS), which are aimed for industrial use.
Calorimetry, static manometry, and theoretical calculations for properties in the state of ideal gas were used to obtain new data. These were combined with selected literature data that passed thermodynamic consistency tests. As a result, vapor pressures, vaporization enthalpies, and heat capacities of liquid and ideal gas were established, with a focus on biologically relevant ambient temperature region.

2. Results and Discussion

2.1. Thermogravimetry

While DMF is thermally stable even at elevated temperatures, thermal stability of NMF at higher temperatures (and especially in presence of water traces) represent a well-known issue [13]. Moreover, NMF is rather hygroscopic [23]. This instability might affect the measured quantities published in the literature (for example, scatter of published vapor pressures is unusually high) as well as values in this work. We have, therefore, performed TGA experiment coupled with mass spectrometry to evaluate NMF stability under dynamic argon atmosphere. We do not want to discuss all possible mechanism of NMF decomposition, however, there are two pathways, which we took into account.
  • Reaction between two molecules of NMF to yield N-methyl-diformylamine and gaseous methylamine. This path does not require any further reagent and might occur even in pure NMF.
  • Reaction with trace water (or any nucleophilic impurities, e.g., alcohols), which yields formic acid (or its derivates) and methylamine.
The mass spectrum of NMF, according to NIST database,[24] is composed of following major ions, which are relevant for our analysis: 59 (100%), 31 (2%), 30 (54%); followed by other ions: 58 (24%), 29 (13%), 28 (34%) and 15 (7%). Ion 59 represents the molecular peak, 31 represents methylamine fragment. The methylamine spectrum is composed of major ions 31 (65%), and 30 (100%), followed by other ions 29 (21%), 28 (54%), 27 (8%) and 15 (4%). Based on these data, it is clear that one has to compare the ratio of the relative intensity of ions 59 and 31, because the ion 31 has negligible intensity in the case of NMF but very high intensity in the case of methylamine. We also used peak 30 as a reference peak, which is present in both compounds (note that the intensity of methylamine and NMF are not directly comparable). The spectrum containing both TG data and ion intensities is shown in Figure 1 for heating rate 2 °C min−1, for heating rate 5 °C min−1, see Figure S1 in the Supporting Materials (SM). Up to 72 °C (heating rate 2 °C min−1) or 82 °C (heating rate 5 °C min−1), the peak 31 has almost zero intensity and ratio between 59 and 30 is almost 2 : 1, which reflects the data for NMF. When that temperature is reached, the intensity of peak 31 is gradually increasing and the 2 : 1 ratio between peaks 59 and 30 is not preserved, which implies its decomposition into gaseous methylamine and other by-products.

2.2. Vapor Pressure

Numerous literature sources providing vapor pressure p data for both titular amides can be found (see summary presented in Table 1). The majority of these sources encompass a pressure range spanning from several kilopascals to the Tnbp. The reported values exhibit some scatter, particularly in the case of NMF, possibly attributable to the thermal instability of NMF discussed in the preceding section.
In the case of DMF, literature results obtained using ebulliometry (at pressures higher than ca 10 kPa) seems to be in a reasonable agreement. Below 1 kilopascal, which corresponds to temperatures close to ambient, data are limited, and the measurements conducted in this study using STAT 6 apparatus [25] were intended to address this informational gap. Note that in the case of NMF, measurements of this work could be extended to supercooled liquid state below the normal melting temperature of 270.6 K [7] (see Table 1).
The available data are graphically compared in Figure 2. Since the ln p-1/T plot is rather insensitive for the purpose of comparing different vapor pressure data sets, the arc visualization [26] is employed in Figure 2, where the differences are magnified. This approach allows for the identification (and rejection) of obvious outliers prior to any data fitting.
The selection of which data should be retained or rejected in the final correlation must be made using thermodynamic consistency testing (SimCor method described in Section 3.6). As this testing requires vaporization enthalpies (discussed in section 2.3) and heat capacities of the liquid and ideal gas (sections 2.4 and 2.5), it will be presented later in Section 2.6.

2.3. Enthalpies of Vaporization

Calorimetric determination of vaporization enthalpies Δ l g H m at ambient temperatures presents a challenge, especially for high-boiling compounds. The sole paper reporting calorimetric vaporization enthalpies is by Barone et al. [16], who studied both NMF and DMF. The authors utilized a modified commercial sorption LKB microcalorimeter operating at 298.15 K. A miniaturized custom-made effusion cell was adapted to the microcalorimeter, and vaporization was performed isothermally into a vacuum through a small orifice, allowing a vapor pressure very close to the equilibrium value. The modified calorimeter was tested by measuring the enthalpies of vaporization at 298.15 K of several reference liquid compounds [49] (see section S2 in the Supplementary Material for more details). Barone et al.’s work [16] appears to have been carried out meticulously, using a purified and dried sample, and a claimed reproducibility of 1 percent. Relative deviation from recommended data [50,51] was well below 1 percent (with the exception of rather volatile benzene, see Table S1 in the SM). It is noteworthy, however, that the samples used for calorimeter testing [49] are more volatile than DMF and especially NMF. SimCor method (section 2.6) will be used to test consistency of calorimetric Δ l g H m with vapor pressures and heat capacities.
In a compilation summarizing phase change enthalpies [52], a paper by Panneerselvam et al. [53] is listed as a source of DMF vaporization enthalpy. However, this work will not be considered for the final regression in our study for two reasons. The first reason is the use of the CGC (Correlation Gas Chromatography) method, an indirect gas-liquid chromatographic method based on an empirical finding that there is a linear relationship between vaporization enthalpies of reference compounds at 298 K and the slope of the logarithm of retention time plotted as a function of 1/T at elevated temperatures (the temperature range of chromatographic measurements in [53] was from 473 K to 513 K). This method was extensively used primarily for the determination of vapor pressures, as it is relatively fast and insensitive to impurities. Our previously published analysis of published CGC results [54,55] revealed that many approximations and extensive extrapolations used in the CGC method can lead to large systematic errors. The second reason for rejection is that DMF was used by Panneerselvam et al. [53] as a reference compound with a known vaporization enthalpy taken from the paper by Barone et al. [16] , and it is therefore not an independent value. The values discussed in this section are summarized in Table 3.

2.4. Liquid Heat Capacities

Reliable adiabatic liquid heat capacities C p , m l can be found for DMF [8], eliminating the need for any experimental efforts. On the other hand, literature data for NMF is fragmented, with four sources reporting heat capacity at single temperature of 298 K, and two sources reporting over a short temperature range (see Table 4). As mutual agreement of literature values was not perfect, we conducted new measurements using Tian-Calvet calorimeter SETARAM Microcalvet. In order to avoid potential issues related to decomposition, as discussed in section 2.1, we restricted the temperature range to temperatures below 300 K. The continuous cooling method allowed us to measure heat capacity of supercooled liquid NMF, too (down to 250 K). The solidification of the sample made it impossible to evaluate the heat capacities from subsequent measurements in heating mode. As results for cooling mode were reproducible (and in accordance with literature data), they were considered for further treatment; resulting heat capacities are presented in Table 5 and graphically compared with literature data in Figure 3.
After the completion of the abomentioned measurements, the experiment was modified to avoid solidification of the sample during cooling. Subsequent heating of the supercooled sample showed a non-monotonic pattern with a local maximum (see Figure S2 in the SM). This interesting (and reproducible) phenomenon would merit further investigation, but is beyond the scope of this paper.

2.5. Ideal Gas Heat Capacities

The heat capacities of studied compounds in the ideal gaseous state C p , m g 0 were calculated by a combination of quantum chemical and statistical-thermodynamic calculations, as generally described in Section 3.5. Details specific for two studied amides are given below.
N-Methylformamide. A vibrational assignment is reported by Popov et al. [69] for a single NMF conformer only. Since NMF molecule can form two non-equivalent conformations cis and trans - regarded with respect to the mutual position of N-hydrogen and C-hydrogen atoms, we decided to adopt the scaled B3LYP-D3 frequencies for both conformers in all subsequent models to be able to follow the equilibrium conformation mixing model. B3LYP-D3/6-311+G(2df,p) level of theory predicts the cis conformer to be more stable which is in agreement with experimental determination [70]. However, the computed enthalpy difference 4.90 kJ∙mol-1 at 298 K is significantly underestimated when compared to the experimental value 7.44 kJ∙mol-1. The latter value was used in the calculations of conformation mixing models [71]. According to the given enthalpy difference, 95 % of molecules are present in the cis form at 300 K and 71 % at 1000 K which makes the use of the conformation mixing model appropriate. Reference spectral data on molecular structure can be found in the literature [72]. Principal moments of inertia based on this reference correspond to the less stable trans form, calling for an uncertainty revision of the thermodynamic properties based on these values which are listed in a handbook by Frenkel at al. [71]. Thus we take our newly calculated ideal-gas data for NMF as more reliable. The calculated products of inertia amount to IABCcis = 1.004∙10-135 kg3∙m6 and IABCtrans = 7.405∙10-136 kg3∙m6. The molar mass used to calculate the translation contributions was M = 59.0672 g∙mol-1. The reduced moments of inertia Ir and barriers to internal rotation for the methyl rotor amount to IMecis = 4.86∙10-47 kg∙m2, VMecis = 0.2 kJ∙mol-1 and IMetrans = 3.95∙10-47 kg∙m2, VMetrans = 3.8 kJ∙mol-1. The VMetrans value is in close agreement with a reference value [73] 4.6 kJ∙mol-1. Properties of both pure conformers have been computed and then the mixing terms were added to evaluate the total thermodynamic properties of NMF, which are listed in Table 6. At 300 K, contribution of the conformer equilibrium to C p , m g 0 amounts to 3.0 J K−1 mol−1, which dominates the difference between our results and the earlier published data [71,73].
N,N-Dimethylformamide. A complete vibrational assignment by Jao et al. [74] is available for DMF. Since this molecule exists in a single unique conformer, there is no need for following the conformer equilibrium mixing model. We thus employed the experimental frequencies for the RRHA calculations No experimental data on barriers to internal rotation or moments of inertia have been found for DMF, so calculated values were used for further calculations. Molar mass M = 79.0938 g∙mol-1 and principal moments of inertia IA = 9.447∙10-46 kg∙m2, IB = 2.018∙10-45 kg∙m2, IC = 2.856∙10-45 kg∙m2 were used for the calculations.
The N-methyl group adjacent to the carbonyl oxygen atom undergoes an internal rotation with computed barrier VCO-N-Me = 4.3 kJ∙mol-1 and ICO-N-Me = 5.18∙10-47 kg∙m2 while the other N-methyl rotation, neighbouring to the carbonyl hydrogen atom, possess parameters VCH-N-Me = 8.7 kJ∙mol-1 and ICH-N-Me = 5.03∙10-47 kg∙m2. The calculated thermodynamic properties arising from calculated or experimental vibration frequencies differ by less than 1.5 % at ambient temperature, which is a satisfying agreement. All values are listed in Table 6.

2.6. Selection of Recommended Data for NMF and DMF Using SimCor Method

The vapor pressures discussed in section 2.2 are thermodynamically linked, via the Clapeyron equation, to the enthalpies of vaporization (section 2.3), which, in turn, correlate with the difference between the heat capacities of an ideal gas (section 2.5) and a liquid (section 2.4). The SimCor method, explained in detail in Section 3.6, allows for the simultaneous correlation of all these related quantities, utilizing a suitable vapor pressure equation. In this study, we employed the Cox equation, Equation (1).
i) Vapor pressures. As described in section 2.2, vapor pressure datasets underwent initial analysis using the arc representation [26]. This analysis revealed outliers, which, being distant from the rest of the data, were excluded from the final correlation (see Figure 2). The remaining vapor pressure datasets were subjected to the SimCor method [75] for consistency, refining the selection of datasets used in the final correlation. For NMF, only two datasets passed thermodynamic tests, with the vapor pressures obtained in this work using the static method proving thermodynamically consistency along with ebulliometric data by Heinrich et al. [13]. Other literature vapor pressure data were either thermodynamically inconsistent with related thermal data [31,36] or exhibited significantly larger scatter than other data available in the same temperature range [23,48].
For DMF, due to the abundance of data, more datasets were considered for the final correlation. Besides vapor pressures from this work obtained using the static method, only several datasets obtained using the ebulliometric method at sufficiently high pressures (above approximately 10 kPa) passed thermodynamic testing [27,28,30]. Similar to NMF, other literature vapor pressure data were either thermodynamically inconsistent with related thermal data [46] or showed larger scatter than other data available in the same temperature range [17,38]. It should be noted that the best available vapor pressure data were selected; however, the uncertainty of ebulliometric data exceeds several hundred pascals, an order of magnitude higher than in the case of standard reference compounds. There might be room for improvement, however, measurements at elevated temperatures are apparently difficult due to the thermal instability of studied componds.
ii) Enthalpy of vaporization (section 2.3). Calorimetric vaporization enthalpy data published by Barone et al. [16] for both NMF and DMF fitted well within their stated uncertainty with that derived from selected vapor pressures, as shown in Figure 5.
iii) Liquid heat capacities (section 2.4). For NMF, only two datasets [60,62] reported liquid heat capacities as a function of temperature over a relatively narrow temperature range (see Table 4). New measurements in this work extended the available temperature range toward the temperature of melting and even below it. They were in very good agreement with single value obtained by drop calorimetry [14] (see Figure 3). Datasets [60,62] differed slightly (though still within combined uncertainties), and were not included in the final correlation. In the case of DMF, reliable adiabatic heat capacities were published by Smirnova et al. [8]. Three other datasets [62,66,68], while in reasonable agreement with adiabatic data [8], were not necessary for final correlation, as heat capacities can be safely included in the final correlation only at temperatures corresponding to vapor pressures lower than approximately 1 kPa (see Section S4 in the SM).
iv) Ideal gas heat capacities (Section 2.5). Due to simplistic approximations used in previously calculated idal gas heat capacities for NMF, data of this work were used. This hold true also for DMF, for which there are no literature data for comparison.
The selected vapor pressure data (given in bold in Table 2) were treated simultaneously with calorimetric enthalpies of vaporization [16], selected liquid heat capacities (given in bold in Table 4), and ideal-gas heat capacities (Table 6), using the SimCor method. The thermal data were employed in the temperature range where the pVT correction in eqs S1 and S2 in the SM does not significantly impact the SimCor method. For pVT corrections, second virial coefficients estimated by the method of Tsonopoulos [76] were used using experimental critical temperatures and pressures [77] and dipole moments [78,79] (see Table S2).
The Cox equation, Equation (1), was employed in the SimCor method; its parameters are presented in Table 7. Deviations of individual datasets from the SimCor results are shown in Figure 4 and Figure 5 for vapor pressures and vaporization enthalpies, respectively.
While vapor pressures can be easily calculated using the Cox equation, the calculation of the enthalpies of vaporization using the Clapeyron equation requires evaluation of the appropriate pVT correction based on the estimated second virial coefficient B. To avoid the need to calculate B, the vaporization enthalpies along with the associated uncertainties are listed in Table S3 in the SM for the convenience of the reader.

3. Materials and Methods

For the calibration purposes and for all the measurements, international temperature scale ITS-90 was used. Molar masses of the compounds were calculated based on IUPAC recommendations [80]. For the calculations, the molar gas constant R = 8.314462618 J K−1 mol−1 was used [81].

3.1. Samples Description

The title amides were of commercial origin. N-methyl formamide was distilled at reduced pressure ca 2.7 kPa under dry atmosphere using spinning band microdistillation column and stored over molecular sieves prior to measurements. DMA was purchased as anhydrous with protecting septum and due to its high purity (see Table 8) it was used as received.

3.2. Thermogravimetry

Thermogravimetric analysis was carried out using a Themys TGA (SETARAM, France) linked to a mass spectrometer with electron impact ionization (OMNI Star) at a temperature range between 30–200 °C and a heating rate of 2 and 5 °C min−1. The instrument was purged with an argon for one hour before the measurement started, and to equilibrate the temperature at 30 °C. Argon was used as a carrier gas with a flow rate of 100 mL min−1 (heating rate 5 °C min−1) or 20 mL min−1 (heating rate 2 °C min−1). About 20 mg of N-methylformamide was used for the analysis. It should be noted that contact of the sample with the laboratory atmosphere was be minimized but not completely eliminated.

3.3. Vapor Pressures

Vapor pressure measurements were performed using static apparatus with capacitance diaphragm gauges STAT6 [25]. The reader is referred to the original paper [25] for details on its design, calibration and measurement procedure. The uncertainty for the STAT6 apparatus, i.e., the combined expanded uncertainty (0.95 level of confidence, k= 2) of vapor pressure measurement is Uc(p/Pa) = 0.005p/Pa + 0.05.

3.4. Heat Capacity Measurements

A Tian-Calvet type calorimeter (SETARAM Microcalvet) was used for the measurement of heat capacities in the temperature range from 250 K to 300 K. As the detailed description of the calorimeter and its calibration and operation was reported previously [82], only most salient information is provided here. The heat capacity measurements were carried out by the continuous heating method [83], using the three-step methodology, i.e., the measurement of sample is followed by the measurement of reference material (synthetic sapphire, NIST Standard reference material No. 720) and by performing a blank experiment. The saturated molar heat capacities Csat obtained in this work are identical to isobaric molar heat capacities C p , m l in the temperature range studied given the very low vapor pressure of the samples. The combined expanded uncertainty (0.95 level of confidence) of the heat capacity measurements is estimated to be U c ( C p , m l ) = 0.006 C p , m l .

3.5. Theoretical Calculations

Thermodynamic properties of both amides in the ideal gaseous state were calculated using the RRHO model [84] with corrections for internal rotations, the 1DHR model [85,86], and optionally assuming an equilibrium mixture [87] of multiple conformations. Optimization of molecular geometries, fundamental vibration frequencies and barriers to internal rotations were calculated using the Gaussian 16 software package [88] by DFT method on B3LYP-D3/6-311+G(2df,p) level of theory [89,90] which has been thoroughly tested in our previous work [91,92]. The calculated fundamental harmonic frequencies were scaled by a double-linear scaling factor (0.9972 −1.48·10-5 ν cm-1) / 0.960 for frequencies below/above 2000 cm-1 [87] developed on experimental vibrational frequencies of n-alkanes. We assume the order of the carbon – nitrogen bond in both molecules to be higher than one so that no internal rotation takes place around this bond, being supported by our relaxed potential energy scans predicting the respective barriers to this rotation over 90 kJ mol−1.
Reduced moments of inertia of the methyl groups, required in the 1DHR model, have been evaluated according to the formula for symmetric tops by Pitzer [93] based on the B3LYP-D3 optimized molecular geometries. Energy levels of the hindered internal rotations were obtained by solving a one-dimensional Schrödinger equation using our code performing the FGH method [94]. The expecteded standard uncertainty of calculated C p , m g 0 does not exceed 2 % for low temperatures where C p , m g 0 were used in the SimCor method (section 3.6); uncertainty at higher temperatures is likely to be lower. Uncertainty in S m g 0 amounts to 0.8 %. These values are based on statistical evaluation of uncertainties of calculated thermodynamic properties published in our previous papers [92,95].

3.6. Simultaneous Treatment of Vapor Pressures and Related Thermal Data (SimCor Method)

The simultaneous correlation of vapor pressures and related thermal properties (SimCor, suggested in a simplified form by King and Al-Najjar [96]) is based on exact thermodynamic relationships and the procedure must therefore yield reliable results providing that the input data are of reasonable accuracy. A great advantage of this approach is that a single equation can furnish a description of the temperature dependences of several thermodynamic properties, resulting in a set of vapor pressure equation parameters which are valid in a combined temperature range of all input experimental values. The SimCor also provides a test on the consistency of different experimental data (vapor pressures p, .calorimetrical vaporization enthalpies Δ l g H m , differences in the heat capacities between ideal-gas and liquid phase, Δ l g C p , m 0 = C p , m g 0 − C p , m l , where C p , m g 0 and C p , m l were obtained as described in previous section and from the calorimetric measurements, respectively). The SimCor method has been described in detail in, e.g., [75,97] and was used in our laboratory to develop recommended vapor pressure and thermophysical data for several groups of crystalline and liquid compounds (see, e.g., Mahnel et al. [98] and references therein). Real behavior of the gas phase was approximated through the method of Tsonopoulos [76] using dipole moments and critical temperatures and pressures. The resulting pVT corrections are small well below the normal boiling point, so that even relatively high uncertainty in the estimated pVT description has negligible impact on final results. Note that the method of Tsonopoulos is utilized since it introduces class-specific corrections to the second virial coefficient, however any amides were not considered during its development. The second virial coefficient is therefore approximated by the equation for ketones, which seem to be most similar molecules, but not forming hydrogen bonds. Thermodynamic equations related to SimCor method are summarized in Section S4 in the SM.
The Cox equation [99] was used within the SimCor procedure to describe the vapor pressures and the linked thermodynamic properties since it requires lower number of adjustable parameters than other equations while keeping comparable description:
ln p p ref = ( 1 − T ref / K T / K ) exp ( ∑ i = 0 2 A i ( T / K ) i )
where pref and Tref are reference pressure and temperature, respectively, and Ai are the adjustable parameters.

4. Conclusions

In this study, we investigated two biologically and industrially important compounds: N-methylformamide and N,N-dimethylformamide, focusing on biologically important near-ambient temperatures. A literature search revealed that new vapor pressures for both compounds as well as liquid heat capacities for N-methylformamide are needed. Additionally, properties in the ideal gaseous state were uncertain or missing.
To address these gaps, we conducted measurements of vapor pressures and liquid heat capacities using the static method and the Tian-Calvet calorimeter, respectively. Properties of the two compound in the ideal gaseous state were obtained using quantum chemical calculations and statistical thermodynamics. By simultaneously correlating the aforementioned properties (along with scarce literature vaporization enthalpies and selected literature vapor pressures), we achieved their thermodynamically consistent description along the saturation curve from the melting to the normal boiling temperature.
It was found that the description could be improved by measurement of vapor pressures above 10 kPa using ebulliometry (not available in our laboratory). Such measurements might be however challenging for such high-boiling and thermally not very stable compounds. In the vicinity of the ambient temperature, the uncertainty is low and the data obtained by the SimCor method can be considered reliable.

Supplementary Materials

The following supporting information can be downloaded at the website of this paper posted on Preprints.org. Thermogravimetric analysis for N-methylformamide (Figure S1), Analysis of literature enthalpies of vaporization (Table S1), Liquid heat capacities of N-methylformamide (comparison of heating and cooling regime, Figure S2), Thermodynamic relations used in simultaneous treatment of vapor pressures and related thermal data (SimCor method) (Table S2), Recommended Vaporization Enthalpies (Table S3).

Author Contributions

Conceptualization, Michal Fulem and Květoslav Růžička; Data curation, Vojtěch Štejfa, Květoslav Růžička and Ctirad Červinka,; Formal analysis, Vojtěch Štejfa, Michal Fulem; Investigation, Květoslav Růžička, Vojtěch Štejfa, Jiří Šturala; Methodology, Vojtěch Štejfa, Ctirad Červinka, Jiří Šturala, and Michal Fulem; Resources, Michal Fulem; Supervision, Květoslav Růžička; Writing – original draft, Květoslav Růžička; Writing – review & editing, Vojtěch Štejfa, Ctirad Červinka, Jiří Šturala, Michal Fulem, and Květoslav Růžička.

Funding

This research was supported by the Czech Science Foundation (GACR No. 22-07164S).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available in the Supplementary Materials.

Conflicts of Interest

The authors declare no conflict of interest.

Sample Availability

Samples of the compounds are not available from the authors.

References

  1. Fulem, M.; Růžička, K.; Červinka, C.; Bazyleva, A.; Della Gatta, G. Thermodynamic study of alkane-α,ω-diamines – Evidence of odd–even pattern of sublimation properties. Fluid Phase Equilibria. 2014, 371, 93–105. [Google Scholar] [CrossRef]
  2. Štejfa, V.; Chun, S.; Pokorný, V.; Fulem, M.; Růžička, K. Thermodynamic study of acetamides. J Mol Liq. 2020, 319. [Google Scholar] [CrossRef]
  3. Pokorný, V.; Červinka, C.; Štejfa, V.; Havlín, J.; Růžička, K.; Fulem, M. Heat Capacities of l-Alanine, l-Valine, l-Isoleucine, and l-Leucine: Experimental and Computational Study. J Chem Eng Data. 2020, 65, 1833–1849. [Google Scholar] [CrossRef]
  4. Pokorný, V.; Štejfa, V.; Havlín, J.; Fulem, M.; Růžička, K. Heat Capacities of L-Cysteine, L-Serine, L-Threonine, L-Lysine, and L-Methionine. Molecules 2023, 28. [Google Scholar] [CrossRef]
  5. Štejfa, V.; Pokorný, V.; Lieberzeitová, E.; Havlín, J.; Fulem, M.; Růžička, K. Heat Capacities of N-Acetyl Amides of Glycine, L-Alanine, L-Valine, L-Isoleucine, and L-Leucine. Molecules 2023, 28. [Google Scholar] [CrossRef] [PubMed]
  6. Basma N, Cullen PL, Clancy AJ, Shaffer MSP, Skipper NT, Headen TF et al. The liquid structure of the solvents dimethylformamide (DMF) and dimethylacetamide (DMA). Mol Phys. 2019, 117, 3353–3363. [CrossRef]
  7. Ahlers, J.; Lohmann, J.; Gmehling, J. Binary Solid−Liquid Equilibria of Organic Systems Containing Different Amides and Sulfolane. J Chem Eng Data. 1999, 44, 727–730. [Google Scholar] [CrossRef]
  8. Smirnova, N.N.; Tsvetkova, L.Y.; Bykova, T.A.; Marcus, Y. Thermodynamic properties of N,N-dimethylformamide and N,N-dimethylacetamide. J Chem Thermodyn. 2007, 39, 1508–1513. [Google Scholar] [CrossRef]
  9. González, J.A. Thermodynamics of mixtures containing a very strongly polar compound: V – application of the extended real associated solution model to 1-Alkanol + Secondary Amide Mixtures. Phys Chem Liq. 2004, 42, 159–172. [Google Scholar] [CrossRef]
  10. Mitzel TM. N-Methylformamide. Encyclopedia of Reagents for Organic Synthesis (EROS). Wiley; 2009. p. 1-5. [CrossRef]
  11. Comins DL, Joseph SP. N,N-Dimethylformamide. Encyclopedia of Reagents for Organic Synthesis (EROS). Wiley; 2001. p. 1-4. [CrossRef]
  12. Bipp, H.; Kieczka, H. Formamides. Ullmann’s Encyclopedia of Industrial Chemistry. 2012, 1-12. [CrossRef]
  13. Heinrich, J.; Ilavský, J.; Surový, J. Temperature Dependence of N-Methylformamide Vapour Pressure, Liquid-Vapour Equilibrium of the N-Methylformamide-Water System (in Slovak). Chemické zvesti. 1961, 15, 414–418. [Google Scholar]
  14. Sköld, R.; Suurkuusk, J.; Wadsö, I. Thermochemistry of solutions of biochemical model compounds 7. Aqueous solutions of some amides, t-butanol and pentanol. J Chem Thermodyn. 1976, 8, 1075–1080. [Google Scholar] [CrossRef]
  15. Rouw, A.; Somsen, G. Solvation and hydrophobic hydration of alkyl-substituted ureas and amides in NN-dimethylformamide + water mixtures. J Chem Soc, Faraday Trans 1: Phys Chem Cond Phases. 1982, 78, 3397–3408. [Google Scholar] [CrossRef]
  16. Barone, G.; Castronuovo, G.; Della Gatta, G.; Elia, V.; Iannone, A. Enthalpies of vaporization of seven alkylamides. Fluid Phase Equilibria. 1985, 21, 157–164. [Google Scholar] [CrossRef]
  17. Zaitseva, K.V.; Zaitsau, D.H.; Varfolomeev, M.A.; Verevkin, S.P. Vapour pressures and enthalpies of vaporisation of alkyl formamides. Fluid Phase Equilibria. 2019, 494, 228–238. [Google Scholar] [CrossRef]
  18. Bendová, L.; Jurečka, P.; Hobza, P.; Vondrášek, J. Model of Peptide Bond−Aromatic Ring Interaction:  Correlated Ab Initio Quantum Chemical Study. J Phys Chem B. 2007, 111, 9975–9979. [Google Scholar] [CrossRef]
  19. Biswas, S.; Mallik, B.S. Probing the vibrational dynamics of amide bands of N-methylformamide, N, N-dimethylacetamide, and N-methylacetamide in water. Computational and Theoretical Chemistry. 2020, 1190, 113001. [Google Scholar] [CrossRef]
  20. Andrushchenko V, Matějka P, Anderson DT, Kaminský J, Horníček J, Paulson LO et al. Solvent Dependence of the N-Methylacetamide Structure and Force Field. J Phys Chem A. 2009, 113, 9727–9736. [CrossRef]
  21. Reimann, M.; Kaupp, M. Evaluation of an Efficient 3D-RISM-SCF Implementation as a Tool for Computational Spectroscopy in Solution. J Phys Chem A. 2020, 124, 7439–7452. [Google Scholar] [CrossRef]
  22. Konicek, J.; Wadsö, I. Thermochemical Properties of Some Carboxylic Acids, Amines, and N-Substituted Amides in Aqueous Solution. Acta Chem Scand. 1971, 25, 1541–1551. [Google Scholar] [CrossRef]
  23. Kortüm, G.; Biedersee, H.V. Dampf/Flüssigkeit-Gleichgewichte (Siedediagramme) binärer Systeme hoher relativer Flüchtigkeit. Wasser/N-Methylacetamid, Wasser/N-Methylformamid und N-Methylformamid/N-Methylacetamid. Chemie-Ing-Techn 1970, 42, 552–560. [Google Scholar] [CrossRef]
  24. NIST Standard Reference Database 1A, NIST Mass Spectral Libraries [database on the Internet]. NIST. 2023. Accessed: 2024-01-22. Accessed.
  25. Fulem M, Růžička K, Morávek P, Pangrác J, Hulicius E, Kozyrkin B et al. Vapor Pressure of Selected Organic Iodides. J Chem Eng Data. 2010, 55, 4780–4784. [CrossRef]
  26. Čenský, M.; Roháč, V.; Růžička, K.; Fulem, M.; Aim, K. Vapor pressure of selected aliphatic alcohols by ebulliometry. Part 1. Fluid Phase Equilibria. 2010, 298, 192–198. [Google Scholar] [CrossRef]
  27. Shealy, G.S.; Sandler, S.I. Vapor-liquid equilibrium for four mixtures containing N,N-dimethylformamide. J Chem Eng Data. 1985, 30, 455–459. [Google Scholar] [CrossRef]
  28. Blanco, B.; Beltrán, S.; Cabezas, J.L.; Coca, J. Phase Equilibria of Binary Systems Formed by Hydrocarbons from Petroleum Fractions and the Solvents N-Methylpyrrolidone and N,N-Dimethylformamide. 1. Isobaric Vapor−Liquid Equilibria. J Chem Eng Data. 1997, 42, 938–942. [Google Scholar] [CrossRef]
  29. Wang, C.; Li, H.; Zhu, L.; Han, S. Isothermal and isobaric vapor + liquid equilibria of N,N-dimethylformamide + n-propanol + n-butanol. Fluid Phase Equilibria. 2001, 189, 119–127. [Google Scholar] [CrossRef]
  30. Muñoz, R.; Montón, J.B.; Burguet, M.C.; de la Torre, J. Phase equilibria in the systems isobutyl alcohol+N,N-dimethylformamide, isobutyl acetate+N,N-dimethylformamide and isobutyl alcohol+isobutyl acetate+N,N-dimethylformamide at 101.3;kPa. Fluid Phase Equilibria 2005, 232, 62–69. [Google Scholar] [CrossRef]
  31. Ushakov, V.S.; Sedov, S.M.; Knyazev, B.A.; Kuchkaev, B.I. The thermodynamic properties of N-methylformamide. Zh Fiz Khim. 1996, 70, 1573–1577. [Google Scholar]
  32. Zielkiewicz J (Vapour+liquid) equilibria in (N-methylformamide+methanol+water) at the temperature 31315, K. J Chem Thermodyn. 1996, 28, 887–894. [CrossRef]
  33. Zielkiewicz J (Vapour + liquid) equilibria in (N-methylformamide + ethanol + water) at the temperature 31315, K. J Chem Eng Data. 1997, 29, 229–237. [CrossRef]
  34. Zielkiewicz, J. Excess Molar Volumes and Excess Gibbs Energies in N-Methylformamide + Water, or + Methanol, or + Ethanol at the Temperature 303. 15 K. J Chem Eng Data. 1998, 43, 650–652. [Google Scholar] [CrossRef]
  35. Harris, R.A.; Wittig, R.; Gmehling, J.; Letcher, T.M.; Ramjugernath, D.; Raal, J.D. Vapor−Liquid Equilibria for Four Binary Systems at 363. 15 K:  N-Methylformamide + Hexane, + Benzene, + Chlorobenzene, and + Acetonitrile. J Chem Eng Data. 2003, 48, 341–343. [Google Scholar] [CrossRef]
  36. Chen, W.-K.; Lee, K.-J.; Chang, C.-M.J.; Ko, J.-W.; Lee, L.-S. Vapor-liquid equilibria and density measurement for binary mixtures of o-xylene+NMF, m-xylene+NMF and p-xylene+NMF at 333. 15 K, 343.15 K and 353.15 K from 0 kPa to 101.3 kPa. Fluid Phase Equilib. 2010, 291, 40–47. [Google Scholar] [CrossRef]
  37. Li, R.; Meng, X.; Liu, X.; Gao, J.; Xu, D.; Wang, Y. Separation of azeotropic mixture (2, 2, 3, 3-Tetrafluoro-1-propanol + water) by extractive distillation: Entrainers selection and vapour-liquid equilibrium measurements. J Chem Thermodyn. 2019, 138, 205–210. [Google Scholar] [CrossRef]
  38. Ivanova, T.M.; Geller, B.E. Properties of the Dimethylformamide-Water System. 2. Vapor Density and Osmotic Pressure of the Aqueous Solutions. Zh Fiz Khim. 1961, 35, 1221–1229. [Google Scholar]
  39. Gopal, R.; Rizvi, S.A. Vapour Pressures of some Mono- and Di-Alkyl Substituted Aliphatic Amides at Different Temperatures. J Ind Chem Soc. 1968, 45, 13–16. [Google Scholar]
  40. Quitzsch, K.; Strittmatter, D.; Geiseler, G. Studien zur Thermodynamik binärer Flüssigkeitsgemische mit homologen Formamiden VIII. Die binären Systeme R-Heptan(l)/Dimethylformamid(2) und n-Heptan(l)/Diäthylformamid(2). Zeitschrift für Physikalische Chemie. 1969, 240, 107–126. [Google Scholar] [CrossRef]
  41. Myasnikova, L.F.; Shmelev, V.A.; Vaisman, I.L.; Bushinskii, V.I.; Novokhatka, D.A. Temperature dependence of the vapor-pressure of dimethylformamide and its aqueous solutions. Zh Prikl Khim (Leningrad). 1974, 47, 2604–2606. [Google Scholar]
  42. Bludilina, V.I.; Baev, A.K.; Matveev, V.K.; Gaidym, I.L.; Shcherbina, E.I. Thermodynamic study of the evaporation of dimethylformamide, N-methylpyrrolidone and tetrahydrofurfuryl alcohol. Zh Fiz Khim. 1979, 53, 1052–1053. [Google Scholar]
  43. Agarwal, R.S.; Bapat, S.L. Solubility characteristics of R22-DMF refrigerant-absorbent combination. Int J Refrig. 1985, 8, 70–74. [Google Scholar] [CrossRef]
  44. Wilding, W.V.; Wilson, L.C.; Wilson, G.M. Vapor liquid equilibrium measurements on five binary mixtures. Fluid Phase Equilibria. 1987, 36, 67–90. [Google Scholar] [CrossRef]
  45. Polishchuk, A.P.; Luk’yanchikova, I.A.; Sergeev, E.N.; Rumyantsev, E.M. Thermodynamic study of the dimethylformamide-ethylene glycol monobutyl ether-ammonium nitrate system. Izv Vyssh Uchebn Zaved, Khim Khim Tekhnol. 1988, 31, 48–52. [Google Scholar]
  46. Marzal, P.; Gabaldon, C.; Seco, A.; Monton, J.B. Isobaric Vapor-Liquid Equilibria of 1-Butanol + N,N-Dimethylformamide and 1-Pentanol + N,N-Dimethylformamide Systems at 50.00 and 100.00 kPa. J Chem Eng Data. 1995, 40, 589–592. [Google Scholar] [CrossRef]
  47. Cui, X.; Chen, G.; Han, X. Experimental Vapor Pressure Data and a Vapor Pressure Equation for N,N-Dimethylformamide. J Chem Eng Data. 2006, 51, 1860–1861. [Google Scholar] [CrossRef]
  48. Messow, U.; Quitzsch, K.; Seyffert, U.; Geiseler, G. Studies on Thermodynamics of Binary-Liquid Mixtures with Homolog Formamides .10. Binary-Systems Benzene(1) and N-Methylformamide(2), Tetrachloromethane(1) and N-Methylformamide(2), Cyclohexane(1) and N-Methylformamide(2), and Heptane(1) and N-Methylformamide(2). Z Phys Chem-Leipzig. 1974, 255, 947–968. [Google Scholar]
  49. Barone, G.; Della Gatta, G.; Elia, V. Direct Determination of Enthalpies of Vaporization of Liquid Compounds by a Miniaturized Effusion Cell Adapted to a Commercial Microcalorimeter. J Therm Anal. 1984, 29, 763–772. [Google Scholar] [CrossRef]
  50. Majer, V.; Svoboda, V. International Union of Pure and Applied Chemistry Chemical Data Series; No. 32: Enthalpies of Vaporization of Organic Compounds; Blackwell Scientific: Oxford, UK, 1985. [Google Scholar]
  51. Herrig, S.; Thol, M.; Harvey, A.H.; Lemmon, E.W. A Reference Equation of State for Heavy Water. J Phys Chem Ref Data 2018, 47. [Google Scholar] [CrossRef]
  52. Acree, W.; Chickos, J.S. Phase Transition Enthalpy Measurements of Organic and Organometallic Compounds. Sublimation, Vaporization and Fusion Enthalpies From 1880 to 2015. Part 1. C1− C10. J Phys Chem Ref Data 2016, 45. [Google Scholar] [CrossRef]
  53. Panneerselvam, K.; Antony, M.P.; Srinivasan, T.G.; Vasudeva Rao, P.R. Enthalpies of vaporization of N,N-dialkyl monamides at 298.15 K. Thermochimica Acta. 2009, 495, 1–4. [Google Scholar] [CrossRef]
  54. Koutek, B.; Mahnel, T.; Řehák, K.; Pokorný, V.; Fulem, M.; Růžička, K. Regression against Temperature of Gas–Liquid Chromatography Retention Factors. Van’t Hoff Analysis. J Chem Eng Data. 2020, 65, 3109–3120. [Google Scholar] [CrossRef]
  55. Koutek B, Pokorný V, Mahnel T, Štejfa V, Řehák K, Fulem M et al. Estimating Vapor Pressure Data from Gas–Liquid Chromatography Retention Times: Analysis of Multiple Reference Approaches, Review of Prior Applications, and Outlook. J Chem Eng Data. 2022, 67, 2017–2043. [CrossRef]
  56. de Visser C, Somsen G. Molar Heat Capacities of Binary Mixtures of Water and Some Amides at 298.15 K. Z Phys Chem Neue Folge 1974, 92, 159–162. [CrossRef]
  57. Bonner, O.D.; Cerutti, P.J. The partial molar heat capacities of some solutes in water and deuterium oxide. J Chem Thermodyn. 1976, 8, 105–112. [Google Scholar] [CrossRef]
  58. de Visser C, Pel P, Somsen G. Volumes and heat capacities of water andN-methylformamide in mixtures of these solvents. J Sol Chem. 1977, 6, 571–580. [CrossRef]
  59. Kolker, A.M.; Kulikov, M.V.; Krestov, A.G. Volumes and heat capacities of binary non-aqueous mixtures. Part 1. The systems acetonitrile—formamide and acetonitrile—N-methylformamide. Thermochimica Acta. 1992, 211, 61–72. [Google Scholar] [CrossRef]
  60. Sharma, V.K.; Dua, R. Topological and thermodynamic investigations of mixtures containing o-chlorotoluene and lower amides. J Chem Thermodyn. 2014, 71, 182–195. [Google Scholar] [CrossRef]
  61. Sharma, V.K.; Dua, R.; Sharma, D. Topological Investigations of Excess Heat Capacities of Binary and Ternary Liquid Mixtures Containing o-Chlorotoluene, Amides and Cyclohexane at 298.15, 303.15 and 308.15 K. J Sol Chem. 2015, 44, 1452–1478. [Google Scholar] [CrossRef]
  62. Kolker, A.M.; Kulikov, M.V.; Krestov, A.G. Volumes and heat capacities of binary non-aqueous mixtures. Part 2. The systems acetonitrile-N,N-dimethylformamide and acetonitrile-hexamethylphosphoric triamide. Thermochimica Acta. 1992, 211, 73–84. [Google Scholar] [CrossRef]
  63. Vittal Prasad, T.E.; Rajiah, A.; Prasad, D.H.L. Heat Capacity of Toluene + Dimethyl Formamide Mixtures. Phys Chem Liq. 1994, 27, 215–218. [Google Scholar] [CrossRef]
  64. Checoni, R.F.; Volpe, P.L.O. Measurements of the Molar Heat Capacities and Excess Molar Heat Capacities for Water + Organic Solvents Mixtures at 288.15 K to 303.15 K and Atmospheric Pressure. J Sol Chem. 2010, 39, 259–276. [Google Scholar] [CrossRef]
  65. Shokouhi, M.; Jalili, A.H.; Hosseini-Jenab, M.; Vahidi, M. Thermo-physical properties of aqueous solutions of N,N-dimethylformamide. J Mol Liq. 2013, 186, 142–146. [Google Scholar] [CrossRef]
  66. Tyczyńska, M.; Jóźwiak, M.; Komudzińska, M.; Majak, T. Effect of temperature and composition on the volumetric, acoustic and thermal properties of N,N-dimethylformamide + propan-1-ol mixture. J Mol Liq. 2019, 290, 111124. [Google Scholar] [CrossRef]
  67. Komudzińska, M.; Tyczyńska, M.; Jóźwiak, M.; Burakowski, A.; Gliński, J. Volumetric, acoustic and thermal properties of aqueous N,N-dimethylformamide system. Effect of temperature and composition. J Mol Liq. 2020, 300, 112321. [Google Scholar] [CrossRef]
  68. Tyczynska, M.; Dentkiewicz, A.; Jozwiak, M. Thermodynamic and Thermal Analyze of N,N-Dimethylformamide + 1-Butanol Mixture Properties Based on Density, Sound Velocity and Heat Capacity Data. Molecules 2023, 28. [Google Scholar] [CrossRef]
  69. Popov, E.M.; Zheltova, V.N.; Kogan, G.A. Vibrational spectra and force fields of the simplest amides. Zh Strukt Khim. 1970, 11, 1053–1060. [Google Scholar] [CrossRef]
  70. Shin S, Kurawaki A, Hamada Y, Shinya K, Ohno K, Tohara A et al. Conformational behavior of N-methylformamide in the gas, matrix, and solution states as revealed by IR and NMR spectroscopic measurements and by theoretical calculations. J Mol Struct. 2006, 791, 30–40. [CrossRef]
  71. Frenkel, M.L. Thermodynamics of organic compounds in the gas state. TRC data series. College Station, Tex.: Thermodynamics Research Center College Station, Tex.; 1994.
  72. Suzuki, I. Infrared Spectra and Normal Vibrations of N-Methylformamides HCONHCH-3, HCONDCH-3, DCONDCH-3, AND DCONDCH-3. Bull Chem Soc Jpn. 1962, 35, 540–551. [Google Scholar] [CrossRef]
  73. Glushko, A.S.; Kabo, G.Y.; Frenkel, M.L. Thermodynamic properties of amides Zh Prikl Khim (Leningrad). 1985, 587, 447–450. [Google Scholar]
  74. Jao, T.C.; Scott, I.; Steele, D. The Vibrational-Spectra of Amides - Dimethyl Formamide. J Mol Spectrosc. 1982, 92, 1–17. [Google Scholar] [CrossRef]
  75. Růžička, K.; Majer, V. Simple and controlled extrapolation of vapor pressures toward the triple point. AIChE Journal. 1996, 42, 1723–1740. [Google Scholar] [CrossRef]
  76. Tsonopoulos, C. Empirical correlation of second virial coefficients. AIChE J. 1974, 20, 263–272. [Google Scholar] [CrossRef]
  77. Wilson LC, Jasperson LV, VonNiederhausern D, Giles NF, Ihmels C. DIPPR Project 851 – Thirty Years of Vapor–Liquid Critical Point Measurements and Experimental Technique Development. J Chem Eng Data. 2018, 63, 3408–3417. [CrossRef]
  78. Kessler, M.; Povarov, J.M.; Gorbanev, A.I. Dipole moment of N-Methylformamid. Chem Zentralblatt. 1967, 138, 445–488. [Google Scholar] [CrossRef]
  79. McClellan, A.L. Tables of experimental dipole moments. Volume 2. El Cerrito, CF: Rahara Enterprises; 1974.
  80. Meija J, Coplen TB, Berglund M, Brand WA, Bièvre PD, Gröning M et al. Atomic weights of the elements 2013 (IUPAC Technical Report). Pur Appl Chem. 2016, 88, 265–291. [CrossRef]
  81. Newell DB, Cabiati F, Fischer J, Fujii K, Karshenboim SG, Margolis HS et al. The CODATA 2017 values of h, e, k, and NA for the revision of the SI. Metrologia. 2018, 55, L13–L6. [CrossRef]
  82. Štejfa, V.; Vojtíšková, O.; Pokorný, V.; Rohlíček, J.; Růžička, K.; Fulem, M. Heat capacities of active pharmaceutical ingredients nifedipine, griseofulvin, probucol, and 5,5-diphenylhydantoin. J Therm Anal Calorimetry. 2024, submitted.
  83. Höhne, G.W.H.; Flammersheim, H.-J.; Hemminger, W. Differential scanning calorimetry; Springer: Berlin, 2003. [Google Scholar]
  84. Irikura, K.K.; Frurip, D.J. Computational thermochemistry: prediction and estimation of molecular thermodynamics; American Chemical Society: Washington, DC, USA, 1998. [Google Scholar]
  85. East, A.L.L.; Radom, L. Ab initio statistical thermodynamical models for the computation of third-law entropies. J Chem Phys. 1997, 106, 6655–6674. [Google Scholar] [CrossRef]
  86. Pfaendtner, J.; Yu, X.; Broadbelt, L.J. The 1-D hindered rotor approximation. Theor Chem Acc. 2007, 118, 881–898. [Google Scholar] [CrossRef]
  87. Štejfa, V.; Fulem, M.; Růžička, K. First-principles calculation of ideal-gas thermodynamic properties of long-chain molecules by R1SM approach—Application to n-alkanes. J Chem Phys. 2019, 150. [Google Scholar] [CrossRef] [PubMed]
  88. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR et al. Gaussian 16 Revision B.01. Wallingford, CT: Gaussian, Inc.; 2016.
  89. Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J Chem Phys. 2010, 132, 154104. [Google Scholar] [CrossRef] [PubMed]
  90. Becke, A.D. Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys. 1993, 98, 5648–5652. [Google Scholar] [CrossRef]
  91. Červinka, C.; Fulem, M.; Růžička, K. Evaluation of Accuracy of Ideal-Gas Heat Capacity and Entropy Calculations by Density Functional Theory (DFT) for Rigid Molecules. Journal of Chemical and Engineering Data. 2012, 57, 227–232. [Google Scholar] [CrossRef]
  92. Červinka, C.; Fulem, M.; Růžička, K. Evaluation of Uncertainty of Ideal-Gas Entropy and Heat Capacity Calculations by Density Functional Theory (DFT) for Molecules Containing Symmetrical Internal Rotors. Journal of Chemical & Engineering Data. 2013, 58, 1382–1390. [Google Scholar] [CrossRef]
  93. Pitzer, K.S.; Gwinn, W.D. Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops. J Chem Phys. 1942, 10, 428–440. [Google Scholar] [CrossRef]
  94. Marston, C.C.; Balintkurti, G.G. The Fourier Grid Hamiltonian Method for Bound-State Eigenvalues and Eigenfunctions. J Chem Phys. 1989, 91, 3571–3576. [Google Scholar] [CrossRef]
  95. Červinka, C.; Fulem, M.; Štejfa, V.; Růžička, K. Analysis of Uncertainty in the Calculation of Ideal-Gas Thermodynamic Properties Using the One-Dimensional Hindered Rotor (1-DHR) Model. Journal of Chemical & Engineering Data. 2017, 62, 445–455. [Google Scholar] [CrossRef]
  96. King, M.B.; Al-Najjar, H. Method for correlating and extending vapor pressure data to lower temperatures using thermal data. Vapor pressure equations for some n-alkanes at temperatures below the normal boiling point. Chem Eng Sci. 1974, 29, 1003–1011. [Google Scholar] [CrossRef]
  97. Pokorný, V.; Štejfa, V.; Klajmon, M.; Fulem, M.; Růžička, K. Vapor Pressures and Thermophysical Properties of 1-Heptanol, 1-Octanol, 1-Nonanol, and 1-Decanol: Data Reconciliation and PC-SAFT Modeling. J Chem Eng Data. 2021, 66, 805–821. [Google Scholar] [CrossRef]
  98. Mahnel, T.; Štejfa, V.; Maryška, M.; Fulem, M.; Růžička, K. Reconciled thermophysical data for anthracene. J Chem Thermodyn. 2019, 129, 61–72. [Google Scholar] [CrossRef]
  99. Cox, E.R. Hydrocarbon vapor pressures. Ind, Eng Chem 1936, 28, 613–616. [Google Scholar] [CrossRef]
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Figure 1. TG-MS spectrum of NMF at heating rate 2 °C min−1. Black solid line is mass, red solid line is temperature, dashed green line is NMF ion with m/z 59, dashed red line is methylamine ion with m/z 31 and dashed brown line is m/z ion 30.
Figure 1. TG-MS spectrum of NMF at heating rate 2 °C min−1. Black solid line is mass, red solid line is temperature, dashed green line is NMF ion with m/z 59, dashed red line is methylamine ion with m/z 31 and dashed brown line is m/z ion 30.
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Figure 2. Arc representation [26] of vapor pressure data p for N—methylformamide (top), and N,N—dimethylformamide (bottom). Data sets used in the SimCor method (section 2.6) are denoted by filled symbols: magenta Preprints 98773 i001; this work; green Preprints 98773 i002, Heinrich et al. [13]; green Preprints 98773 i003; Shealy and Sandler [27]; cyan Preprints 98773 i004, Blanco et al. [28]; dark green Preprints 98773 i005, Wang et al. [29]; red Preprints 98773 i006, Muñoz et al. [30];Other datasets: cyan Preprints 98773 i007, Kortüm and Biedersee [23]; black Preprints 98773 i008, blue Preprints 98773 i009, Ushakov et al. [31]; orange Preprints 98773 i010, Zielkiewicz [32,33,34]; violet Preprints 98773 i011, Harris et al. [35]; brown Preprints 98773 i012, Chen et al. [36]; red Preprints 98773 i013, Li et al. [37]; grey Preprints 98773 i014, Ivanova and Geller [38]; blue Preprints 98773 i015, Gopal et al. [39]; black Preprints 98773 i016, Quitzsch et al.[40]; dark green Preprints 98773 i017, Myasnikova et al. [41] (partially displayed); olive Preprints 98773 i018, Bludilina et al. [42]; red Preprints 98773 i019; Agarwal and Bapat [43]; olive Preprints 98773 i020, Wilding et al. [44]; red Preprints 98773 i021, Polishchuk et al. [45]; red Preprints 98773 i022, Marzal et al. [46]; green Preprints 98773 i023, Cui et al. [47]; blue Preprints 98773 i024; Zaitseva et al. [17]; red Preprints 98773 i025, data obtained by SimCor method.
Figure 2. Arc representation [26] of vapor pressure data p for N—methylformamide (top), and N,N—dimethylformamide (bottom). Data sets used in the SimCor method (section 2.6) are denoted by filled symbols: magenta Preprints 98773 i001; this work; green Preprints 98773 i002, Heinrich et al. [13]; green Preprints 98773 i003; Shealy and Sandler [27]; cyan Preprints 98773 i004, Blanco et al. [28]; dark green Preprints 98773 i005, Wang et al. [29]; red Preprints 98773 i006, Muñoz et al. [30];Other datasets: cyan Preprints 98773 i007, Kortüm and Biedersee [23]; black Preprints 98773 i008, blue Preprints 98773 i009, Ushakov et al. [31]; orange Preprints 98773 i010, Zielkiewicz [32,33,34]; violet Preprints 98773 i011, Harris et al. [35]; brown Preprints 98773 i012, Chen et al. [36]; red Preprints 98773 i013, Li et al. [37]; grey Preprints 98773 i014, Ivanova and Geller [38]; blue Preprints 98773 i015, Gopal et al. [39]; black Preprints 98773 i016, Quitzsch et al.[40]; dark green Preprints 98773 i017, Myasnikova et al. [41] (partially displayed); olive Preprints 98773 i018, Bludilina et al. [42]; red Preprints 98773 i019; Agarwal and Bapat [43]; olive Preprints 98773 i020, Wilding et al. [44]; red Preprints 98773 i021, Polishchuk et al. [45]; red Preprints 98773 i022, Marzal et al. [46]; green Preprints 98773 i023, Cui et al. [47]; blue Preprints 98773 i024; Zaitseva et al. [17]; red Preprints 98773 i025, data obtained by SimCor method.
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Preprints 98773 g003
Figure 3. Comparison of available liquid heat capacities C p , m l for N-methylformamide (left) and N,N –dimethylformamide (right). Data accepted for SimCor method (section 2.6) are denoted by filled symbols: magenta Preprints 98773 i026, this work; red Preprints 98773 i027, Sköld et al. [14] ; green Preprints 98773 i028, Smirnova et al. [8]; Other data sets: black Preprints 98773 i029, de Visser and Somsen [56] ; black Preprints 98773 i030, Bonner and Cerutti [57] ; black Preprints 98773 i031, de Visser et al. [58]; black Preprints 98773 i032, Kolker et al. [59,62]; magenta Preprints 98773 i033, Sharma and Dua [60,61]; blue Preprints 98773 i034, Prasad et al. [63]; magenta Preprints 98773 i035, Checoni and Volpe [64]; red Preprints 98773 i036, Shokouhi et al. [65]; red Preprints 98773 i037, Tyczyńska et al. [66,67]; blue Preprints 98773 i038, Tyczyńska et al. [68].
Figure 3. Comparison of available liquid heat capacities C p , m l for N-methylformamide (left) and N,N –dimethylformamide (right). Data accepted for SimCor method (section 2.6) are denoted by filled symbols: magenta Preprints 98773 i026, this work; red Preprints 98773 i027, Sköld et al. [14] ; green Preprints 98773 i028, Smirnova et al. [8]; Other data sets: black Preprints 98773 i029, de Visser and Somsen [56] ; black Preprints 98773 i030, Bonner and Cerutti [57] ; black Preprints 98773 i031, de Visser et al. [58]; black Preprints 98773 i032, Kolker et al. [59,62]; magenta Preprints 98773 i033, Sharma and Dua [60,61]; blue Preprints 98773 i034, Prasad et al. [63]; magenta Preprints 98773 i035, Checoni and Volpe [64]; red Preprints 98773 i036, Shokouhi et al. [65]; red Preprints 98773 i037, Tyczyńska et al. [66,67]; blue Preprints 98773 i038, Tyczyńska et al. [68].
Preprints 98773 g003
Preprints 98773 g004
Figure 4. Relative deviations of vapor pressures p for N—methylformamide (top), and N,N—dimethylformamide (bottom) from the recommended values pcalc calculated with the Cox equation, Equation (1), with parameters listed in Table 7. Green Preprints 98773 i039, Heinrich et al. [13]; cyan Preprints 98773 i040, Kortüm and Biedersee [23]; black Preprints 98773 i041, blue Preprints 98773 i042, Ushakov et al. [31]; orange Preprints 98773 i043, Zielkiewicz [32,33,34]; violet Preprints 98773 i044, Harris et al. [35]; brown Preprints 98773 i045, Chen et al. [36]; red Preprints 98773 i046, Li et al. [37]; magenta Preprints 98773 i047; this work; grey Preprints 98773 i048, Ivanova and Geller [38]; blue Preprints 98773 i049, Gopal et al. [39]; black Preprints 98773 i050, Quitzsch et al.[40]; dark green Preprints 98773 i051, Myasnikova et al. [41] (partially displayed); olive Preprints 98773 i052, Bludilina et al. [42]; red Preprints 98773 i053; Agarwal and Bapat [43]; green Preprints 98773 i054; Shealy and Sandler [27]; olive Preprints 98773 i055, Wilding et al. [44]; red Preprints 98773 i056, Polishchuk et al. [45]; red Preprints 98773 i057, Marzal et al. [46]; cyan Preprints 98773 i058, Blanco et al. [28]; dark green Preprints 98773 i059, Wang et al. [29]; red Preprints 98773 i060, Muñoz et al. [30]; green Preprints 98773 i061, Cui et al. [47]; blue Preprints 98773 i062; Zaitseva et al. [17]; Preprints 98773 i063, absolute deviations. Data sets represented by filled symbols were used in the SimCor method.
Figure 4. Relative deviations of vapor pressures p for N—methylformamide (top), and N,N—dimethylformamide (bottom) from the recommended values pcalc calculated with the Cox equation, Equation (1), with parameters listed in Table 7. Green Preprints 98773 i039, Heinrich et al. [13]; cyan Preprints 98773 i040, Kortüm and Biedersee [23]; black Preprints 98773 i041, blue Preprints 98773 i042, Ushakov et al. [31]; orange Preprints 98773 i043, Zielkiewicz [32,33,34]; violet Preprints 98773 i044, Harris et al. [35]; brown Preprints 98773 i045, Chen et al. [36]; red Preprints 98773 i046, Li et al. [37]; magenta Preprints 98773 i047; this work; grey Preprints 98773 i048, Ivanova and Geller [38]; blue Preprints 98773 i049, Gopal et al. [39]; black Preprints 98773 i050, Quitzsch et al.[40]; dark green Preprints 98773 i051, Myasnikova et al. [41] (partially displayed); olive Preprints 98773 i052, Bludilina et al. [42]; red Preprints 98773 i053; Agarwal and Bapat [43]; green Preprints 98773 i054; Shealy and Sandler [27]; olive Preprints 98773 i055, Wilding et al. [44]; red Preprints 98773 i056, Polishchuk et al. [45]; red Preprints 98773 i057, Marzal et al. [46]; cyan Preprints 98773 i058, Blanco et al. [28]; dark green Preprints 98773 i059, Wang et al. [29]; red Preprints 98773 i060, Muñoz et al. [30]; green Preprints 98773 i061, Cui et al. [47]; blue Preprints 98773 i062; Zaitseva et al. [17]; Preprints 98773 i063, absolute deviations. Data sets represented by filled symbols were used in the SimCor method.
Preprints 98773 g004
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Figure 5. Calorimetric enthalpy of vaporization Δ 1 g H m : blue , Barone et al. [16]; red , enthalpy of vaporization Δ 1 g H m , and red , quantity Δ 1 g H m / Δ 1 g z (see eq S1 in the SM) obtained by the SimCor method. Data sets published by Barone et al. [16] were used in the SimCor method.
Figure 5. Calorimetric enthalpy of vaporization Δ 1 g H m : blue , Barone et al. [16]; red , enthalpy of vaporization Δ 1 g H m , and red , quantity Δ 1 g H m / Δ 1 g z (see eq S1 in the SM) obtained by the SimCor method. Data sets published by Barone et al. [16] were used in the SimCor method.
Preprints 98773 g005
Table 1. Experimental Vapor Pressures p for N-methylformamide N,N-dimethylformamide measured with STAT6 Apparatusa.
Table 1. Experimental Vapor Pressures p for N-methylformamide N,N-dimethylformamide measured with STAT6 Apparatusa.
T / K pb/ Pa T / K pb / Pa T / K pb / Pa
N-methylformamide
248.35 0.323 268.22 2.685 288.19 16.21
248.35 0.322 268.22 2.684 293.18 24.36
248.35 0.322 273.21 4.321 293.18 24.36
253.26 0.566 273.21 4.319 293.18 24.36
253.26 0.565 273.22 4.322 298.17 36.02
253.26 0.566 278.21 6.844 298.17 36.02
258.25 0.973 278.21 6.841 298.17 36.02
258.25 0.973 278.21 6.844 303.15 52.44
258.25 0.972 283.20 10.63 303.15 52.45
263.24 1.634 283.20 10.63 303.15 52.44
263.24 1.632 283.20 10.63 308.14 75.34
263.24 1.634 288.19 16.21 308.14 75.33
268.22 2.684 288.19 16.21 308.15 75.38
N,N-dimethylformamidee
238.15 3.847 263.15 39.95 288.15 264.71
238.16 3.844 263.15 39.96 288.15 264.77
238.16 3.841 263.15 39.96 288.15 264.85
243.15 6.390 268.15 60.26 293.15 369.48
243.16 6.389 268.15 60.27 293.15 369.48
243.16 6.392 268.15 60.26 293.16 369.49
248.15 10.37 273.15 89.36 298.15 508.91
248.15 10.38 273.15 89.37 298.15 508.93
248.15 10.38 273.15 89.37 298.15 508.74
253.15 16.60 278.15 130.35 303.15 691.81
253.15 16.59 278.15 130.33 303.15 691.79
253.15 16.59 278.15 130.35 303.15 691.83
258.15 25.97 283.15 187.19 308.15 930.12
258.15 25.99 283.15 187.2 308.15 929.99
258.15 25.98 283.15 187.17 308.16 929.99
a The standard uncertainty in the sample temperature measurements is u(T) = 0.01 K, and combined expanded uncertainty (0.95 level of confidence, k = 2) in the vapor pressure measurements is Uc(p) = 0.005 p + 0.05 Pa. b Values are reported with one digit more than is justified by the experimental uncertainty to avoid round-off errors in calculations based on these results.
Table 2. Overview of vapor pressures p of N--Methylformamide and of N,N--Dimethylformamide.
Table 2. Overview of vapor pressures p of N--Methylformamide and of N,N--Dimethylformamide.
Year Reference a N b (Tmin – Tmax) / K (pmin – pmax) / Pa Method
N-methylformamide
1961 Heinrich et al. [13] 19 370-472 2653-100405 Ebulliometry
1970 Kortüm and Biedersee [23] 33 343-456 773-101000 Ebulliometry
1974 Messow et al. [48] 19 311-391 89-6920 Isoteniscope
1996 Ushakov et al. [31] Sc 340-440 532-39312 Static
1996-8 Zielkiewicz [32,33,34] 3 303,313 60,95 Static
2003 Harris et al. [35] 4 363 1950-2130 Static
2010 Chen et al. [36] 3 333-353 370-1150 Static/dynamic
2019 Li et al. [37] 1 471 101325 Ebulliometry
2024 This work 39 248-308 0.3-75 Static
N,N-dimethylformamided
1961 Ivanova and Geller [38] 22 304-425 666-101325 Ramsay Young
1968 Gopal et al. [39] 7 303-363 733-14532 Static
1969 Quitzsch et al.[40] 5 278-358 141-9775 Isoteniscope
1974 Myasnikova et al. [41] 17 331-426 2266-101325 Ebulliometry
1979 Bludilina et al. [42] Sc 318-423 1784-95906 Static.
1985 Agarwal and Bapat [43] 6 313-353 1366-14818 Static
1985 Shealy and Sandler [27]e 8 363-398 11900-44740 Ebulliometry
1987 Wilding et al. [44] 6 293-363 380-14520 Static.
1988 Polishchuk et al. [45] 9 293-373 376-17091 Static
1995 Marzal et al. [46] 20 338-425 4600-100780 Ebulliometry
1997 Blanco et al. [28] 13 376-426 21400-101310 Ebulliometry
2001 Wang et al. [29] 6 353-426 8660-101300 Ebulliometry
2005 Muñoz et al. [30] 26 346-426 6300-101200 Ebulliometry
2006 Cui et al. [47] 32 307-369 922-18806 Static
2019 Zaitseva et al. [17] 12 276-305 123-847 Gas saturation
2024 This work 45 238-308 4-930 Static
a Data sets printed in bold were used in the SimCor method (section 2.6). b N = number of data points. c S denotes data in the form of equation only. Such datasets are excluded from further fitting as their statistically rigorous treatment is not possible. d Sources containing one or two vapor pressure points are not listed. e The value of 12.71 kPa at 368.15 K in Shealy and Sandler [27] is an obvious printing error and value of 15.71 kPa was used.
Table 3. Summary of vaporization enthalpies Δ l g H m (in kJ mol−1) at 298.15 K obtained using calorimetry [16] and indirect chromatographic method [53], which used calorimetric data [16] as an input reference values.
Table 3. Summary of vaporization enthalpies Δ l g H m (in kJ mol−1) at 298.15 K obtained using calorimetry [16] and indirect chromatographic method [53], which used calorimetric data [16] as an input reference values.
Compound N-methylformamide N,N-dimethylformamide N,N-dimethylformamide
Literature Barone et al. [16] Barone et al. [16] Panneerselvam et al. [53]
Method Calorimetry Calorimetry GLC
psat /kPa 0.036 0.509 0.509
Δ l g H m exp. 56.38 47.16 47.45
56.11 47.29 46.31
56.22 46.21 46.80
56.30 46.56
46.60
Δ l g H m avg. 56.25 ±0.12 46.89 ±0.59 46.65 ±0.45
Mean rel. dev. ±0.20% ±1.26% ±0.97%
a Data points printed in bold were used in the SimCor method (section 2.6).
Table 4. Overview of the Literature Heat Capacities C p , m l of N-Methylformamide and N,N-Dimethylformamide.
Table 4. Overview of the Literature Heat Capacities C p , m l of N-Methylformamide and N,N-Dimethylformamide.
Year Reference a Nb (Tmin-Tmax)/K 100ur( C p , m l )c Method
N-methylformamide
1974 de Visser and Somsen [56] 1 298.15 0.7 J/mol/K Isoperibol
1976 Bonner and Cerutti [57] 1 298.15 1.0 Isoperibol
1976 Sköld et al. [14] 1 298.15 0.2 J/mol/K Drop
1977 de Visser et al. [58] 1 298.15 1.0 Isoperibol
1992 Kolker et al. [59] 4 283-328 0.05 “Adiabatic”d
2014 Sharma and Dua [60,61] 3 298-308 0.3 Tian Calvet
2024 This work 11 250-300 0.6 Tian-Calvete
N,N-dimethylformamidee
1974 de Visser and Somsen [56] 1 298.15 0.3 J/mol/K Isoperibol
1976 Bonner and Cerutti [57] 1 298.15 1.0 Isoperibol
1992 Kolker et al. [62] 6 283-323 0.05 “Adiabatic”d
1994 Prasad et al. [63] 4 293-323 nosp DTA
2007 Smirnova et al. [8] 57 216-302 0.3 Adiabatic
2010 Checoni and Volpe [64] 4 288-303 nosp solution
2013 Shokouhi et al. [65] 6 303-353 0.2 Hot wire
2014 Sharma and Dua [60,61] 3 298-308 0.3 Tian Calvet
2019 Tyczyńska et al. [66,67] 6 293-318 0.2 Tian-Calvet
2023 Tyczyńska et al. [68] 6 293-318 0.2 Tian-Calvet
a The data from references written in bold were considered for inclusion in SimCor method (section 2.6). b N = number of data points. c ur C p , m l stands for relative uncertainty in heat capacity as stated by the authors. d “Adiabatic shell calorimeter of container type“ used primarily for measurement of mixtures. Claimed uncertainty is overoptimistic. There is no reference material for which heat capacities uncertainty is lower than 0.1 percent. e Due to sufficient amount of sources reporting liquid heat capacity of N,N-Dimethylformamide as a function of temperature, some sources containing heat capacity at single temperature are not listed.
Table 5. Experimental Liquid Heat Capacities C p , m l of N-Methylformamide at p = (100 ± 5) kPa.a,b.
Table 5. Experimental Liquid Heat Capacities C p , m l of N-Methylformamide at p = (100 ± 5) kPa.a,b.
T / K C p , m l / J·K−1·mol−1 T / K C p , m l / J·K−1·mol−1 T / K C p , m l / J·K−1·mol−1
250.0 115.9 270.0 119.0 290.0 122.8
255.0 116.5 275.0 120.0 295.0 123.6
260.0 117.2 280.0 120.9 300.0 124.4
265.0 118.0 285.0 121.9
a Standard uncertainty u is u(T) = 0.05 K, and the combined expanded uncertainty of the heat capacity is U c ( C p , m l ) = 0.006 ⋅ C p , m l (0.95 level of confidence). b Values are reported with one digit more than is justified by the experimental uncertainty to avoid round-off errors in calculations based on these results.
Table 6. Standard Molar Thermodynamic Functions (in J·K−1·mol−1) of Amides in the Ideal Gaseous State at p = 105 Paa.
Table 6. Standard Molar Thermodynamic Functions (in J·K−1·mol−1) of Amides in the Ideal Gaseous State at p = 105 Paa.
N-Methylformamide N,N-Dimethylformamide
T/K C m g 0 S m g 0 Δ 0 T H m g 0 / T − Δ 0 T G m g 0 / T C p , m g 0 C m g 0 Δ 0 T H m g 0 / T − Δ 0 T G m g 0 / T
100 42.5 234.6 38.6 196.0 53.6 242.7 40.4 202.3
150 49.2 253.0 40.9 212.2 65.4 266.8 46.9 219.9
200 56.3 268.1 43.5 224.6 74.5 286.9 52.7 234.2
210 57.8 270.9 44.1 226.8 76.2 290.5 53.8 236.8
220 59.3 273.6 44.7 229.0 77.9 294.1 54.8 239.3
230 60.8 276.3 45.2 231.1 79.6 297.6 55.8 241.8
240 62.4 278.9 45.8 233.1 81.3 301.0 56.9 244.2
250 63.9 281.5 46.4 235.1 83.1 304.4 57.9 246.5
250 63.9 281.5 46.4 235.1 83.1 304.4 57.9 246.5
260 65.5 284.0 47.0 237.0 84.8 307.7 58.9 248.8
270 67.1 286.5 47.6 238.9 86.7 310.9 59.9 251.1
273.15 67.6 287.2 47.8 239.4 87.2 311.9 60.2 251.7
280 68.7 289.0 48.2 240.7 88.5 314.1 60.9 253.2
290 70.3 291.4 48.9 242.5 90.4 317.3 61.9 255.4
298.15 71.6 293.3 49.4 243.9 91.9 319.7 62.6 257.1
300 71.9 293.8 49.5 244.3 92.3 320.4 62.8 257.5
310 73.5 296.2 50.2 246.0 94.2 323.4 63.8 259.6
320 75.1 298.5 50.8 247.7 96.2 326.4 64.8 261.6
330 76.7 300.8 51.5 249.4 98.2 329.4 65.8 263.6
340 78.4 303.2 52.1 251.0 100.2 332.4 66.8 265.6
350 80.0 305.4 52.8 252.6 102.2 335.3 67.8 267.6
360 81.6 307.7 53.5 254.2 104.2 338.2 68.7 269.5
370 83.2 310.0 54.2 255.8 106.2 341.1 69.7 271.4
380 84.7 312.2 54.9 257.3 108.3 344.0 70.7 273.3
390 86.3 314.4 55.6 258.8 110.3 346.8 71.7 275.1
400 87.9 316.6 56.3 260.3 112.3 349.6 72.7 276.9
500 102.4 337.8 63.5 274.3 131.9 376.8 82.6 294.2
600 115.0 357.5 70.6 286.9 149.6 402.5 92.3 310.1
700 125.8 376.0 77.4 298.6 165.0 426.7 101.6 325.1
800 135.0 393.4 83.8 309.6 178.3 449.6 110.4 339.2
900 142.9 409.8 89.8 320.0 189.8 471.3 118.6 352.7
1000 149.8 425.2 95.3 329.9 199.7 491.8 126.2 365.6
a Values were calculated with B3LYP-D3/6-311+G(2df,p) level of theory, as described in text. Values are reported with one digit more than is justified by the experimental uncertainty to avoid round-off errors in calculations based on these results.
Table 7. Parameters of the Cox Equation, Equation (1).
Table 7. Parameters of the Cox Equation, Equation (1).
Compound A0 A1·103 A2·106 Tref/K pref/Paa (Tmin-Tmax)/K σp/Pab
N-Methylformamide 2.8557046
± 0.0012520		 −1.0672816
±0.0104324		 0.79531683
±0.02584536		 472.3457
±0.0903		 100000 248 - 473 152
N,N-Dimethylformamide 2.8526857
± 0.0009345		 −1.5975105
± 0.0083250		 1.5729198
±0.0203733		 425.1013
±0.0263		 100000 215 - 427 441
apref was not considered an adjustable parameter, but was set to a constant value. b σp is the standard deviation of the fit defined as σ p = [ ∑ i = 1 n ( Δ p ) i 2 / ( n − m ) ] 1 / 2 , where Δp is the difference between the experimental and the smoothed values, n is the number of experimental points used in the fit and m is the number of adjustable parameters of the Cox equation.
Table 8. Sample Description.
Table 8. Sample Description.
Compound CAS number Supplier Prufication method Mole fraction purity Mass fraction water content
N-Methylformamide 123-39-7 Aldrich Distillation, molecular sieves 0.988a, 0.9990b 30·10-6 d
N,N-Dimethylformamide 68-12-2 Aldrich Vapor pressure measurements 0.9999a; 1.0000b,c 30·10-6 e
a From certificate of analysis supplied by the manufacturer determined by gas-liquid chromatography (GLC). d Purity determined by GLC using the chromatograph Hewlett-Packard 6890A equipped with a column HP-1, length 25 m, film thickness 0.52 µm, diameter 0.32 mm, and a FID detector. Average of two determinations. c No detectable peaks found. d Fraction of water determined by Karl-Fischer analysis by Metrohm 831. Average of four determinations. e From certificate of analysis supplied by the manufacturer; determined by coulometry.
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