Experimental and Computational Thermochemistry of 3-and 4

Article pubs.acs.org/JPCA

Experimental and Computational Thermochemistry of 3- and 4‑Nitrophthalic Anhydride Miguel A. García-Castro, Patricia Amador,* Julio M. Hernández-Pérez, Adrián E. Medina-Favela,† and Henoc Flores Facultad de Ciencias Químicas de la Benemérita Universidad Autónoma de Puebla, 14 Sur y Avenida San Claudio, C.P. 72570, Puebla Pue, México S Supporting Information *

ABSTRACT: In order to understand the influence that the position of the nitro group on the aromatic ring has on the relative stability of two isomers, the standard enthalpies of formation of 3- and 4-nitrophthalic anhydride in the gaseous phase, at T = 298.15 K, were obtained by experimental thermochemistry and theoretical studies. The standard enthalpies of formation in the crystalline phase, at T = 298.15 K, were obtained by combustion calorimetry and the enthalpies of sublimation by the Knudsen method. For the theoretical calculations, a standard ab initio molecular orbital method at the G3 level was used. The enthalpies of formation in the gaseous phase were obtained from atomization and isodesmic reactions. A theoretical study of the molecular and electronic structures of these compounds was also performed. Differences of −9.7 kJ·mol−1, for 3-nitrophthalic anhydride, and −2.6 kJ·mol−1 for 4-nitrophthalic anhydride, were found from a comparison between our theoretical and experimental results. interest,15 in the obtaining of liquid crystals,16 and in the synthesis of phthalocyanines with optical properties.17 Previous research on several liquid crystal systems, in which the effect of the change of the nitro group from one position to another on the aromatic ring has been studied, has found great differences in phase behavior, that is, in the stability of the liquid crystalline phases and in the kinds of mesophases appearing.18,19 Thermochemical properties, such as the enthalpies of formation, are useful in understanding the difference between the stabilities of isomers due to the change in position of a substituent group. In addition, combining theoretical and experimental results, it is possible to find evidence of the interactions determining the relative stability of each isomer. In this work, we present the values of the enthalpies of formation obtained by experimental and theoretical methods for two isomeric species: 3NFA and 4NFA. Combustion calorimetry was used to measure standard molar energies of combustion of the solid compounds at T = 298.15 K by means of a static bomb calorimeter. The standard molar enthalpies of sublimation were found by the Knudsen−Effusion method, and they were used to calculate the standard molar enthalpies of formation in the gaseous phase, at T = 298.15 K. The theoretical studies were conducted using Gaussian-n theory, at the G3 level. From the energies determined, the standard molar enthalpies of formation for the two anhydrides

1. INTRODUCTION Obtaining standard molar enthalpies of formation of chemical compounds and relating them to molecular structure and chemical binding are some of the main objectives of thermochemistry.1−3 Furthermore, the enthalpies of formation are essential for the determination of reaction and process energies, the evaluation of reaction pathways, and the calculation of chemical equilibrium constants. The cyclic anhydrides and their derivatives are substances used as monomers or precursors of monomers for the preparation of high temperature polymers such as polyesters, polyimides, and poly(ether imide)s.4 The properties of these materials are determined by their chemical structure, morphology, and molecular orientation, which mainly depend on the structure of the monomers.5−7 The compounds studied here, 3-nitrophthalic anhydride (3NFA) and 4-nitrophthalic anhydride (4NFA), are derivatives of phthalic anhydride, and their molecular structures are shown in Figure 1. These compounds, besides being a raw material in the production of several kinds of polymers,8−12 have other applications; they are precursors, for example, in the preparation of new building blocks of possible interest in medicine,13,14 in the preparation of membranes of ecological

Received: January 13, 2014 Revised: May 7, 2014 Published: May 8, 2014

Figure 1. Structural formula of 3NFA and 4NFA. © 2014 American Chemical Society

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dx.doi.org/10.1021/jp5003929 | J. Phys. Chem. A 2014, 118, 3820−3826

The Journal of Physical Chemistry A

Article

titrimetric method, using a dissolution of NaOH(aq) 0.1 M. Energy corrections corresponding to the formation of HNO3(aq) were made, using the value of −59.7 kJ·mol−1, an accepted value for the standard molar energy of formation of 0.1 mol·dm−3 HNO3(aq).28 The apparent masses of all the substances participating in the combustion processes were measured with a ME215S Sartorius balance (accuracy: ± 0.01 mg). To make the Washburn corrections and obtain the values of the energy in standard conditions and at the temperature of 298.15 K, we used the values given in Table 1. Such corrections

in the gas phase were estimated using atomization and isodesmic reactions. The values obtained experimentally and theoretically were used in the discussion of the relative stability of these compounds.

2. EXPERIMENTAL SECTION 2.1. Materials and Purity Control. The 3NFA and 4NFA were commercial products of Sigma-Aldrich Chemical with a reported molar fraction of 0.98 and 0.92, respectively. Before the calorimetric experiments, the compounds were further purified twice by recrystallization from acetic anhydride, and they were dried under vacuum pressure at 100 °C. After purification, the molar fractions of the anhydrides were superior to 0.99. The purities, fusion temperatures, and enthalpies of fusion were measured by means of a differential scanning calorimeter (TA Instruments 2010 DSC). These properties were obtained from the analysis of the peak of fusion using the fractional fusion technique. To contain the samples, nonhermetic aluminum cells were used, and the heating was conducted in an atmosphere of dry nitrogen at constant flow.20 Before the experiments, the device was calibrated using highpurity indium to thereby obtain the calibration constant to correct the peak areas and the value of the thermal resistance to correct temperatures.21 The molar heat capacities were measured also with the DSC, using the method of “three steps” with synthetic sapphire as a reference, over the temperature interval going from 266.15 to 333.15 K.22−24 No phase transitions were observed between 298.15 K and the melting temperature of the compounds. The specific densities of the compounds were calculated by pycnometry as ρ = 1.364 g·cm−3 (3NFA) and ρ = 1.441 g·cm−3 (4NFA). 2.2. Combustion Calorimetry. The energies of combustion were determined using an isoperibolic calorimeter with a static bomb. This calorimeter has been described in a previous work.25 Its energy equivalent was found from the combustion of benzoic acid, which, under the conditions specified by the NIST certificate, has a massic energy of combustion Δcu = (−26434.0 ± 3.0) J·g−1. Seven calibration experiments were performed in oxygen at 3.04 MPa and with 1.00 cm3 of water added to the bomb. An energy equivalent εcal = 10135.1 ± 2.5 J· K−1 was obtained for the calorimeter. The uncertainty given is twice the standard deviation of the mean. The procedure used to determine the energies of combustion of 3NFA and 4NFA was the same used for the calibration experiments, namely, the solid compounds were oxidized with an excess of oxygen and with 1 cm3 of water added to the bomb. The small amount of water added prior to combustion serves to maintain the watersaturated vapor phase throughout the experiment, so that liquid water is formed in the combustion reaction and the correction to standard states dealing with the vaporization of water is minimized. This also ensures the reaction with water of the small amounts of nitrogen oxides produced by the combustion, without affecting the water vapor saturation of the gases of the bomb.26,27 The combustion bomb was flushed and filled with high purity gaseous oxygen (Airgas Co, x = 0.99999) at a pressure of 3.04 MPa. The empirical formula of our cottonthread fuse was C1.000H1.742O0.921, and it had a massic energy of combustion of −(16945.2 ± 4.2) J·g−1. To achieve the complete oxidation of the compounds, paraffin oil was used as auxiliary compound. Its specific combustion energy is Δcu° = −(46238.5 ± 6.6) J·g−1.25 The concentration of nitric acid in the final solution, after each combustion, was determined by a

Table 1. Physical Properties at T = 298.15 K compound 3NFA 4NFA benzoic acid paraffin oil cotton a b

M/g·mol−1 ρ/g·cm−3

(δu/δp)T/J·g−1·MPa−1

Cp/J·g−1·K−1

193.113 193.113 122.122

c

1.364 1.441c 1.320b

0.2 0.2 0.115b

1.16 ± 0.01c 0.91 ± 0.01c 1.21b

14.027 28.502

0.857b 1.500b

0.257b 0.289b

2.22b 1.67b

Molecular masses are based on 2009 IUPAC recommendations.31 Estimated values as in ref 32. cExperimental values.

were made according to the procedure of Hubbard et al.29 To calculate the energy change associated with the change of pressure of the compound, we used the estimated value (δu/ δp)T = −0.2 J·g−1 MPa−1 at T = 298.15 K, which is a typical value for most solid organic compounds.30 The atomic weights of the elements were those recommended by IUPAC in 2009.31 2.3. Knudsen-Effusion Method. The enthalpy of sublimation was obtained by the Knudsen effusion technique. This method enables the determination of the average number of vapor molecules that leave the cell through an effusion orifice during a given period of time when the vapor is in equilibrium with its condensed phase. The change of the mass of the sample Δm during a period of time Δt is proportional to the vapor pressure at constant temperature. Using the Clausius− Clapeyron equation and the Knudsen effusion equation,33−35 one can obtain the following equation: Δcrg Hm 1 (1) R T 1/2 where ν is(Δm/Δt)·T and ln B includes the integration constant and the term (1/Awo)(2πR/M)1/2, where A is the area of the effusion orifice, R the ideal gas constant, w0 the Clausing factor (which depends on the dimensions of the orifice), and M the molar mass.36 This equation allows the determination of the enthalpy of sublimation ΔgcrHom, for a given temperature range. The effusion apparatus used in this work has four cells, which are maintained at constant temperature. In each cell, an orifice with different diameter was used in order to verify that the hole diameter had no effect on the results. The cells are made of aluminum, and they consist of two parts, the cell body and its lid, which are attached by means of a fine-pitched screw thread. The closed cell has a height of 23 mm and a diameter of 15 mm. The lid of the cell has a hole with a diameter of 12.5 mm. A silver disk (diameter of 13.5 mm and thickness of 0.15 mm, approximately) is placed between the cell and its lid; the effusion orifice is made at the center of this silver disk. The orifices of the different cells were made with drills of different sizes. In order to ensure a perfect closing of the cell, a Teflon ring is placed at the junction of the disk and the top of the cell. ln ν = ln B −

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4. RESULTS AND DISCUSSION 4.1. Experimental Results. The results obtained by differential scanning calorimetry, that is, the purities, enthalpies, and temperatures of fusion, are shown in Table 2. The assigned uncertainties are twice the standard deviation of the mean of seven independent runs.

The cells are introduced into an aluminum block, with capacity for four cells, which is placed inside a Nylamid helmet. An O-ring is placed between the block and the helmet, and the pieces are joined by compression with screws. The temperature of the block is kept constant by recirculation of a liquid using a thermostatic circulator (LAUDA model RK 20 KS). The temperature range depends on the compound being studied. The temperature of the block is detected with a thermistor (Hart Scientific model A1143-01), previously calibrated, which generates a resistance, and its signal is received and measured by a multimeter (Agilent model 34420A) with a resolution of 10−7 Ω. The thermistor is put in the aluminum block, just in the middle of the four cells, and it is assumed that thermal equilibrium is achieved. Most pieces of the sublimation chamber are standard parts for vacuum line installations; they are made of stainless steel (VARIAN). All the connections between the chamber pieces were fitted with O-rings to ensure good performance under high vacuum conditions. With the purpose of protecting the pumping system from sample contamination, a condenser coldfinger made of Pirex glass was adapted at the top of the chamber; this coldfinger is 20 cm long and has a diameter of 3.5 cm. During the experiments, the condenser coldfinger always remains full of liquid nitrogen. The pumping system is constituted of two vacuum pumps. A mechanical pump (VARIAN model DS 102) serves as support for the starting of a turbomolecular pump (VARIAN model V70D) through which the high vacuum is reached (less than 1· 10−4 Pa). A high vacuum sensor (VARIAN525 high-vacuum cold cathode gauge) is used to follow up the pressures reached along the experiments. Pressure readings were made by a vacuum gauge controller (VARIAN SenTorr model CC2C). The test of the Knudsen effusion system was performed by using three sublimation primary standards: benzoic acid, anthracene, and ferrocene. Benzoic acid was provided by NIST, and it was used without further purification. The last two were provided by Sigma-Aldrich with a minimum mass fraction purity of 0.99 and 0.98, respectively. After further purification of these compounds by sublimation under reduced pressure, their purities, determined by differential scanning calorimetry, were of 0.9998 for anthracene and 0.9997 for ferrocene. The values obtained for the standard molar enthalpy of sublimation at T = 298.15 K were (89.43 ± 3.07) kJ·mol−1 for benzoic acid, (103.95 ± 0.94) kJ·mol−1for anthracene, and (73.61 ± 0.52) kJ· mol−1for ferrocene, in excellent agreement with literature values.37

Table 2. Purity, Molar Enthalpy, and Temperature of Fusion of Two Isomers compound

molar purity

ΔlcrH/kJ·mol−1

Tfus/K

3NFA 4NFA

0.9991 ± 0.0002 0.9952 ± 0.0014

20.30 ± 0.08 22.74 ± 0.82

434.44 ± 0.06 389.75 ± 0.08

Results for all combustions realized for both anhydrides are given in detail in Tables S1 and S2 of the Supporting Information. Table 3 shows results for a typical combustion run Table 3. Typical Combustion Experiments at T = 298.15 K m (compound)/g m (paraffin oil)/g m (cotton)/g m (platinum)/g ΔTc/K ε (calor) (−ΔTc)/kJ ε (cont) (−ΔTc)/kJ ΔUign/kJ ΔUIBP/kJ ΔUdec(HNO3)/kJ ΔUcorr/kJ (−mΔcu°)(paraffin oil)/kJ (−mΔcu°) (cotton)/kJ (−mΔcu°) (compound)/kJ Δcu°(compound)/kJ·g−1

3NFA

4NFA

0.825 11 0.231 77 0.002 27 11.515 24 2.3712 −24.0320 −0.0402 0.0042 −24.0680 0.0412 0.0146 10.7169 0.0389 13.2564 −16.0662

0.933 04 0.180 00 0.001 86 11.513 69 2.2959 −23.2694 −0.0381 0.0042 −23.3033 0.0304 0.0156 8.3231 0.0319 14.9023 −15.9718

m(compound), m(cotton), and m(paraffin oil) are the mass of compound, cotton, and paraffin oil, respectively; ΔTc is the corrected temperature rise; ε (calor) is the energy equivalent of the system; ε (cont) is the energy equivalent of the contents of the bomb: ε(cont)· (−ΔTc)) = εi(cont)·(Ti − 298.15 K) + εf(cont)·(298.15 K − Tf + ΔTcorr), ΔUign is the experimental energy of ignition, ΔUIBP is the energy change for the isothermal bomb process, ΔUdec (HNO3) is the experimental energy of formation of nitric acid, ΔUcorr is the correction to standard states, and Δcu° is the standard massic energy of combustion.

3. COMPUTATIONAL DETAILS The ab initio calculations to determine the energies of the isomers were made with the Gaussian-3 theory, which was developed by Curtiss et al.38 These authors found, when determining the enthalpies of formation for 148 compounds, a mean absolute deviation (MAD) from experimental values of 3.93 kJ·mol−1.38 However, Ruscic39 has recently pointed out that “the MAD is smaller than the 95% confidence interval by a factor of (2π)1/2”. Therefore, from the MAD obtained by Curtiss et al. for G3, this interval is ± 9.9 kJ·mol−1. The enthalpies of formation at 298.15 K were obtained from the energies calculated at 0 K by using standard thermodynamics relations and taking into account the considerations made by Radom et al.40 All the calculations were performed using Gaussian 09,41 and all the structures were visualized using the Chemcraft 1.6 program.42

for each compound. There, ΔTc is the corrected temperature rise; ΔUcorr is the correction to standard states, εcont is the heat capacity of all the contents of the bomb, ΔUign is the ignition energy, ΔUIBP is the energy change for the isothermal bomb process, and it was determined using the following equation: ΔUIBP = εcalor( −ΔTc) + εcont( −ΔTc) + ΔUign

(2)

The energy of combustion, Δcu°, at T = 298.15 K, for each experiment and each compound, the mean value, and the respective standard deviation are shown in Table 4. The standard molar energies and enthalpies of combustion, ΔcUom(cr) and ΔcHom(cr), and the standard molar enthalpies of formation of the isomers in the crystalline phase,ΔfHom(cr), at T = 298.15 K, are given in Table 5. The assigned uncertainties are, in all the cases, the expanded standard deviation and include the uncertainties in calibration and in the values of the 3822



Article o Cp,m (g)/(J·mol−1·K−1) = −4.84 × 10−7(T /K)3

Table 4. Individual Values of the Massic Energy of Combustion, at T = 298.15 K 3NFA

+ 1.25 × 10−4(T /K)2 + 5.13 × 10−1(T /K) + 19.12

4NFA

(r 2 = 0.999)

Δcu°/(kJ·g−1) −16.0662 −16.0554 −16.0456 −16.0448 −16.0563 −16.0715 −16.0602 −16.0596

−15.9718 −15.9628 −15.9631 −15.9693 −15.9590 −15.9673 −15.9540 −15.9623

⟨Δcu°⟩ (kJ·g−1)

−16.0575 ± 0.0033

o Cp,m (g)/(J·mol−1·K−1) = −4.04 × 10−7(T /K)3

+ 2.09 × 10−5(T /K)2 + 5.58 × 10−1(T /K) + 13.60 (r 2 = 0.999)

The equations of as a function of temperature for 3NFA and 4NFA were derived from the experimental results obtained by differential scanning calorimetry and are given, respectively, by the following equations:

−15.9637 ± 0.0020

o Cp,m (cr)/(J ·mol−1· K−1) = (3.68 ± 0.51) × 10−4(T /K)3

− (3.44 ± 0.47) × 10−1(T /K)2 + (1.08 ± 0.15)

Table 5. Derived Standard (P° = 0.1 MPa) Molar Values in the Crystalline Phase at T = 298.15 K compound

ΔcUom(cr)/kJ·mol−1

ΔcHom(cr)/kJ·mol−1

ΔfHom(cr)/kJ·mol−1

3NFA 4NFA

−3100.9 ± 1.8 −3082.8 ± 1.7

−3095.3 ± 1.8 −3077.2 ± 1.7

−481.5 ± 2.1 −499.60 ± 2.0

× 102(T /K) − (1.10 ± 0.15) × 104

(r 2 = 0.997) (6)

o Cp,m (cr)/(J ·mol−1· K−1) = (2.12 ± 0.27) × 10−3(T /K)3

− (1.95 ± 0.25)(T /K)2 + (5.98 ± 0.77) × 102(T /K)

The uncertainty assigned corresponds to the expanded uncertainty.

− (6.10 ± 0.79) × 104

(r 2 = 0.994)

(7)

The standard molar enthalpies of sublimation and formation in the crystalline and gaseous states, at T = 298.15 K, are summarized in Table 7. The uncertainty is the expanded

43−46

energies of the auxiliaries used. In the calculation of ΔfHom(cr) from ΔcHom(cr), the standard molar enthalpies of formation of H2O(l) and CO2(g), at T = 298.15 K, were taken respectively as −(285.83 ± 0.04) kJ·mol−1and −(393.51 ± 0.13) kJ·mol−1.47 Detailed results of the Knudsen-effusion experiments for 3NFA and 4NFA are given in Table S3, Figure S1, and Figure S2 of the Supporting Information. Using the least-squares method, eq 1 was applied to calculate the enthalpy of sublimation. The enthalpy of sublimation at mean temperature, ΔgcrHm(Tm), is the weighted average of the set of data given in Table S3 and the uncertainty is the standard deviation of the mean.45,48 These values are shown in Table 6. The standard molar enthalpies of sublimation at T = 298.15 K (Table 6) were calculated by Kirchoff’s law:

Table 7. Enthalpy of Sublimation and Standard (P° = 0.1 MPa) Molar Enthalpies compound

ΔfHom(cr)/kJ·mol−1

ΔgcrHom/kJ·mol−1

ΔfHom(g)/kJ·mol−1

3NFA 4NFA

−481.5 ± 2.1 −499.6 ± 2.0

100.4 ± 3.5 103.6 ± 5.9

−381.1 ± 4.1 −396.0 ± 6.2

The assigned uncertainty corresponds to the expanded uncertainty with a level of confidence of approximately 95%.

uncertainty and includes the uncertainty in the experimental capacities. We did not find values for the enthalpies of formation of 3NFA and 4NFA in the literature, and it was not possible to make a comparison. 4.2. Molecular and Electronic Structures. Reports on crystallographic studies or the molecular structures in the gas phase for the two isomers studied here were not found in the literature. The molecular structures of 3NFA and 4NFA were optimized using the MP2(full)/6-31G(3df,2p) level of theory. The structures are shown in Figure 2. The values of distances and angles are given in Table S4 of the Supporting Information. 4NFA shows a planar structure, with an oxygen atom of the nitro group (O14) at a distance of 2.38 Å from a hydrogen of the aromatic ring (H16). In contrast, the dihedral angle of the

Tm

o dT ∫298.15K ΔCp,m

(3) o ΔCp,m

(5)

Cop,m(cr)

The uncertainty assigned corresponds to the standard deviation of the mean.

Δcrg Hmo(T = 298.15 K) = Δcrg Hmo(Tm) −

(4)

o o Cp,m (g) − Cp,m (cr). The o Cp,m(g) on temperature for

where is the difference equations for the dependence of 3NFA and 4NFA were obtained from vibrational frequencies calculated using density functional theory with the B3LYP density functional and the 6-311G++** basis set. These relations are given, respectively, by the following equations:

Table 6. Mean Experimental Temperature, Standard (P° = 0.1 MPa) Molar Enthalpies of Sublimation, at Mean Experimental Temperature and T = 298.15 K compound

no. exp.

Tm/K

ΔgcrHm(Tm)a/kJ·mol−1

ΔgcrHom(T = 298.15 K)b/kJ·mol−1

3NFA 4NFA

8 8

360.7 351.3

96.6 ± 1.7 101.4 ± 2.9

100.4 ± 3.5 103.6 ± 5.9

a

The assigned uncertainty is the standard deviation of the mean. bThe assigned uncertainty is the expanded uncertainty with a level of confidence of approximately 95%. 3823



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frequencies below 260 cm−1. With this consideration and using thermodynamic relations, the difference between the enthalpies at 298.15 and 0 K was calculated considering the vibrational, rotational, translational, and PV terms.40,55 The theoretical enthalpies of formation in the gas phase were obtained using the energies calculated by Gaussian 3, and atomization and isodesmic reactions,54−57 as proposed by Raghavarchari et al.56 The isodesmic reactions used in this work are the following: 3‐ or 4‐NFA + ethene + methane → benzene + maleic anhydride + nitromethane Figure 2. Optimized structures of 3NFA and 4NFA at the MP2(full)/ 6-31G(3df,2p) level of theory.

(i)

3‐ or 4‐NFA + methane → phthalic anhydride + nitromethane

o

nitro group in 3NFA is 45.7 (O14−N12−C3−C2). Partial optimization of 3NFA with this dihedral angle fixed at 0.0 o leads to a more unstable molecular structure. These geometrical features suggest the presence of intramolecular interactions. In order to provide even more evidence for the existence of these intramolecular interactions, we performed a more detailed analysis using natural bond orbital (NBO) analysis.49−53 This shows that a 4NFA conformer has a n O14 → σ* H16C5 intramolecular donor−acceptor interaction, where electron density from the lone pair of the oxygen of the nitro group delocalizes into the unfilled σ*H16C5 antibonding orbital of a hydrogen on the aromatic ring. For 3NFA, the NBO method shows nO14 ↔ nO11 steric repulsion (Figure 3).

(ii)

3‐ or 4‐NFA + ethane + methane → benzene + succinic anhydride + nitromethane

(iii)

3‐ or 4‐NFA + 8 methane → 3 ethene + dimethyl ether + 2 acetone (iv)

+ nitroethane

The values of the standard enthalpy of formation of the compounds considered in the isodesmic reactions were obtained from literature.58 Table 8 shows the experimental and theoretical enthalpies of formation obtained in this work. It may be observed that the molar enthalpies of formation obtained by atomization and isodesmic reactions are in good agreement with the experimental values. The smallest deviations from experiment were −9.7 kJ·mol−1for 3NFA and −2.6 kJ·mol−1for 4NFA; they were obtained using isodesmic reaction iii. 4.4. Enthalpic Increments and Correlations. Using the experimental values of enthalpy obtained, it is possible to carry out an analysis of the enthalpic differences existent between the two isomers. This is shown in Figure 4. The enthalpic increments for the change from position 3 to 4 are −18.1 kJ· mol−1, in the crystalline phase, and −14.9 kJ·mol−1, in the gas phase. This suggests that the nitro group in position 4 produces a slightly larger stability than in position 3, in both phases. The result for the gas phase is supported by the above discussion by NBO analysis. That is, the difference found between the two anhydride isomers (enthalpy of isomerization) may be explained by the steric repulsion (nO14↔nO11) for 3NFA.

Figure 3. NBO orbital interactions in (a) 3NFA and (b) 4NFA.

4.3. Theoretical Results. The energies, calculated by G3 at 0 K, for 3NFA and 4NFA are shown in Table S5 of the Supporting Information. The enthalpy values at 298.15 K were calculated as suggested by Radom and co-workers,40 who handled them as free rotors to the internal rotations with

Table 8. G3 Calculated Enthalpies of Formation for 3NFA and 4NGA in the Gas Phase,a both from Atomization and from Isodesmic Reactionsb ΔfHom(g) G3

a

compound

atomization

3NFA

−370.5(−10.6)

4NFA

−392.5(−3.5)

isodesmic reaction i ii iii iv i ii iii iv

−368.4 −357.4 −371.4 −366.6 −390.4 −379.4 −393.4 −388.6

exp. (−12.7) (−23.7) (−9.7) (−14.5) (−5.6) (−16.6) (−2.6) (−7.4)

−381.1 ± 4.1

−396.0 ± 6.2

All values in kJ·mol−1. bValues in parentheses are the differences between experimental and calculated values. 3824



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ASSOCIATED CONTENT

S Supporting Information *

Tables S1 and S2 show the experimental values of all experiments of combustion, for 3- and 4- nitrophthalic anhydrides. Table S3 registers the results of sublimation experiments for both anhydrides. Table S4 gives the distances and angles of bond of the molecular structures optimized. Table S5 shows the G3 calculated energies at 0 K and enthalpies at 298.15 K, for both anhydrides and other compounds used in isodesmic reactions. This material is available free of charge via the Internet at http://pubs.acs.org

Figure 4. Enthalpic differences due to the nitro-group position for 3NFA and 4NFA. (a) Experimental enthalpy of formation in the crystalline phase in kJ·mol−1; (b) experimental enthalpy of formation in the gas phase in kJ·mol−1.

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Therefore, the 4-isomer is more stable than the 3-isomer in both phases. Using the experimental enthalpies of formation obtained in gas phase, it is also possible to make a comparison with analogous compounds. The enthalpy difference between 3NFA and phthalic anhydride (ΔfHom(g) = −(371.4 ± 1.9) kJ· mol−1)58 is −(9.7 ± 4.5) kJ·mol−1. The corresponding difference between the enthalpies of formation for 4NFA and phthalic anhydride is −(24.6 ± 6.5 kJ·mol−1). On the other hand, the difference between the enthalpies of formation of benzene (ΔfHom(g) = (82.6 ± 0.7) kJ·mol−1) and nitrobenzene (ΔfHom(g) = (67.5 ± 0.5) kJ·mol−1) is −(15.1 ± 0.9 kJ· mol−1).58 This enthalpic increment is close to the mean of the enthalpic increments (−(17.2 ± 7.9) kJ·mol−1) obtained from the comparison between the isomers studied and the phallic anhydride. These comparatives are shown in Figure 5.

AUTHOR INFORMATION

Corresponding Author

*Phone: (52222)2295500, Ext. 7388; E-mail: maria.amador@ correo.buap.mx. Present Address

́ ́ y FarmUnidad Académica de Ciencias Quimico-Biologi cas aceutica, Universidad Autónoma de Nayarit, Boulevard TepixXalisco s/n, C.P. 63155, Ciudad de la Cultura “Amado Nervo”, tepic, Nayarit, México. †

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the VIEP-BUAP for financial support through Project AMRM-NAT13-I. One of the authors (M.A.G.C.) thanks the CONACyT (México) for a scholarship (Registration Number 200481).

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REFERENCES

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Figure 5. Enthalpy differences between 3NFA, 4NFA, and phthalic anhydride, their isomerization enthalpy, and a comparative with the analogous substituted benzene. All values of ΔΔfH°m(g) are in kJ· mol−1.

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CONCLUSIONS A computational and experimental thermochemical study of 3NFA and 4NFA was presented in this work. The experimental molar standard enthalpies of formation obtained for the crystalline and gaseous phases showed that 4-nitrophtalic anhydride is stabler than its isomer 3- nitrophtalic anhydride. Enthalpic increments of about −18.1 kJ·mol−1, in the crystalline phase, and −14.9 kJ·mol−1, in the gas phase, were found. This is supported by results from the study of the molecular and electronic structures and by a NBO analysis. The estimated values of the standard molar enthalpies of formation in the gas phase for the two compounds show that the atomization and the isodesmic reactions producing succinic anhydride (reaction iii) gave values for the enthalpies of formation closer to the experimental values. 3825



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Experimental and Computational Thermochemistry of 3-and 4

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