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Experimental and Theoretical Thermochemistry of the Isomers: 3- and 4-Nitrophthalimide Karina Salas, Patricia Amador, Aarón Rojas, Francisco J. Melendez, and Henoc Flores J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b02508 • Publication Date (Web): 03 Jul 2017 Downloaded from http://pubs.acs.org on July 4, 2017

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The Journal of Physical Chemistry

Experimental and Theoretical Thermochemistry of the Isomers: 3- and 4Nitrophthalimide Karina Salas-López,1 Patricia Amador,1* Aarón Rojas, 2Francisco Javier Melendez,1 Henoc Flores1

1

Facultad de Ciencias Químicas de la Benemérita Universidad Autónoma de Puebla, 14 Sur

y Av. San Claudio, C.P. 72570, Puebla, Pue, México 2

Departamento de Química, Centro de Investigación y de Estudios Avanzados del IPN, Av.

Instituto Politécnico Nacional 2508, C.P. 072360, México, México

ACS Paragon Plus Environment


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Abstract This work presents a thermochemical study of two derivatives of phthalimide: the isomers 3-nitrophthalimide and 4-nitrophthalimide. The enthalpies of formation for these compounds in the solid phase were obtained by combustion calorimetry. Using thermogravimetry technique, the enthalpies of vaporization were obtained. The enthalpies of sublimation were calculated from enthalpies of fusion and vaporization respective. From experimental data and by ab initio methods, the enthalpies of formation in the gas phase were calculated. With these results, it was possible to determine their relative stability, and it was found that 4-nitrophthalimide is more stable than its isomer 3nitrophthalimide. This tendency is similar to that of 3-nitrophthalic anhydride and 4nitrophthalic anhydride, as reported in a previous work by our research group. The enthalpy of isomerization was also obtained, and a good correlation with that of phthalic anhydride derivatives was found. Finally, with the values obtained, the enthalpic difference resulting when the imide group is substituted by an anhydride group was determined.


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1. Introduction Phthalimide and its derivatives form an interesting group of compounds, which have diverse applications in several areas. For example, in recent years, research groups have synthesized phthalimide derivatives with anti-inflammatory, analgesic, and antiviral activity;1-5 these compounds are also used as organocatalyst in solvent-free reactions.6 However, their major potential is as precursors in the synthesis of polymers with different characteristics and properties.7 Some of these polymers have antimicrobial activity,8 photovoltaic properties for manufacturing solar cells,9,10 or other diverse properties.11-13 In particular, the isomers studied in the present work, 3- and 4-nitrophthalimide (see their molecular structures in Figure 1), have shown biological properties such as herbicidal, antibacterial,14,15 anxiolytical, and antimicrobial activity.16-18. Also, they are raw materials for the development of new drugs,19,20 as aminephthalocyanines, with antibacterial properties.19 In the materials area, these compounds are precursors in the synthesis of polymers with high heat resistance,21 with applications in photolithography,22 as colorants, 23,24

or polymers with potential for the production of proton exchange (or polymer

electrolyte) fuel cells (PEMFCs).25 Thermochemical studies of phthalimide and N-substituted phthalimides have been carried out by other authors. There are three reports about the standard molar enthalpy of formation in the crystalline phase of phthalimide.26- 28 The last of these reports is of Ribeiro et al., who studied, in addition to phthalimide, three N-alkylphthalimides.28 In two other works, Ribeiro et al. reported thermochemical studies of N-phenyl and N-chloro and bromo alkyl substituted phthalimides.29,30 Roux et al.31 studied the aromaticity of Nmethyl-1,8-naphthalimide, which has a chemical structure similar to that of phthalimide,



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and determined its enthalpy of formation, We did not find other experimental thermochemical works on phthalimides. Despite the importance of these 3- y 4- nitrophthalimide isomers, especially in the polymer industry, there are no reports about its thermochemical properties, which are essential for the thermodynamic study of reactions in which these compounds participate. Furthermore, the phthalimides are compounds strongly related to derivatives of phthalic anhydride. These two compound families are involved in several reactions where the anhydrides are transformed to phthalimide.32-35 By this reason, our research group is studying, from a thermochemical point of view, derivatives of phthalic anhydride and of phthalimide. Besides, knowledge of the thermochemical properties allows us to find the enthalpic change due to the replacement of the oxygen heteroatom by nitrogen, and in the case of isomers, it is possible to determine their relative stabilities.36-38

3NFT

4NFT

Figure 1. Chemical structures of 3-nitrophthalimide (3NFT) and 4-nitrophthalimide (4NFT).

In this work, we report the standard molar enthalpies of formation of 3-nitrophthalimide (3NFT) and 4-nitrophthalimide (4NFT) in the solid and gas phases. The enthalpies of formation in the solid phase were determined by combustion calorimetry, using an isoperibolic calorimeter with a static bomb. The enthalpies of fusion were obtained by differential scanning calorimetry (DSC) and the enthalpies of vaporization by thermogravimetry (TG). From enthalpies of fusion and vaporization, the enthalpies of


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sublimation were obtained. To find the enthalpy of formation in the gas phase, the enthalpy of formation in the solid phase and the enthalpy of sublimation, of each compound, were used. The enthalpies of formation in the gas phase were also theoretically determined.

2. Experimental Section 2.1. Materials and purity control. The compounds studied are commercially supplied by Sigma-Aldrich. The mole fractions reported by the provider were 0.97 and greater than 0.98, for 3NFT and 4NFT, respectively. The purity of these compounds was analyzed by DSC using the fractional melting technique.39 A Perkin-Elmer DSC 8000 and a TA Instruments Q2000 differential scanning calorimeters, both previously calibrated for temperature and heat flow, were used. The thermogram obtained by DSC showed that 4NFT had high purity, and this was corroborated by HPLC analysis. In the case of 3NFT, the compound was subjected to a heat treatment, which consisted of heating to 460 K under a nitrogen atmosphere. Table 1 gives the source and purity of the compounds studied and of the standard compounds used. TABLE 1. Source and purity of compounds used in this work. Compound

CAS

Source

3NFT

603-62-3

Sigma-Aldrich

Reported mole fraction purity 0.97

4NFT

89-40-7

Sigma-Aldrich

>0.98

Indium

7440-74-6

NIST

0.999999

Aluminium oxide

1344-28-1

NIST

0.9995

Benzoic acid

65-85-0

NIST

0.999996

Pyrene

129-00-0

Fluka

 0.99

Purification method

Final mole fraction purity

Heating under N2 (g)

0.9999 ± 0.0001

Method used to obtain purity or composition DSC

0.9988 ± 0.104

DSC, HPLC

0.9996 ± 0.0003

DSC

Sublimation



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The same two calorimeters were also used to determine the temperatures and enthalpies of fusion. The experiments were performed under nitrogen flow to prevent the sample from decomposing. The temperature ranges were from 423.2 K to 503.2 K, for 3NFT, and from 463.2 K to 483.2 K, for 4NFT, at a heating rate of 1.0 K∙min-1, for both compounds, with a nitrogen flow of 20.0 cm3·min-1. To obtain the heat capacities of the two compounds, the TA Instruments Q2000 calorimeter was used (which was previously calibrated for temperature and heat flow with indium and aluminium oxide standards, respectively). The experimental conditions were the following: nitrogen flow of 50.0 cm3∙min-1; heating rate of 10.0 K∙min-1; temperature range, for 4NFT, from 283.2 K to 443.2 K and, for 3NFT, from 283.2 K to 443.2 K.

2.2. Combustion calorimetry. Due to the available amount of each compound, two static bomb calorimeters were used, a semi-micro combustion bomb for 3NFT and a conventional combustion bomb for 4NFT. The methodology has been described in previous works.40,41 To determine the calorimeter energy equivalents, benzoic acid, whose combustion energy is Δcu = – (26434.0 ± 3.0) J·g−1, was used, under the conditions mentioned in the NIST certificate. Seven calibration runs were performed for the conventional combustion bomb calorimeter and six for the semi-micro combustion bomb calorimeter. In both cases, benzoic acid is oxidized under a pressure of 3.04 MPa, with 1.00 cm3 and 0.10 cm3 of water added to the conventional bomb and the semi-micro bomb, respectively. The energy equivalent for the conventional bomb calorimeter is ε(calor) = (10135.1 ± 2.5) J·K−1 and for the semi-micro bomb calorimeter is ε(calor)= (1281.4 ± 0.8) J·K−1. The uncertainties associated to these quantities are the standard deviation of the mean of at least six calibration runs.


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The combustion experiments for each compound were performed under the same conditions as the calibration runs for the respective calorimeters. Since the 3NFT exhibits polymorphism, it was necessary to perform the above-described heat treatment, to ensure that the combustion energy determined, corresponds to only one of the polymorphs, this is, to the majority crystalline phase. In all experiments, a cotton thread fuse was used. This cotton is well characterized, its empirical formula is C1.000H1.742O0.921, and its energy of combustion is Δcu = – (16945.2 ± 4.2) J·g−1 (the uncertainty is the standard deviation of the mean). 42,43 High purity (x = 0.99999) oxygen, supplied by Airgas Co., was used. The quantity of nitric acid after each combustion, was determined by titration; its energetic contribution was calculated from molar energy of formation of HNO3 (aq, 0.1 mol·dm-3), –59.7 kJ·mol−1,44 value corresponding to the formation of the acid from N2(g), O2(g) and H2O(l). The values used in this work for the physical properties of the compounds are shown in Table 2.

TABLE 2. Values used in this work for the physical properties of the compounds.

a

a

M

compound

g∙mol

-1

ρ g∙cm-3

J·g-1 ∙MPa-1

(δu/δp)T

3NFT

192.139

1.705b

0.2

4NFT

192.139

1.716b

0.2

benzoic acid

122.129

1.32c

0.115c

cotton

28.504

1.50c

0.289c

Molecular masses are based on the 2011 IUPAC recommendations45

b

Taken from reference 46.

c

Estimated values as in reference 47.



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2.3. Thermogravimetry. The indirect method of thermogravimetry (TG) was used to determine the enthalpy of sublimation. Price and Hawkins48 demonstrated that, using TG, g

it is possible to determine enthalpies of phase changes (vaporization, ∆l H, or sublimation ∆gcr H). Such a method is based on the application of the Langmuir equation, 49 which relates the velocity of mass loss and the vapor pressure. This equation may be written as dm 1

-

dt

M

( ) = p∙α ( A

1/2

) ,

(1)

2πRT

where dm/dt is the rate of mass loss, A is the area of vaporization, p is the vapor pressure of the sample at temperature T, R is the universal gas constant, M is the molar mass of the substance and α is the coefficient of vaporization, which equals unity for vacuum or for molecules with a high molecular weight. From another point of view, this equation can be ordered in two terms as shown in equation 2, where can see that the vapor pressure is proportional to υ. p = k ∙υ

(2)

where υ=(1⁄A)∙(dm⁄dt)∙(T⁄M)1/2 and .𝑘 = 2𝜋𝑅

1⁄2

⁄α .

If equation (2) is substituted in the Clausius-Clapeyron equation, we get:49 𝑑ln(𝑘∙υ) 𝑑𝑇

𝛽

∆ 𝐻

= 𝑅𝛼𝑇 2

(3)

Integrating equation (3), is obtained equation (4), that may be used to find the enthalpy of phase change: ln υ = C -

β

∆α H 1 R

∙T

(4)

where C is a constant, which includes integration constant and the term k.


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If the mass loss occurs at a temperature lower than the melting temperature, then the enthalpy of sublimation is determined; if it occurs at a temperature higher than the melting temperature, then the enthalpy of vaporization is determined. In the current work, this last enthalpy was determined for the two compounds under study. The thermogravimetric analysis was carried out using a simultaneous DSC-TG analyzer, a TA Instruments Q600 SDT simultaneous thermal analyzer, which has a thermobalance with a sensitivity of 0.1 μg. The sample pans used are of platinum with an area of 2.16 ∙ 10-5 m2, and the temperature controller has an accuracy of ± 1.0 K. This device was previously calibrated for mass and temperature. For calibrating in mass a traceable to NIST standard mass of (315.1620 ± 0.0048) mg was used. The temperature calibration involved the melting of a SRM 2232 NIST indium sample with melting temperature equal to (429.7485 ± 0.00034) K. The heating rate for the calibration runs was of 10.0 K∙min-1 and they were made under a nitrogen flow of 100.0 cm3∙min-1. For measuring experiments masses of 10 to 18 mg were used; while the heating rate and the nitrogen flow were the same as in the calibration runs. For the validation of the method, pyrene was used as a secondary standard because in addition to its high stability and purity, its vapor pressure values are well known over a wide temperature range.50-53 The result obtained for this substance was ∆gcr 𝐻m (298.15 K) = (101.1 ± 0.6) kJ·mol−1 (the uncertainty corresponds to the combined uncertainty) at T = 298.15 K. This value is in good agreement with that found in the literature: ∆gcr 𝐻m ( (298.15 K) = (100.2 ± 3.6) kJ·mol-1.54



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3. Computational Chemistry The energy of each isomers was calculated by ab initio methods using Gaussian-n theory at the G4 level. This theory was assessed for the calculation of energies by Curtiss et al. (2007) using a set of 454 experimental energy values. The mean absolute deviation (MAD), reported by these authors, was of 3.47 kJ·mol-1. 55 However, according to Ruscic, 56

“the MAD is smaller than the 95% confidence interval by a factor of (2π)1/2”.

Therefore, considering this, and the MAD obtained by Curtiss et al. for G4, the 95% confidence interval will be ± 8.7 kJ·mol-1. The most stable structures for 3NFT and 4NFT, were determined with the MP2 (Full) level of theory,57 using the more extended Pople basis set, 6-311++G(3df,3pd).58 The charge distribution in the structures was studied by the natural bond orbital (NBO) analysis59 with Density Functional Theory (DFT) at B3LYP/6-311++G(3df,3pd) theory level using the Gaussian 09 package.60 The structures and the NBO analysis were visualized with the GaussView 5.0.8 graphical application.61 The heat capacity values were calculated using the real vibrational frequencies for the minimum-energy structures in the temperature range 295 K - 450 K at the B3LYP/6311++G(3df,3pd) theory level.62,63 The methodology implemented in the Gaussian09 package, which is known as an adequate approach for a wide range of chemical systems, was used.60 On the basis that enthalpy is a state function, atomization and isodesmic reactions64 were used to calculate the standard enthalpy of formation in the gas phase at T = 298.15 K, from the energy calculated by ab initio methods. For the atomization reactions, the energies at 298.15 K were calculated from energies at 0 K taking into account the


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corrections suggested by Nicolaides et al.65 , that is, “treating internal rotations with frequencies below 260 cm-1 as free rotors” and applying the scaling factor of 0.9854 to obtain the zero-point values at the G4 level.60,66 4. Results and discussion 4.1 Purity of compounds. The purity of the commercial 4NFT was obtained by DSC analysis, using the fractional fusion technique. The results showed an impurities around 0.001 (see Figure S1 in the supplementary information). Also the purity for this compound, was corroborated by HPLC analysis (Figure S2). In the case of 3NFT, the thermogram showed two endothermal peaks, a small one at a temperature around 455 K and a large one (the main peak) at around 495 K. When the same sample was subjected to a second heating DSC scan, the smallest endothermal peak disappeared. Since, during all the process, the mass of the sample remained constant, it was inferred that the peak disappearance was due to a crystalline transition, this means that the 3NFT possibly exhibits polymorphism. Several experiments were performed to verify that the compound, after the heat treatment, only exhibited a peak in the DSC thermogram. In Figure 2 is shown a comparison between commercial sample diffractogram (without heat treatment) with the calculated powder diffraction pattern (λ = 1.54 Å) based on the single-crystal refinement for 3nitrophthalimide published by Glidewell et al.,46 deposited in the CSD with Refcode MAJTEX. The spectrum has been calculated using Mercury.67 The difractogram of the commercial source was obtained with a Bruker D8 Discover Diffractometer X-Ray. It can be seen that there is a correspondence between the two diffractograms.



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a)

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b)

Figure 2. X-ray powder diffractogram a) calculated on the base of the single-crystal structure and b) obtained experimentally in this work, from commercial 3NFT sample.

In Figure 3 the DSC thermograms of 3NFT and their respective DRX, before and after the thermal treatment, are shown. It can be seen that after the treatment, the endotherm at 464.39 K had disappeared and that the diffractogram correspond to a more symmetric structure. It is important to emphasize that all the experimental studies realized to the 3NFT were made using samples thermally treated thermally. Table 3 shows the molar fraction and the properties determined by DSC for 3NFT and 4NFT. For each compound, five experiments were performed. The results of all the experiments are shown in Table S1 in the supplementary information.

b)

a)


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d)

c)

Figure 3. a) DSC thermogram of 3NFT before heat treatment and b) its X-ray powder diffractogram, c) DSC thermogram of 3NFT after heat treatment and d) its X-ray powder diffractogram.

TABLE 3. Specific heat, melting temperature, and enthalpy of melting for both compounds.

a

𝑐𝑝

a

Tfus K

∆lcr 𝐻 o

compound

J∙g−1 ∙K−1

3NFT

1.157 ± 0.225

491.00 ± 0.32

25.45 ± 0.35

4NFT

1.039 ± 0.224

473.73 ± 0.39

28.58 ± 0.43

kJ∙mol-1

Value at 298.15 K..

The uncertainties are twice the overall standard deviation of the mean, and include the contributions from the calibration and u(T)=0.1 K. The experiments were realize under average atmospheric pressure (78.8 kPa), u(P)= 1 kPa.

The heat capacities in the solid phase were determined in the temperature ranges 298.15 K to 435.15 K, for 3NFT, and 298.15 K to 442.15 K, for 4NFT. From the individual values, equations for the heat capacities as functions of temperature, were obtained. These are equations 5 and 6, given below, for 3NFT and 4NFT, respectively. The mean values (of three experiments) of the heat capacity at different temperatures for the two isomers are shown in Tables S2 and S3 in the supplementary information.



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Cp,m(cr)⁄(J∙mol-1 ∙K-1 )= − (7.7324 ± 1.2765 )∙10-8 (T⁄K)4 + (21.1886 ± 0.1382) ∙10-4 (T⁄K)3 − (6.8209 ± 0.0.4694)∙10-2 (T⁄K)2 + (1.7947 ± 0.0238)∙101 (T⁄K) − 1.6046 ∙ 103 (r2 =0.9999)

(5)

Cp,m(cr)⁄(J∙mol-1 ∙K-1 )= − (2.2520 ± 0.0063)∙10-7 (T⁄K)4 + (3.3075 ± 0.0699) ∙10-4 (T⁄K)3 − (1.8107 ± 0.0257)∙10-1 (T⁄K)2 + (4.4160 ± 0.0313) (T⁄K) ∙ 101 − 3.8579 ∙ 103

(𝑟 2 =0.9994)

(6)

From the values obtained by combustion calorimetry, the energy of combustion ΔUIBP for the process under isothermal conditions at 298.15 K, was calculated using the following equation: ΔU

  (calor)

IBP

T i

- T f   T corr

   i (cont)

T i

- 298 . 15    (cont) f

 298

. 15  T f   T corr



U

ign

(7)

where Ti and Tf are the initial and final temperatures; Tcorr is the temperature correction for non adiabaticity;  (cont) i

and

 (calor)

 (cont) f

is the energy equivalent of the calorimeter;

are the calorimetric energy equivalents of the initial and final

substances, respectively. In each experiment, the energy of ignition, ΔUign, was 0.0042 kJ. The energy to standard conditions (0.1 MPa), was determined by the equation Δ cU

 m

( 298.15

K )  ΔU

IBP

 ΔU

corr

(8)

where ΔUcorr are the Washburn corrections (see supporting information for details). Table 4 shows representative experimental data related to the combustion experiments for 3NFT and 4NFT. The values of the specific energies of combustion from all the experiments for the two compounds, are given in Tables S4 and S5 of the supplementary information.


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TABLE 4. Experimental values of the energy of combustion of 3NFT and 4NFT at T=298.15 K (po=0.1 MPa). 3NFT

4NFT

m (C8H4N2O4)/g

0.046440

1.10300

m (cotton)

0.000537

0.00190

m (platinum)/g

0.230959

11.50974

ΔTc/K

0.6546

1.9245

(calor) (ΔTc)/kJ

0.8388

19.5051

(cont) (ΔTc)/kJ

0.0008

0.0284

ΔUign/kJ

0.0042

0.0042

UIBP/kJ

-0.8354

-19.5293

U (HNO3) /kJ

-0.0029

-0.0525

Ucorr/kJ

0.0008

0.0088

(-mcu°) (cotton)/kJ

0.0092

0.0325

(-mcu°) (C8H4N2O4)/kJ

0.8225

19.4355

 cu° (C8H4N2O4)/kJ∙g-1

-17.7104

-17.6206

m (C8H4N2O4), m (cotton) and m (platinum) are the mass of the compound, cotton and platinum respectively, ΔTc is the temperature increment corrected for adiabatic condition, ε(calor) is the equivalent calorimeter of system, ε(cont) is the equivalent content calorimetric pump: ε(cont.)(∆Tc) = εi (cont.)( 298.15 K - Ti) + εf(cont.)( Tf -298.15 K - ∆Tcorr). ΔUign is the experimental ignition energy, ΔUIBP is the change energy for isothermal bomb process, U (HNO3) is the energy correction for the nitric acid formation, ΔUcorr is the correction to standard state and cu° is the specific energy of combustion (of cotton and C8H4N2O4, respectively).

Using the molar standard energies of combustion, ΔcU°m, it is possible to determine the standard enthalpies of combustion from the equation: ΔcH°m = ΔcU°m + Δ(g) RT,

(9)



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where R is the universal gas constant, T is the temperature, and Δ (g) is the difference between the stoichiometric coefficients of the gaseous products and reagents in the following idealized combustion reaction: C8H4N2O4 (cr) + 7 O2 (g) = 8 CO2 (g) + 2 H2O (l) + N2 (g)

(10)

To calculate ΔfH°m (cr) for the compounds, their ΔcH°m and the enthalpy of formation of the products of the combustion reaction were used; these values were taken from the literature as – (285.83 ± 0.04) kJ·mol−1, for H2O (l), and – (393.51 ± 0.13) kJ·mol−1, for CO2 (g) (the uncertainties are the standard deviation of mean).68 The values obtained are shown in Table 5 and its uncertainties were calculated considering the contributions of all the values involved in the calculation; this gives the combined uncertainty.

TABLE 5. Standard molar energies and enthalpies of combustion, and enthalpies of formation at T=298.15 K for the isomers, in condensed phase. ∆c Uom (cr)

∆c Hom (cr)

∆f Hom (cr)

kJ∙mol-1

kJ∙mol-1

kJ∙mol-1

3NFT

-3399.1± 5.6

-3394.1 ± 5.6

-325.6 ± 6.0

4NFT

-3385.8 ± 1.6

-3380.8 ± 1.6

-338.9 ± 2.6

compound

The uncertainties correspond to the expanded uncertainty with confidence level of 95 %, including calibration contributions with benzoic acid, energy of combustion of cotton. For ∆f Hom (cr), are included the uncertainties of standard enthalpy of formation of H2O and CO2, too.

Using thermogravimetry, the variation of mass as a function of temperature was obtained. From the values obtained by this technique it was possible to determine the rate of mass loss or weight derivative (dm/dt). Mass loss is considerable for temperatures higher than the melting temperature and up to 580 K for both compounds; this indicates that the


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compounds are vaporizing, rather than subliming (the thermograms for two compounds can be seen in Figures S3 and S4 of supplementary information). Thus, the enthalpy of phase change determined was the enthalpy of vaporization at mean temperature (Tm). The analysis was carried out in the temperature range 510 K to 520 K, with increments of 1 K. The values obtained by thermogravimetry are listed in Tables 6 and 7 for both compounds. Also, all the data of the thermogravimetry experiments are given in Tables S7 and S8 (supplementary information).

TABLE 6. Summary of the thermogravimetry experimental series for 3NFT g

series

Equation

r2

σm

σy

∆l Hm (515 K)

1

ln υ = 16.26 - 10,580.94/T

0.9977

168.94

0.33

88.0 ± 1.4

2

ln υ = 16.66 - 10,802.06/T

0.9985

139.16

0.27

89.8 ± 1.2

3

ln υ = 17.09 - 11,017.57/T

0.9992

104.93

0.20

91.6 ± 0.9

4

ln υ = 16.66 – 10,889.32/T

0.9987

130.69

0.25

90.5 ± 1.1

kJ∙mol-1

g

Weighted average value = (90.4 ± 2.2) kJ∙mol-1 Here, m and y represent the standard deviation of the slope and the intercept, respectively. The uncertainty associated to each enthalpy of vaporization corresponds to σi=m∙R, where R is the universal gas constant (8.31410-3 kJK-1). The weighted average value (μ) and its standard deviation (σ) were calculated as μ = Σ(x i/σi2)/ Σ(1/σi2) and σ2 = N[1/Σ(1/σi2)], where xi is each one of the N enthalpy of vaporization data, and σi is its respective standard deviation. The uncertainty presented correspond to twice σ.



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TABLE 7. Summary of the thermogravimetry experimental series for 4NFT g

series

Equation

r2

σm

σy

∆l Hm (515 K)

1

ln υ = 16.87 - 10,544.71/T

0.9994

86.25

0.17

87.7 ± 0.7

2

ln υ = 16.87 - 10,526.88/T

0.9996

73.49

0.14

87.5 ± 0.6

3

ln υ = 17.12 - 10,653.72/T

0.9989

117.8

0.23

88.6 ± 1.0

kJ∙mol-1

g

Weighted average value =( 87.8 ± 1.4) kJ∙mol-1 Here, m and y represent the standard deviation of the slope and the intercept, respectively. The uncertainty associated to each enthalpy of vaporization corresponds to σi=m∙R, where R is the universal gas constant (8.31410-3 kJK-1). The weighted average value (μ) and its standard deviation (σ) were calculated as μ = Σ(xi/σi2)/ Σ(1/σi2) and σ2 = N[1/Σ(1/σi2)], where xi is each one of the N vaporization enthalpy data, and σi is its respective standard deviation. The uncertainty presented correspond to twice σ.

The enthalpy of vaporization was calculated at Tfus using the equation

g

g

T

∆l Hm (Tfus ) = ∆l Hm (Tm) − ∫T m [Cp,m (g)- Cp,m(l)] dT fus

(11)

As the heat capacities in the liquid phase for the isomers were not known, the equation proposed by Chickos et al.69 was used, where the difference [Cp,m (g) – Cp,m (l)] is approximately equal to – (64.2 ± 32.1) J∙mol-1∙K-1. After this, the enthalpy of sublimation at Tfus was then determined from the equation g

∆gcr Hm (Tfus ) = ∆l Hm (Tfus ) + ∆lcr Hm (Tfus )

(12)

Finally, the enthalpy of sublimation at 298.15 K was calculated from T

fus ∆gcr Hm (298.15 K) = ∆gcr Hm (Tfus ) − ∫298.15 [C (g)- Cp,m (s)] dT K p,m

(13)

where Cp,m (g) was calculated, in the temperature range 296 K to 450 K, from Cv,m (g), which, in turn, was calculated from the harmonic frequencies in the gas phase. These frequencies were obtained at the B3LYP/6-311++G(3df,3pd) level for both compounds.


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Individual data are given in Table S9 in the supplementary information. The heat capacities as functions of temperature are given by equations 14 and 15 for 3NFT and 4NFT, respectively.

Cp,m(g)⁄(J∙mol-1 ∙K-1 )=(1.5439 ± 0.1854 )∙10-9 (T⁄K)4 − (2.5548 ± 0.2760) ∙10-6 (T⁄K)3 + (1.1736 ± 0.1531)∙10-3 (T⁄K)2 + (2.9736 ± 0.3754)∙10-1 (T⁄K) + (3.6817 ± 0.3429) ∙ 101

( r2 = 0.9999)

(14)

Cp,m(g)⁄(J∙mol-1 ∙K-1 )=(1.3338 ± 0.1803 )∙10-9 (T⁄K)4 − (2.2235 ± 0.2684) ∙10-6 (T⁄K)3 + (9.6531 ± 1.4894)∙10-4 (T⁄K)2 + (3.6196 ± 0.3650)∙10-1 (T⁄K) + (2.8236 ± 0.3334 ) ∙ 101

( r2 = 0.9999)

(15)

Table 8 gives the enthalpies of vaporization at the mean experimental temperature, the enthalpies of vaporization at fusion temperature, the enthalpies of sublimation at fusion temperature, and the enthalpies of sublimation at 298.15 K.

TABLE 8. Molar enthalpies of phase change at the mean experimental temperature, at the temperature of fusion, and at T = 298.15 K. g

a

g

a

∆gcr Hm (𝑇fus )b

∆gcr Hm (298.15K)c

kJ∙mol-1

kJ∙mol-1

kJ∙mol-1

90.4 ± 2.2

91.9 ± 2.2

117.3 ± 2.4

130.5 ± 2.9

87.8 ± 1.4

90.4 ± 1.4

119.0 ± 1.6

122.6 ± 2.4

compound

∆l Hm (515 K)

∆l Hm (𝑇fus )

kJ∙mol-1

3NFT 4NFT

Calculed with eq 11, b calculed by eq 12, c calculed with eq 13; the uncertainties correspond to the

expanded uncertainty with a level of confidence of approximately 95%. The experiments of vaporization were realized under average atmospheric pressure (78.8 kPa), u(P)= 1 kPa.



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Page 20 of 38

g

With the values of ΔfH°m (cr) and ∆cr 𝐻m , it was calculated the ΔfH°m (g) at T = 298.15 K, as is shown in equation 16. The results are shown in Table 9. ∆f Hom (g,298.15 K)=∆gcr Hm (298.15 K)+∆f Hom (cr,298.15 K)

(16)

TABLE 9. Standard molar enthalpies of formation in the solid and gas phases. compound

∆f Hom (cr)

∆gcr Hm (298.15 K)

∆f Hom (g)

kJ∙mol-1

kJ∙mol-1

kJ∙mol-1

3NFT

-325.6 ± 6.0

130.5 ± 2.9

-195.1 ± 6.7

4NFT

-338.9 ± 2.6

122.6 ± 2.4

-216.3 ± 3.5

The uncertainties correspond to the expanded uncertainty with a level of confidence of approximately 95%.c

For isomers, it is possible to determine the relative stability from the standard enthalpies of formation in the gas phase of each isomer.70 As it can see in Table 8, this enthalpy is more negative for 4NFT than for 3NFT; this means that the isomer with the nitro group in position 4 is more stable than with the nitro group in position 3. The enthalpic difference, which equals (-21.2 ± 7.6) kJ∙mol-1, corresponds to the enthalpy of isomerization, i.e., to the enthalpy due to the change in position of the nitro group from position 3 to 4. On the other hand, this value differs only in - 6.3 kJ in from the enthalpy of isomerization of 3nitrophthalic anhydride to 4-nitrophthalic anhydride, which is - (14.9 ± 7.4) kJ∙mol-1.36 This comparison is shown in Figure 4.


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NO2

O

O O2N

O

O

-(14.9 ± 7.4) -(381.1 ± 4.1) NO2

-(396.0 ± 6.2)

O

O O

O O2N

NH

NH

-(21.2 ± 7.6) -(195.1 ± 6.7)

O

-(216.3 ± 3.5)

O

Figure 4. Enthalpy of isomerization resulting from the change of the nitro group from position 3 to 4 for derivatives of phthalic anhydride and of phthalimide in the gas phase. All the values are in kJ∙mol-1.

Also, with the values of the standard molar enthalpy of formation, in the crystalline and gas phases, it was possible to determine the enthalpic increases when going from phthalic anhydride to phthalimide derivatives. These increases are shown in Figure 5. It may be observed there that the enthalpies of formation, in both phases, are more negative for the phthalic anhydride than for the phthalimide derivatives; it may be seen also that the enthalpic increment due to the replacement of the heteroatom, in both phases, is almost the same for both isomers.



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NO2

NO2

O

O

-(481.5 ± 2.1)a -(381.1 ± 4.1)b

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O

NH

(155.9 ± 6.4)a (186.0 ± 7.8)b -(325.6 ± 6.0)a -(195.1 ± 6.7)b

O O

O O

O2N

O2N O

-(499.6 ± 2.0)a -(396.0 ± 6.2)b

O

NH

(159.7 ± 3.3)a (179.7 ± 7.1)b -(339.9 ± 2.6)a -(216.3 ± 3.5)b

O

Figure 5. Enthalpic increase when the group anhydride is replaced by the group imide, a) in the solid phase and b) in the gas phase. All the values are in kJ∙mol-1.

4.2. Theoretical results. Molecular structure and NBO analysis. A computational optimization of the structures for 3NFT and 4NFT in the gas phase was carried out at the MP2(Full)/6-311++G(3df,3pd) level of theory. The optimized structures are shown in Figure 6. The theoretical structural parameters for the equilibrium geometries are given in Table S11. In this table, bond distances and angles obtained by X-ray diffraction are given too.46 It may be observed that, in general, there is a good correlation between crystallographic and theoretical values. The largest difference was found for the N-H bond lengths. In the crystalline phase, the bond lengths are 0.817 Å and 0.918 Å for 3NFT and 4NFT, respectively 46 and in the gas phase, the bond length is 1.0077 Å for both isomers. These results are similar to those obtained by Riehn et al.71 who studied the molecular structure of p-cyclohexyaniline and found that the bond lengths obtained by X-ray diffraction, for NH2 group, are 0.86(3)


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Å and 0.91(4) Å for N-H(1A) and N-H(1B), respectively; for gas phase they found also a theoretical value (MP2/6-31+G(d)) of 1.016 Å.

(a)

(b)

Figure 6. Optimized molecular structures for (a) 3NFT and (b) 4NFT at the MP2(Full)/6311++G(3df,3pd) level of theory. The numerical labeling of the atoms is also shown.

The minimum-energy structure for 3NFT shows a non planar geometry between the NO2 group and the phenyl ring, as clearly indicated by the value of -128.3° for the dihedral angle C4C3N13O15. In contrast, the structure for 4NFT shows a planar geometry, as can be seen in Figure 6b, with a torsional angle of 0° between the plane of the NO2 group and the phenyl ring. Additionally the magnitude of the distances O14···H17 and O15···H16 are 2.35 Å and 2.39 Å, respectively, in 4NFT suggests the presence of intramolecular interactions, which may contribute to the stability of the molecule.72 This can explain why at the G4 level of theory, 4NFT is more stable than 3NFT by 23.0 kJ·mol-1 (obtained of values of Table S12).



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With the hope of further characterizing this supposed stabilizing intramolecular interaction, an NBO analysis was performed in the region where these interactions are possible. This analysis provides a convenient basis for investigating conjugative interactions in molecular systems and the energies calculated correspond to a stabilizing donor–acceptor interaction.73 The possible interactions obtained were between filled donor (bond or lone pair) and empty acceptor (antibonding or Rydberg) NBOs and their energies were estimated using second-order perturbation theory. From the nearly overlapped NBO isosurfaces in Figure 7a for 3NFT, it can be inferred that there is an intramolecular repulsive interaction between the lone pairs on O14 (n14)O15 (n15) and O11 (n11); this repulsive interaction causes the out-of-plane orientation of the NO2 moiety. By NBO theory, the stability energy was calculated and found to be less than 2.09 kJ·mol-1. For 4NFT, the strongest interactions identified are the interactions of the lone pairs localized on O15 and O14 (n15 and n14) with the adjacent sigma*(C5-H17) and sigma*(C3-H16) bonds (*C5H17 and *C3H16) of the aromatic ring, respectively (Figure 7b). Thus, the highest perturbation energy is 11.60 kJ·mol-1 for the interactions n15*C5H17 and n14*C3H16. These stabilizing energy values imply that the 4NFT molecule is more stable than the 3NFT molecule.


Page 24 of 38

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(a)

(b)

Figure 7. Molecular graph and the NBO interaction in the isomers (a) 3NFT and (b) 4NFT.

Determination of standard enthalpy of formation. In the determination of the standard enthalpy of formation for each isomer, atomization and isodesmic reactions were used. The atomization reaction for both compounds is: C8H4N2O4 (g) = 8 C (g) + 4 H (g) + 2 N (g) + 4O (g)

(17)

The isodesmic reactions used, were the following: 3NFT or 4NFT + ethane = nitrobenzene + succinimide

(18i)

3NFT or 4NFT + dimethyl ether + ethene + methane = benzene + maleic anhydride + nitromethane + dimethylamine

(18ii)

3NFT or 4NFT + 5 methane = nitrobenzene + dimethylamine + 2 ethane + carbono dioxide

(18 iii)

3NFT or 4NFT + 7 methane = succinimide +3 ethene + 2 ethane + nitromethane

(18iv)

The experimental values of the enthalpy of formation in the gas phase were taken from the literature.74,75 These values and the energies calculated at 0 and 298.15 K (E0 and H298,



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respectively) at the G4 level, for all the compounds involved in each reaction, are shown in Table S12 of the supplementary information. In Table 10 the theoretical values of enthalpy of formation in the gas phase and a comparison with respective experimental values, are showed. As can be seen the values obtained via atomization reactions, are not in agreement with the experimental values; however the differences between the values, experimental and theoretical, of enthalpies of formation for the two isomers, are very close. This is, the isomerization enthalpy from experimental values is 21.2 kJ mol-1 and the correspondent enthalpy, from values obtained by atomization, is 20.8 kJ mol-1. In order to minimize the errors, by effects of strain and delocalization energies, the isodesmic reactions i, iii and iv, were used. The standard enthalpies of formation, obtained for these reactions, are in greater agreement with the experimental enthalpies.


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TABLE 10. Comparison of the enthalpies of formation in the gas phase obtained experimentally and theoretically (at the G4 level). ∆fH°m(g)/kJ·mol-1 G4

Compound

3NFT

4NFT

aNumbers

Atomization

Exp.

Isodesmic reaction

i

-190.3(-4.8)

ii

-205.7 (10.6)

-211.1 (16)

-195.1 ± 6.7

iii

-198.1 (3.0)

iv

-199.1 (4.0)

i

-213.2 (-3.1)

ii

-228.7 (12.4)

iii

-221.1 (4.8)

iv

-222.1 (5.8)

-231.9 (15.6)

-216.3 ± 3.5

in parentheses are the differences between experimental and calculated

values.

5. Conclusions In agreement with the experimental and theoretical values for the standard enthalpy of formation in the gas phase, the isomer 4NFT is more stable than 3NFT. This was confirmed by the NBO analysis, which showed that in 3NFT there exists a repulsive interaction between the oxygen atoms of the carbonyl and nitro groups. Regarding the estimation of the standard enthalpies of formation by theoretical methods, the values closest to experimental results for both compounds were those obtained using isodesmic reaction 18 i, iii and iv. On the other hand, by comparing the standard enthalpies of



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formation of the isomers 3- and 4-nitrophthalimide with those of the isomers 3- and 4nitrophthalic anhydride, the enthalpic increase when going from anhydrides to phthalimides is (158.3 ± 7.2) kJ·mol-1, in the solid phase, and (182.8 ±10.5) kJ·mol-1, in the gas phase. Also, there is good correlation between the enthalpy of isomerization of the derivatives of phthalimide and that of the derivatives of phthalic anhydride.

Acknowledgment. K.S.L. thanks Conacyt (Mexico) for her scholarship (registration number 388573).

Supplementary Information The Supporting Information is available free of charge on the ACS Publications website at: Tables: heat capacity in function of temperature, in solid and gas phases; vibrational frequencies (cm-1) for the determination of heat capacities in the gas phase; main values of combustion experiments and Washburn corrections; experimental values obtained by thermogravimetry, to calculate the enthalpy of vaporization at mean temperature; theoretical MP2(Full) structural parameters of equilibrium structure and comparison with values obtained from crystallographic data; enthalpies of formation and values of energy at 0 K and 298.15 K at G4 level theory, for compounds used in the isodesmic reactions. Figures: thermograms of DSC and chromatogram of 4NFT; TGA graphs of the two isomers; linear regression graphs obtained by thermogravimetry for the two isomers.


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