Experimental Determination of the Standard Enthalpy of Formation of Trimellitic Acid and Its Prediction by Supervised Learning

The standard molar enthalpy of formation for trimellitic acid (TMAc) in the crystalline phase at 298.15 K, ΔfHm°(cr), was calculated experimentally from the enthalpy of combustion through combustion calorimetry experiments. Likewise, the standard molar enthalpy of sublimation was determined from the standard molar enthalpy of fusion and from the standard molar enthalpy of vaporization from differential scanning calorimetry and thermogravimetry, respectively. Subsequently, the standard molar enthalpies of formation in the gas-phase at 298.15 K, ΔfHm°(g), were calculated. The enthalpies of formation for TMAc, hemimellitic, and trimesic acids were predicted using multiple linear regression (MLR) with a nonreplacement evaluation technique. MLR was applied to the data set that allowed estimating these thermochemical properties with an R2 greater than 0.99. This model was used to compare the predicted and experimental results for benzene carboxylic acids.


Enthalpy of Formation of Trimellitic Acid and its Prediction by Supervised Learning
Fausto Díaz-Sánchez, † Miguel Angel García-Castro, * , † María Patricia Amador-Ramírez, ‡ Jesús Andrés Arzola-Flores, † and Ximena Limón Aguilar † †Facultad de Ingeniería Química de la Benemérita Universidad Autónoma de Puebla, 18 Sur y Av.San Claudio, C.P. 72570, Puebla Pue, Mexico ‡Facultad de Ciencias Químicas de la Benemérita Universidad Autónoma de Puebla, 14 Sur y Av.San Claudio, C.P. 72570, Puebla Pue, Mexico E-mail: miguel.garciacastro@correo.buap.mxS1: Thermogravimetric data of Pyrene to determine vaporization enthalpy Table S2: Thermogravimetric data of Phenanthrene to determine vaporization enthalpy Table S3: Thermogravimetric data of Pyrene to determine sublimation enthalpy Table S4: Thermogravimetric data of Anthracene to determine sublimation enthalpy Table S5: Comparison of vaporization and sublimation enthalpies for standard compounds Table S6: Comparison of sublimation enthalpies of pyrene at T =298.15K calculated by two routes Table S7: Experimental values of C p,m (cr) of TMAc at different temperatures Table S8: Thermogravimetric data of TMAc to determine vaporization enthalpy Figure S6: Linear regression of TMAc data as function of 1/T to determinate the enthalpy of vaporization, ∆ g l H m (T m ) Table S9: Thermogravimetric data of TMAc to determine sublimation enthalpy Figure S7: Linear regression of TMAc data as function of 1/T to determinate the enthalpy of sublimation, ∆ g cr H m (T m ) Table S10: Calculation of formation enthalpy in kJ mol −1 .

Table S11: Group reparametrization
In Figure S1, obtained by thermogravimetric analysis, the thermogram of TMAc purified is disclosed.As shown in figure, at 373 K there is no mass loss due to the vaporization of water.
The uncertainty for each enthalpy of vaporization value was calculated with standard deviation of the slope, which is a standard uncertainty.b The weighted average value µ and its standard deviation σ, were The uncertainty for each enthalpy of vaporization value was calculated with standard deviation of the slope, which is a standard uncertainty.b The weighted average value µ and its standard deviation σ, were Table S3: Thermogravimetric data of Pyrene to determine sublimation enthalpy The uncertainty for each enthalpy of vaporization value was calculated with standard deviation of the slope, which is a standard uncertainty.b The weighted average value µ and its standard deviation σ, were The uncertainty for each enthalpy of vaporization value was calculated with standard deviation of the slope, which is a standard uncertainty.b The weighted average value µ and its standard deviation σ, were        Table S10 shows an example of how to perform the prediction manually with this method, the correction factors added to this method were the functional group to which the compounds belong, radical 1-4 where it is specified where the substituents are positioned within a molecule (excluding the base compound), i.e., in the case of benzoic acid as there is no difference where the COOH group is positioned that parameter does not consider, If a compound has several corrections due to aromaticity (for example, two meta corrections), correction 1 meta, correction 2 meta, correction 3 and correction 4 will be used, the latter indicating that the compound in question only has 2 corrections for aromaticity instead of 4, which is the maximum that the model can predict, in the case of a compound that does not have corrections for aromaticity, the values of corrections 1-4 will be used (this indicates that the molecule does not have corrections ortho, meta or para within its structure), in addition a starting value H f 0 must be used, which represents the intersection (a 0 ) obtained by the regression.Type: Discrete 0 (absence), 1 to infinity (presence).

CO-(CD)(O)
A carbonyl group attached to a carbon double bond and an oxygen.

CO-(C)(O)
A carbonyl group attached to a carbon and an oxygen.

Figure S1 :
Figure S1: TGA thermogram of TMAc Figure S2: Diffractogram of TMAc Figure S3: Example of Thermogram of TMAc, obtained in DSC using gold crucibles and mass around 6 mg Figure S4: Example of thermogram of TMAc, obtained by SDT.In these experiments was used an alumina crucible and the values of mass were around 9.0 mg.The red line corresponds to DSC signal.The little peak observed near of 50 °C corresponds to a stabilization period of the DSC signal (these peak is observed in all thermograms, included to the reference

Figure S4 :
Figure S4: Example of thermogram of TMAc, obtained by SDT.In these experiments was used an alumina crucible and the values of mass were around 9.0 mg.The red line corresponds to DSC signal.The little peak observed near of 50 °C corresponds to a stabilization period of the DSC signal (this peak is observed in all thermograms, included to the reference compounds).

Figure S5 :
Figure S5: Thermogram of Indium obtained in DSC using gold capsules.
where x i is each of the N vaporization enthalpy data and its respective standard deviation σ i .The experiments of vaporization were realized under average atmospheric pressure (78.8 kPa), u(P )= 1 kPa.The uncertainty corresponds to combined uncertainty.c The standard molar enthalpy of vaporization was obtained by equations 11, 12 and 13 where C p,m (g) = 204.2J• mol −1 where x i is each of the N vaporization enthalpy data and its respective standard deviation σ i .The experiments of vaporization were realized under average atmospheric pressure (78.8 kPa), u(P )= 1 kPa.The uncertainty corresponds to combined uncertainty.c The standard molar enthalpy of vaporization was obtained by equations 11, 12 and 13 where C p,m (g) = 185.7 J• mol −1 • K −1 according to Rojas et al. i i Rojas, A.; Orozco, E. Measurement of the enthalpies of vaporization and sublimation of solids aromatic hydrocarbons by differential scanning calorimetry.T hermochim.Acta, 2003, 405, 93-107.doi:10.1016/S0040-6031(03)00139-4 where x i is each of the N vaporization enthalpy data and its respective standard deviation σ i .The experiments of vaporization were realized under average atmospheric pressure (78.8 kPa), u(P )= 1 kPa.The uncertainty corresponds to combined uncertainty.c The standard molar enthalpy of vaporization was obtained by equations 11, 12 and 13 where C p,m (g) = 204.2J• mol −1 where x i is each of the N vaporization enthalpy data and its respective standard deviation σ i .The experiments of vaporization were realized under average atmospheric pressure (78.8 kPa), u(P )= 1 kPa.The uncertainty corresponds to combined uncertainty.c The standard molar enthalpy of sublimation was obtained by equation 15 according to Chickos et al. i i Chickos, J.S.; Hosseini, S.; Hesse, D.G.; Liebman, J.F.Heat capacity corrections to a standard state: a comparison of new and some literature methods for organic liquids and solids, Struct.Chem., 1993, 4, 271-278.https://doi.org/10.1007/BF00673701.

Figure S7 :
Figure S7: Linear regression of TMAc data as function of 1/T to determinate the enthalpy of sublimation, ∆ g cr H m (T m ).

Type:
Discrete 0 (absence), 1 to infinity (presence).C-(H)(O)(CO)(C) A carbon atom attached to a hydrogen, an oxygen, a carbonyl, and another carpage Table S11 -continued from previous page Correction 2 meta Correction used for having radicals in the meta position and one of the ortho, meta, or para corrections at 1. Type: dichotomous 0 (absence), 1 (presence).Correction 2 ortho Correction used for having radicals in the ortho position and one of the ortho, meta, or para corrections at 1. 0 (absence), 1 (presence).Correction 2 para Correction used for having radicals in the para position and one of the ortho, meta, or para corrections at 1. Type: dichotomous 0 (absence), 1 (presence).Correction 3 Correction used in case there are no corrections for aromaticity in the molecule.Type: dichotomous 0 (absence), 1 (presence).Correction 3 meta Correction used for having radicals in the meta position and one of the ortho, meta, or para corrections at 1 and 2. Type: dichotomous 0 (absence), 1 (presence).Correction 3 ortho Correction used for having radicals in the ortho position and one of the ortho, meta, or para corrections at 1 and 2. Type: dichotomous 0 (absence), 1 (presence).Correction 3 para Correction used for having radicals in the para position and one of the ortho, meta, or para corrections at 1 pageTable S11 -continued from previous page Correction 4 meta Correction used for having radicals in the meta position and one of the ortho, meta, or para corrections at 1, Correction used for having radicals in the ortho position and one of the ortho, meta, or para corrections at 1, 2, and 3.

Table S5 :
Comparison of vaporization and sublimation enthalpies for standard compounds

Table S6 :
Comparison of sublimation enthalpies of pyrene at T =298.15K calculated by two routes a a The uncertainty corresponds to twice the standard combined.bMethod: Correlation of Gas Chromatography (CGC); Thermogravimetry (TGA); Gas Chromatography (GC); Inclined pistón gauge (IPG); Method of effusion (ME); Transpiration (T); Static Isoteniscope (I); Drop Calorimeter (DC).cData provided in the references: All uncertainties correspond to twice the combined standard.b The values were taken from Rojas et al. i c Fusion enthalpies calculated at 298.15 K using equation 8 and the capacities for liquid and solid pyrene were 290.2 and 234.9 J mol −1 K −1 , respectively.i d,e This work i Rojas, A.; Orozco, E. Measurement of the enthalpies of vaporization and sublimation of solids aromatic hydrocarbons by differential scanning a calorimetry.T hermochim.Acta, 2003, 405, 93-107.doi:10.1016/S0040-6031(03)00139-4

Table S7 :
Experimental values of C p,m (cr) of TMAc at different temperatures.a • K −1

Table S8 :
• K −1 (C p,m )= 6.33 J• mol −1 • K −1 ,which correspond to twice the combined uncertainty with a 95% confidence level, and include the contributions from the calibration and u(T ) = 0.1 K.The experiments were performed at an average pressure of 78.8 kPa.Standard uncertainty for P is u(P )= 1 kPa.Thermogravimetric data of TMAc to determine vaporization enthalpy a U

Table S9 :
Thermogravimetric data of TMAc to determine sublimation enthalpy

Table S10 :
Calculation of formation enthalpy in kJ mol −1 .