Vapor Pressures of Four Methyl Esters of Substituted Benzoic Acids

Article pubs.acs.org/jced

Vapor Pressures of Four Methyl Esters of Substituted Benzoic Acids. The Intermolecular Hydrogen Bond OH···O Ana R. R. P. Almeida and Manuel J. S. Monte* Centro de Investigaçaõ em Química da Universidade do Porto, Department of Chemistry and Biochemistry, Faculty of Science, University of Porto, Rua do Campo Alegre, 687, P-4169-007 Porto, Portugal S Supporting Information *

ABSTRACT: This paper reports experimental vapor pressures of condensed phases of methyl p-cyano, p-formyl, p-nitro, and p-(methylamino) benzoates measured over the temperature ranges (303.9 to 393.0) K, (303.1 to 388.2) K, (319.0 to 415.8) K, and (332.9 to 392.4) K, respectively, using a static method based on capacitance diaphragm manometers. The Knudsen mass-loss effusion technique was also used to measure the vapor pressures of crystalline methyl p-(methylamino)benzoate in the temperature range (317.1 to 339.2) K. These results enabled the calculation of the standard molar enthalpies and entropies of sublimation and of vaporization, at reference temperatures as well as the (p,T) values of the triple point of each compound. The temperatures and molar enthalpies of fusion were determined using differential scanning calorimetry and were compared with the values derived indirectly from the vapor pressure measurements. The enthalpies of the intermolecular hydrogen bonds O−H···O in the crystalline phase of the parent benzoic acids were determined. respective parent benzoic acids.7,9,10 To compare the previously reported results with the enthalpy of O−H···O intermolecular bonds present in the crystals of para cyano, formyl, nitro, and methylamino benzoic acids, it was decided to determine enthalpies of sublimation from vapor pressure measurements of the corresponding methyl benzoates (Figure 1). Moreover, the experimental results of standard Gibbs energies and enthalpies of sublimation of the compounds studied in this work were compared with values estimated using a method that takes into account the influence of 30 different substituents of benzene derivatives on their thermodynamic properties.11

1. INTRODUCTION Methyl benzoate has an agreeable odor and is present in different flower oils, cherry, banana, pimento berry, mustard, clove bud and stem, black tea, coffee, dill, starfruit, and also in allspice.1,2 In industry it is frequently used as a solvent, flavoring ingredient, dye carrier, and in perfume manufacturing. It may be released in the environment from both natural and anthropogenic origins. This ester is one of numerous substances that is appellative to males of many species of orchid bees, who seemingly use the compound to produce pheromones.2 Some of its derivatives are used in pigments, pesticides or agriculture industries and as precursors of important pharmaceuticals. Methyl p-cyanobenzoate may be an intermediate of useful chemicals including drugs, liquid crystals, monomers for functional polymers, and agrochemicals.3 Nitrobenzoates, such as methyl p-nitrobenzoate, are used in the manufacture of dyes, explosives, pesticides, and industrial solvents. They enter industrial waste streams and accumulate in the environment very quickly.4 Methyl 4-formylbenzoate is used as a raw material for producing fluorescent whitening and aromatic agents as well as for producing high-value-added compounds as p-aminobenzoate.5 It is also a starting material in the synthesis of “high affinity folate receptor-specific glycinamide ribonucleotide formyltransferase inhibitors with antitumor activity”.6 Vapor pressure measurements of several methyl benzoates have been reported previously,7−10 and the derived enthalpies of sublimation enabled the calculation of the enthalpy of intermolecular hydrogen bonds O−H···O formed in the © 2016 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials. Table 1 presents information about the origin and purification process of the compounds studied in this work: methyl p-cyanobenzoate (C9H7NO2, CASNR 1129-357), methyl p-formylbenzoate (C9H8O3, CASNR 1571-08-0), methyl p-(methylamino)benzoate (C9H11NO2, CASNR 1835863-9), and methyl p-nitrobenzoate (C8H7NO4, CASNR 61950-1). While the former three compounds were further purified by sublimation under reduced pressure, the latter one was studied without purification. Prior to the experimental determinations, the degree of purity of each sample studied was evaluated by GC, performed using an Agilent 4890D equipped with an HP-5 column (cross-linked, 0.05 diphenyl Received: November 18, 2015 Accepted: January 14, 2016 Published: January 28, 2016 1012

DOI: 10.1021/acs.jced.5b00978 J. Chem. Eng. Data 2016, 61, 1012−1020

Journal of Chemical & Engineering Data

Article

Figure 1. Structural formulas of (a) methyl p-cyanobenzoate, (b) methyl p-formylbenzoate, (c) methyl p-nitrobenzoate, and (d) methyl p(methylamino)benzoate.

Table 1. Origin and Purity Details of the Methyl Benzoates Studied in This Work chemical name methyl methyl methyl methyl a

p-cyanobenzoate p-formylbenzoate p-nitrobenzoate p-(methylamino)benzoate

source

minimum initial puritya

purification methodb

final mass fraction purity (dry base)

analysis methodc

Sigma-Aldrich Alfa Aesar Alfa Aesar Alfa Aesar

0.996 0.985 0.999 0.984

sublimation sublimation

0.9978 0.9967 0.9990 0.9985

GC GC GC GC

sublimation

b

As stated in the certificate of analysis from the manufacturer. Under reduced pressure (p = 1 Pa). cGas−liquid chromatography.

and 0.95 dimethylpolysiloxane by mass fraction), and a flame ionization detector (FID), using nitrogen as the carrier gas and acetone as solvent. 2.2. Differential Scanning Calorimetry. The onset temperatures and enthalpies of fusion were determined using a power compensated PerkinElmer DSC calorimeter (Diamond Pyris 1). Its calibration was achieved using the following high purity compounds: benzoic acid, naphthalene, anthracene, triphenylene, 1,3,5-triphenylbenzene, perylene, o-terphenyl, diphenylacetic acid, and 4-methoxybenzoic acid. For each compound studied five fresh samples (sealed in aluminum crucibles) were scanned under a controlled nitrogen flux from T/K = 298 to a temperature ca. 20 K above the fusion temperature, using a heating rate of 3.3·10−2 K·s−1. No phase transitions in the crystalline phase were identified between 298 K and the temperature of fusion. 2.3. Vapor Pressures Measurements. The vapor pressures of both condensed phases (crystalline and liquid) of the four methyl benzoates studied were measured at different temperatures by means of a static apparatus based on capacitance diaphragm gauges that was previously tested and described.12,13 This equipment integrates two capacitance diaphragm absolute gauges (MKS Instruments, Inc.) at selfcontrolled constant temperatures: (gauge I) Baratron 631A01TBEH (Tgauge = 423 K) for measuring pressures in the range (0.5 to 1.3·102) Pa and (gauge II) Baratron 631A11TBFP (Tgauge = 473 K) for pressures in the range (3 to 1.3·103) Pa. The standard uncertainty of the temperature measurements was estimated to be u(T/K) = 0.01. The expressions u(p/Pa) = 0.01 + 0.0025 (p/Pa) for gauge 1 and u(p/Pa) = 0.1 + 0.0025 (p/Pa) for gauge 2 are used to describe the standard uncertainties of the pressure measurements. Before starting the vapor pressure measurements the sample is fully outgassed under reduced pressure in order to get rid of eventual volatile impurities, including water (much more volatile than the samples studied) that would not be detected through the GC analysis. The Knudsen mass-loss effusion technique was used for additional measurements of vapor pressures of the crystals of methyl p-(methylamino)benzoate over the temperature range (317.1 to 339.2) K. The apparatus allows the simultaneous operation of nine aluminum effusion cells at three different temperatures in each experimental run, and has been described

in detail previously.14 The effusion cells with different circular effusion orifices made in platinum discs of 0.0125 mm thickness are introduced in cylindrical holes inside three temperature controlled aluminum blocks. Each block is kept at a constant temperature, different from the other two, and contains three effusion cells with orifices of different areas: one “small” (Ao ≈ 0.5 mm2: series A), one “medium” (Ao ≈ 0.8 mm2: series B) and one “large” (Ao ≈ 1.1 mm2: series C). In each effusion experiment, the loss of mass m of the samples, during a convenient effusion time period t, is determined by weighing the effusion cells to ±1·10−5 g before and after the effusion period. The vapor pressure p at the temperature T of the crystalline sample contained in each effusion cell is calculated by eq 1, where A0 is the area of the effusion orifice, R is the gas constant (R = 8.3144598 J·K−1·mol−1),15 M is the molar mass of the vapor assumed monomeric, and Wo is the transmission probability factor. p = (m /Aowot )(2πRT /M )0.5

(1)

The areas and the transmission probability factors of each effusion orifice are given in the Supporting Information (Table S1). The standard uncertainties of the vapor pressure and temperature measurements are estimated as u(p/Pa) = 0.01 and u(T/K) = 0.01.

3. RESULTS AND DISCUSSION 3.1. Vapor Pressures. Table 2 reports the vapor pressures measured using the static method in the crystalline and liquid phases of the four substituted methyl benzoates. The mean vapor pressure values of the crystalline methyl p(methylamino)benzoate derived from the Knudsen effusion experiments, are also listed in this Table. The detailed experimental results derived from each effusion cell at each temperature studied are summarized in Table S2 (Supporting Information). The experimental data of the solid and liquid vapor pressures were independently fit by the truncated form of Clarke and Glew eq (eq 2).16 ⎛ p⎞ Δg G o (θ ) ⎛1 1⎞ g Hmo(θ )⎜ − ⎟ R ln⎜ o ⎟ = − cd m + Δcd ⎝θ θ T⎠ ⎝p ⎠ ⎡⎛ θ ⎞ ⎛ T ⎞⎤ g o + Δcd C p ,m(θ )⎢⎜ ⎟ − 1 + ln⎜ ⎟⎥ ⎝ θ ⎠⎦ ⎝ ⎠ ⎣ T 1013

(2)



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Table 2. Vapor Pressure Resultsa T/K

p/Pa

303.93 306.95 309.92 312.93

0.66 0.92 1.30 1.83

339.83 342.81 345.80 348.76 351.75 354.72 357.79

26.86 33.10 40.54 49.32 60.07 73.14 89.12

303.10 305.04 307.04 309.04 311.05

0.69 0.86 1.09 1.37 1.73

326.93 328.93 330.90 332.84 334.84 336.84 338.85 340.80 342.76 344.76 346.67

11.65** 13.57** 15.73** 18.23** 21.22** 24.58 28.03 32.52 37.10 42.83 48.56

319.01 321.07 322.98 325.03 326.97 328.99 330.91 332.94

0.74 0.92 1.15 1.44 1.77 2.20 2.65 3.33

360.47 362.46 364.43 370.48 372.46 374.39 376.40 378.37 380.36

54.33** 61.50** 69.71** 101.9 114.9* 128.1* 144.6* 161.5* 180.9*

317.09 319.16 321.19 323.08

0.079 0.102 0.131 0.167

332.90 334.88 336.87 338.87 340.85

0.54 0.68 0.86 1.08 1.34

100 Δp/pb

T/K

p/Pa

100 Δp/pb

T/K

Methyl p-Cyanobenzoate (Crystalline Phase,Static) 315.91 2.52 0.0 327.89 318.88 3.47 0.3 330.89 321.94 4.79 0.5 333.86 324.93 6.49 0.3 336.84 Methyl p-Cyanobenzoate (Liquid Phase,Static) 0.1 360.66 105.9 −0.2 381.25 0.2 363.64 127.6* 0.3 384.19 −0.1 366.47 150.8* 0.1 387.18 −0.4 369.42 179.3* 0.1 390.14 −0.4 372.40 213.1* 0.2 393.05 0.1 375.39 250.8* −0.5 0.4 378.30 295.7* −0.2 Methyl p-Formylbenzoate (Crystalline Phase,Static) 0.6 313.01 2.16 0.4 323.02 −0.4 314.99 2.68 0.0 324.99 −0.1 317.07 3.35 −0.4 326.97 −0.3 319.02 4.12 −0.8 328.97 0.2 321.01 5.11 −0.4 330.92 Methyl p-Formylbenzoate (Liquid Phase,Static) 0.1 348.71 55.84 0.2 370.41 −0.1 350.65 63.47 0.1 372.39 −0.3 352.66 72.23 0.0 374.28 −0.1 354.52 81.23 −0.3 376.36 0.4 356.60 93.14 0.2 378.24 0.5 358.58 105.1 −0.1 380.30 −0.8 360.55 118.2* −0.5 382.21 0.2 362.49 133.8* 0.0 384.22 −0.3 364.51 151.9* 0.6 386.18 0.3 366.47 169.8* 0.1 388.17 −0.1 368.46 190.2* −0.2 Methyl p-Nitrobenzoate (Crystalline Phase,Static) 0.3 334.86 4.04 0.3 350.59 −1.0 336.90 4.97 0.4 352.71 0.2 338.83 5.97 −0.5 354.57 0.4 340.86 7.34 0.1 356.66 0.1 342.77 8.78 −0.6 358.51 0.4 344.81 10.73 −0.1 360.61 −1.1 346.71 12.86 −0.1 362.47 0.7 348.76 15.64 0.2 364.55 Methyl p-Nitrobenzoate (Liquid Phase,Static) 0.0 382.30 200.8* −0.4 400.05 −0.4 384.27 224.1* −0.3 401.96 −0.3 386.24 250.2* −0.1 403.96 0.4 388.24 279.2* 0.0 405.95 0.6 390.19 309.1* −0.2 407.87 0.0 392.19 344.9* 0.2 409.86 0.4 394.11 379.6* −0.3 411.81 0.1 396.19 424.8* 0.3 413.78 0.1 398.07 465.5* −0.2 415.75 Methyl p-(Methylamino)benzoate (Crystalline Phase, Knudsen Eff usion)c 0.6 325.15 0.212 −0.2 333.17 0.1 327.18 0.268 −1.1 335.09 −0.1 329.12 0.339 −0.4 337.17 1.0 331.22 0.430 −1.1 339.18 Methyl p-(Methylamino)benzoate (Crystalline Phase, Static) −1.3 342.84 1.67 0.4 352.76 −0.9 344.81 2.07 0.6 354.74 0.0 346.80 2.57 1.0 356.73 0.4 348.79 3.17 1.1 358.71 0.1 350.81 3.90 0.8 360.69 0.4 −1.3 −0.4 0.4

1014

p/Pa

100 Δp/pb

8.72 11.65 15.62 20.58

0.1 −0.5 0.0 −0.6

348.7* 406.1* 476.7* 555.4* 644.0*

0.2 −0.3 0.0 0.0 0.1

6.35 7.80 9.65 11.65 14.05

0.2 0.3 1.3 0.0 −0.7

213.8* 239.5* 265.7* 298.0* 330.6* 369.3* 408.5* 455.8* 502.8* 562.0*

0.2 0.2 0.0 −0.1 −0.1 −0.2 −0.3 0.1 −0.4 0.5

18.43 22.55 26.56 32.13 37.67 45.42 53.31 63.62

−0.3 0.4 −0.1 0.2 −0.2 0.1 0.0 −0.1

514.1* 566.5* 624.4* 689.4* 754.1* 830.2* 907.8* 995.2* 1088*

−0.2 0.0 −0.1 0.2 0.0 0.2 0.0 0.1 0.0

0.536 0.689 0.865 1.065 4.77 5.75 7.03 8.50 10.33

−1.5 1.8 1.2 −0.2 0.9 −0.5 −0.4 −1.1 −1.0



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Table 2. continued T/K

p/Pa

100 Δp/pb

348.77 350.76 352.75 354.74 356.72 358.69 360.67 362.67

4.82** 5.60** 6.55** 7.60** 8.76** 10.17** 11.73** 13.51**

0.1 −0.3 0.2 0.1 −0.4 0.1 0.1 −0.1

T/K

p/Pa

100 Δp/pb

Methyl p-(Methylamino)benzoate (Liquid Phase, Static) 364.65 15.61** 0.5 366.64 17.88 0.2 368.55 20.15 −0.9 370.60 23.31 −0.2 372.58 26.69 0.1 374.55 30.49 0.4 376.53 34.59 0.1 378.50 39.35 0.3

T/K 380.51 382.47 384.46 386.45 388.41 390.40 392.35

p/Pa 44.46 50.44 56.82 64.35 72.41 81.50 91.54

100 Δp/pb −0.2 0.1 −0.3 0.0 0.0 −0.1 0.1

a

Estimated uncertainties: u(T/K) = 0.01; u(p/Pa) = 0.01 + 0.0025 (p/Pa) for pressures below 1.3·102 Pa (measured using gauge 1), and u(p/Pa) = 0.1 + 0.0025 (p/Pa) for the pressures measured using gauge 2 (∗); u(p/Pa) = 0.01 for the effusion pressures; vapor pressures of the supercooled liquid are marked with a double asterisk (∗∗). bΔp = p − pcalc., where pcalc is calculated from the Clarke and Glew eq 2 with parameters given in Table 3. cThe reported effusion pressures are the mean of the values obtained using the small, medium, and large effusion orifices.

Table 3. Standard (po = 0.1 MPa) Molar Properties of Sublimation and of Vaporization Derived from the Fitting of eq 2 to the Experimental (p, T) Results ΔT

θ

Δgcr,lGom(θ)a

Δgcr,lHom(θ)a

Δgcr,lSom(θ)b

K

K

kJ·mol−1

kJ·mol−1

J·K−1·mol−1

303.9 to 336.8

298.15 320.38d 338.87f

339.8 to 393.0

298.15 366.44d 338.87f

303.1 to 330.9

298.15 317.01d 335.58f

326.9 to 388.2

298.15 357.55d 335.58f

319.0 to 364.6

298.15 341.78d 369.15f

360.5 to 415.8

298.15 388.11d 369.15f

317.1 to 339.2

298.15 328.14d

332.9 to 360.7

298.15 346.80d 365.32f

348.8 to 392.4

298.15 370.56d 365.32f

−Δgcr,lCop,ma R2

Methyl p-Cyanobenzoate (Crystalline Phase, Static) 31.29 ± 0.01 89.9 ± 0.1 196.6 ± 0.3 1.0000 26.94 ± 0.01 89.2 ± 0.1 23.36 ± 0.01 88.6 ± 0.1 192.5 ± 0.3 Methyl p-Cyanobenzoate (Liquid Phase, Static) 28.88 ± 0.01 70.5 ± 0.4 139.6 ± 1.3 1.0000 19.80 ± 0.01 66.2 ± 0.1 23.36 ± 0.01 67.9 ± 0.1 131.4 ± 0.3 Methyl p-Formylbenzoate (Crystalline Phase, Static) 30.96 ± 0.01 91.3 ± 0.1 202.4 ± 0.3 27.16 ± 0.01 90.7 ± 0.1 1.0000 23.46 ± 0.01 90.1 ± 0.1 198.6 ± 0.3 Methyl p-Formylbenzoate (Liquid Phase, Static)h 28.64 ± 0.02 71.4 ± 0.2 143.4 ± 0.7 20.58 ± 0.01 66.6 ± 0.1 1.0000 23.46 ± 0.01 68.4 ± 0.1 133.9 ± 0.3 Methyl p-Nitrobenzoate (Crystalline Phase, Static) 35.55 ± 0.03 96.0 ± 0.5 202.8 ± 1.7 1.0000 26.80 ± 0.01 94.6 ± 0.1 21.40 ± 0.01 93.7 ± 0.3 195.9 ± 0.8 Methyl p-Nitrobenzoate (Liquid Phase, Static)h 31.14 ± 0.05 74.6 ± 0.4 145.8 ± 1.4 1.0000 19.00 ± 0.01 67.4 ± 0.1 21.40 ± 0.01 69.0 ± 0.1 128.9 ± 0.3 Methyl p-(Methylamino)benzoate (Crystalline Phase, Knudsen Ef f usion) 41.20 ± 0.04 106.7 ± 0.4 219.7 ± 1.3 0.9999 34.66 ± 0.01 105.6 ± 0.4 Methyl p-(Methylamino)benzoate (Crystalline Phase, Static Method) 41.21 ± 0.04 107.6 ± 0.3 222.7 ± 1.0 0.9999 30.50 ± 0.01 105.9 ± 0.3 26.50 ± 0.02 105.3 ± 0.3 215.7 ± 0.8 Methyl p-(Methylamino)benzoate (Liquid Phase,Static)h 36.41 ± 0.07 83.2 ± 0.7 156.9 ± 2.4 1.0000 25.77 ± 0.01 76.8 ± 0.1 26.50 ± 0.01 77.3 ± 0.1 139.1 ± 0.3

J·K−1·mol−1

sc

31.6e

0.0051

62.3 ± 5.6g

0.0026

32.2e

0.0057

80.7 ± 3.9g

0.0031

32.8 ± 11.0g

0.0046

79.8 ± 4.9g

0.0025

35.3e

0.0105

35.3e

0.0084

87.8 ± 9.6g

0.0031

a

Uncertainties are standard deviations of the least-squares regressions. bCalculated through eq 3; uncertainties calculated through the RSS method. s is the standard deviation of the fit defined as s = [Σin= 1(ln p − ln pcalc)2i /(n − m)]1/2 where n is the number of experimental points used in the fit and m is the number of adjustable parameters of Clarke and Glew eq 2. dMean temperature. eEstimated value. fTemperature of triple point. g Adjustable parameter derived from fitting eq 2 to the (pressure−temperature) data. hIncluding supercooled liquid. c

where p is the vapor pressure at the temperature T, po is a selected reference pressure (po = 105 Pa in this work), θ is a

reference temperature and R is the molar gas constant. ΔgcdGom(θ) is the difference in molar Gibbs energy between 1015



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the gaseous and the crystalline or liquid phase at the selected g reference pressure, Δcd Hmo(θ) is the difference in molar enthalpy between the gas and the condensed phases, and ΔgcdCop,m(θ) is the difference in molar heat capacity at constant pressure between the gaseous and the condensed phase. Considering the low vapor pressures, ideal gas behavior was assumed for the vapor of all the compounds studied. The g g thermodynamic properties, Δ cd H mo (θ), Δ cd G mo (θ), and ΔgcdCop,m(θ), derived from the fittings, the related uncertainties (standard deviations of the least-squares regressions of the fittings) and the values of ΔgcdSom(θ), calculated through eq 3, are reported in Table 3. g o Δcd Sm(θ ) =

g g Δcd Hmo(θ ) − Δcd Gmo(θ ) θ

(3)

When accurate experimental crystalline or liquid vapor pressures are measured over a large temperature interval (ca. 50 K), the fit of the Clarke and Glew equation to the experimental values frequently yields reliable values of g o o Δcd Cp,m(θ). Thus, the values of ΔlgCp,m (θ) of the four compounds studied and also the value of ΔgcrCop,m(θ) of methyl p-nitrobenzoate, were derived from the fittings of eq 2 to the (p,T) experimental results. Because of the short temperature range, the values of ΔgcrCop,m(θ) for the other three methyl benzoates studied were estimated from the values of gas phase heat capacity at 298.15 K using eq 4 proposed by Monte et al.17 as a rearrangement of eq 5 derived by Chickos et al.18

Figure 2. Phase diagram of methyl p-cyanobenzoate: ○, liquid vapor pressures; □, crystalline vapor pressures; ▲, boiling point at 1.6·102 Pa.21 Triple point coordinates: T = 338.87 K, p = 25.08 Pa.

Δcrg C po,m(θ )/J·K−1·mol−1 = −{0.9 + 0.176(C po,m(g)/J ·K−1·mol−1)}

(4)

Δcrg C po,m(θ )/J·K−1·mol−1 = −{0.75 + 0.15(C po,m(cr)/J ·K−1·mol−1)}

(5)

To use eq 4, values of the gas phase molar heat capacity over the temperature interval (100 to 1000) K (presented in Table S3 of Supporting Information), were derived in this work from statistical thermodynamics, computed by means of the Gaussian 03 software package,19 using the vibrational frequencies from B3LYP/6-31G(d) calculations scaled by a factor of 0.9614. This scaling factor is recommended for “relating theoretical harmonic frequencies to observed fundamentals”, although a value closer to the unity may be more appropriate for the prediction of low-frequency vibrations.20 At 298.15 K, the results are Cop,m (g, methyl po cyanobenzoate) = 174.6 J·K−1·mol−1, Cp,m (g, methyl p−1 −1 formylbenzoate) = 177.6 J·K ·mol , and Cop,m (g, methyl p(methylamino)benzoate) = 192.3 J·K−1·mol−1. For methyl pnitrobenzoate, the value Cop,m (g, 298.15 K) = 185.4 J·K−1·mol−1 was also calculated computationally yielding the result ΔgcrCop,m = −33.6 J·K−1·mol−1 when using eq 4. This result is in good agreement with the selected value ΔgcrCop,m = −32.8 J·K−1·mol−1 that was derived from the fittings of eq 2 to the (p,T) experimental results. Figures 2 to 5 show the phase diagrams in the neighborhood of the triple points of the four compounds studied in this work as well as literature boiling points of methyl p-cyanobenzoate21 (Figure 2) and p-formylbenzoate21 (Figure 3). The crystalline vapor pressure of methyl p-(methylamino)benzoate, determined using the two different experimental methods are equal when extrapolated to the temperature 298.15 K (p = 6.0·10−3

Figure 3. Phase diagram of methyl p-formylbenzoate: ○, liquid vapor pressures; ●, undercooled liquid vapor pressures; □, crystalline vapor pressures; ▼, boiling point at 1.0·105 Pa.21 Triple point coordinates: T = 335.58 K, p = 23.31 Pa.

Figure 4. Phase diagram of methyl p-nitrobenzoate: ○, liquid vapor pressures; ●, undercooled liquid vapor pressures; □, crystalline vapor pressures. Triple point coordinates: T = 369.15 K, p = 93.75 Pa. 1016



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triple point temperature of methyl p-cyanobenzoate is 0.7 K larger than the value of the temperature of fusion obtained through DSC analysis while the enthalpy of fusion derived indirectly from vapor pressures is 1.1 kJ·mol−1 smaller than the DSC value; for methyl p-formylbenzoate the temperature of the triple point is 0.4 K larger than the value of the temperature of fusion (DSC) and the indirect and calorimetric enthalpies of fusion are identical within the experimental uncertainty; the enthalpy of fusion of methyl p-(methylamino)benzoate determined calorimetrically is in excellent agreement with the value derived from static vapor pressure measurements and the temperature of the triple point is only 0.7 K smaller than the calorimetric result. Table 4 also presents the standard molar enthalpies of fusion adjusted to T = 298.15 K using the results of ΔlcrCop,m(θ) estimated by inputting in eq 6 the values of Cop,m(g) referred to above. This equation was suggested by Almeida and Monte22 after combining eqs 4 and 7, proposed by Monte et al.17,23

Figure 5. Phase diagram of methyl p-(methyamino)benzoate: o, static liquid vapor pressures; ●, undercooled liquid vapor pressures; □, static crystalline vapor pressures; ×, effusion vapor pressures. Triple point coordinates: T = 365.32 K, p = 16.26 Pa.

Δcrl C po,m(θ )/J·K−1·mol−1 = 13.4 + 0.174(C po,m(g)/J ·K−1·mol−1)

Pa) and the results of the enthalpy of sublimation derived from the two techniques agree within 0.8%. Since the effusion vapor pressures depend on the molar mass of the effusing vapor (eq 1) in contrast to the ones measured using the static method, the concordance between enthalpies of sublimation derived from both techniques confirms the assumption of the monomeric gas phase. To the best of our knowledge, no vapor pressure data have been published before for the methyl p-substituted benzoates studied in this work. 3.2. Fusion Properties. Table 4 presents the results of the onset temperatures and enthalpies of fusion derived from the DSC experiments as well as the temperatures and pressures of the triple points for the four compounds studied, and the enthalpies of fusion derived indirectly from the vapor pressure measurements. The DSC fusion properties and those derived indirectly differ only slightly from each other. The temperature of fusion (DSC) of methyl p-nitrobenzoate is only 0.2 K larger than the value derived from vapor pressure measurements and the respective enthalpy of fusion derived indirectly is equal within the experimental uncertainty to the DSC result; the

(6)

Δgl C po,m(θ )/J·K−1·mol−1 = −{14.3 + 0.35(C po,m(g)/J ·K−1·mol−1)}

(7)

The results of ΔlcrHom(298.15 K) calculated from the difference between the enthalpies of sublimation and of vaporisation, at that temperature, are in excellent agreement with the ones determined from the DSC measurements. The nearness between the calorimetric values and those derived indirectly strengthens the reliability of the vapor results. 3.3. Hydrogen Bonds in Substituted Benzoic Acids. Enthalpies of intermolecular hydrogen bonds, ΔHBH(N−H··· O), ΔHBH(O−H···O), and ΔHBH(N−H···N) were calculated before for several organic crystalline compounds, using the following approach that was also used in this study.7,9,10,24−29 Comparing the enthalpies of sublimation of the parent acid and of the related methyl ester, at T = 298.15 K, ΔHBH may be determined accordingly to eq 8. In this equation the parameter B symbolizes the mean increment in the enthalpy of

Table 4. Temperatures, Molar Enthalpies, and Entropies of Fusion of the Compounds Studied Ttp K

Tfusa K

p(T)b,c Pa

338.2 ± 0.8 25.08 ± 0.01

338.9 335.2 ± 0.3

22.31 ± 0.01

335.6 369.4 ± 0.6

93.75 ± 0.01

369.2 366.0 ± 0.2 365.3

16.26 ± 0.02

Δ1crHom(T)c kJ·mol

−1

Δ1crSom(T)c,d −1

−1

J·K ·mol

Methyl p-Cyanobenzoate 64.4 ± 0.9 21.8 ± 0.3a 20.7 ± 0.1d 61.1 ± 0.4 Methyl p-Formylbenzoate 21.4 ± 0.2a 63.8 ± 0.6 21.7 ± 0.1d 64.7 ± 0.4 Methyl p-Nitrobenzoate 24.4 ± 0.4a 66.1 ± 1.1 24.7 ± 0.3d 67.0 ± 0.8 Methyl p-(Methylamino)benzoate 27.5 ± 0.2a 75.1 ± 0.6 28.0 ± 0.3d 76.6 ± 0.8

Δ1crHom(298.15 K)d kJ mol−1

method

20.0 ± 0.3a 19.4 ± 0.4d

DSC vapor pressure measurements

19.8 ± 0.2a 19.9 ± 0.2d


21.1 ± 0.4a 21.4 ± 0.6d


24.3 ± 0.2a 24.4 ± 0.8d


The uncertainties assigned are expanded uncertainties (k = 2). bUncertainty estimated accordingly to the uncertainty of the results of Δgcr,1Gom presented in Table 3. cT stands for the temperature of fusion or the temperature of the triple point. dUncertainties calculated through the RSS method. a

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symmetry,32 forming one O−H···O bond per molecule with l(O−H···O) = 266 pm.32 Later, Thakur and Singh reported a high resolution experimental X-ray charge density study performed on p-nitrobenzoic acid and revealed that the carboxylic acid O−H···O dimer units arrange in one-dimensional zigzag chains held together by other dimers (C−H··· O).33 Taking into account the published crystal structure data of methyl p-nitrobenzoate,34 it is possible to notice that this ester also presents weak intermolecular C−H···O hydrogenbonding interactions but does not form any O−H···O hydrogen bond. Therefore, the enthalpy of the intermolecular hydrogen bond O−H···O per molecule of NBA was calculated as ΔHBH = 26.7 ± 0.8 kJ·mol−1, inserting in eq 8 the value B = (6.10 ± 0.27) kJ·mol−1, and the results of ΔgcrHom(298.15 K) of methyl p-nitrobenzoate (Table 3) and of NBA.31 Hydrogen Bonds in p-Formylbenzoic Acid. FBA may exist in two crystalline forms. Form I is stable at low temperature but transforms into form II at about 140 °C.35 The structure of form I involves a dimer linked by O−H···O hydrogen bonds between carboxylic groups, which are held together by C−H··· O interactions.35 No crystal structure data of methyl pformylbenzoate was found in the literature, but we assumed that the intermolecular interactions, with the exception of hydrogen bonding, are identical in the methyl benzoate and in the parent acid. Thus, the value ΔHBH = 24.6 ± 1.5 kJ·mol−1 was calculated by introducing in eq 8 the values of ΔgcrHom(298.15 K) of methyl p-formylbenzoate (Table 3) and of FBA.36 Hydrogen Bonds in p-(Methylamino)benzoic Acid. The reported crystal structure of this substituted benzoic acid reveals that “the asymmetric unit of p-(methylamino)benzoic acid contains three crystallographically independent molecules”.37 These three molecules all form O−H···O hydrogen bonded dimers, between molecules lying about inversion centers, forming eight-membered rings. Furthermore, N−H··· O hydrogen bonding and C−H···π interactions reinforce the crystalline packing.37 Therefore, the crystals of this compound present one O−H···O and half N−H···O intermolecular hydrogen bonds per molecule. The crystal structure of methyl p-(methylamino)benzoate was not found in the literature but we assumed that only the N−H···O intermolecular hydrogen bond (half per molecule) exists in the crystalline packing of this compound. So, the enthalpy of the mean intermolecular hydrogen bond O−H···O (of the three independent molecules with different O−H···O lengths l1 = 266.1 pm, l2 = 262.7 pm, and l3 = 267.8 pm) in p-(methylamino)benzoic acid was calculated using eq 8 as ΔHBH = 22.4 ± 0.6 kJ·mol−1. Comparing to the results of ΔHBH estimated for the other benzoic acids and for methyl p-hydroxybenzoate (Table 5), this latter value is somewhat lower seeming to indicate that the N− H···O intermolecular hydrogen bond weakens the O−H···O hydrogen bonded dimers. 3.4. Estimation of Sublimation Properties of Substituted Benzenes. A recent study for estimating vapor pressures and enthalpies of sublimation of substituted benzenes that considers the influence of 30 different substituents proposes eq 11 and eq 12, respectively, for these estimations.11 The influence of each substituent was estimated taking into account the sublimation results of those thermodynamic properties of ca. 240 substituted benzenes. The database that supports the estimation method contains also the groups of substitued benzenes studied in the present work: 48 compounds substituted with nitro, 20 compounds with methyl

sublimation of a crystalline compound when a non-H-bonding hydrogen atom is substituted by a methyl group. ΔHBH = Δcrg Hmo (parent acid) − Δcrg Hmo (methyl ester) + B (8)

Equation 8 may be derived from eqs 9 and 10, where the parameter A refers to the contribution of the common intermolecular interactions (i.e., discounting those due to hydrogen bonding or included in the parameter B) to the enthalpy of sublimation of the acid or of the corresponding methyl ester, presumed to be identical in both. Δcrg Hmo(parent acid) = A + ΔHBH

(9)

Δcrg Hmo(methyl ester) = A + B

(10)

Hydrogen Bonds in p-Cyanobenzoic Acid. Accordingly to crystal structure data, the molecules of this compound (CNBA) are linked by O−H···O hydrogen bonds forming dimers, which are gathered together via antiparallel contacts of the cyano groups.30 Thus, the intermolecular interactions related to the crystalline packing of CNBA include one O−H···O bond per molecule, with l(O−H···O) = 261 pm.30 To the best of our knowledge no crystal structure data of methyl p-cyanobenzoate has been reported in the literature. Assuming that with the exception of hydrogen bonding all other intermolecular forces existing in the crystalline packing of this compound are similar to those present in the parent acid, the enthalpy of the intermolecular hydrogen bond O−H···O in CNBA was calculated using eq 8. By introducing in this equation the value B = (6.10 ± 0.27) kJ·mol−1, determined accordingly to a recent estimation,11 and the results of ΔgcrHom(298.15 K) of methyl p-cyanobenzoate (Table 3) and of the parent acid,31 the value ΔHBH = 27.4 ± 0.5 kJ·mol−1 reported in Table 5 was calculated. Hydrogen Bonds in p-Nitrobenzoic Acid. Sakore and Pant32 determined the crystal structure of p-nitrobenzoic acid and concluded that the molecules of p-nitrobenzoic acid (NBA) are O−H···O hydrogen bonded in pairs across a center of Table 5. Enthalpies of Intermolecular Hydrogen Bond OH··· O compound benzoic acid p-methylbenzoic acid p-(dimethylamino)benzoic acid p-fluorobenzoic acid p-chlorobenzoic acid p-bromobenzoic acid p-iodobenzoic acid methyl p-hydroxybenzoate p-cyanobenzoic acid p-formylbenzoic acid p-nitrobenzoic acid p-(methylamino)benzoic acid mean

ΔgcrHom(298.15 K)

ΔHBH(crystal)

kJ·mol−1

kJ·mol−1

111.2 109.8 116.6 123.9

± ± ± ±

0.4e 1.5g 0.6e 0.4e

24.9 23.5 25.5 26.1 27.1 25.8 22.7 26.5 27.4 24.6 26.7 22.4 25.8

± ± ± ± ± ± ± ± ± ± ± ± ±

0.5a 0.6a 0.5a 0.9b 0.7b 0.7b 0.9b,c 0.7d 0.5f 1.5f 0.8f 0.6c,f 1.2

a

Corrected in this work from the value reported in ref 7 considering the estimated value B = (6.10 ± 0.27) kJ·mol−1. bCorrected in this work from the value reported in ref 9 considering the estimated value B = (6.10 ± 0.27) kJ·mol−1. cValue not included in the calculation of the mean value. dReference 10. eReference 31. fThis work. gReference 36. 1018



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Table 6. Experimental and Estimated Results of Standard Gibbs Energy and of Enthalpy of Sublimation of the Four Methyl Benzoates Studied in This Work ΔgcrGom(298.15 K)

ΔgcrHom(298.15 K)

−1

kJ·mol−1

kJ·mol compound methyl methyl methyl methyl

exp.

p-cyanobenzoate p-formylbenzoatec p-nitrobenzoate p-(methylamino)benzoate

31.29 30.96 35.55 41.21

± ± ± ±

0.01 0.01 0.03 0.04

est. (eq 11)a

exp.

est. (eq 12)b

± ± ± ±

89.9 ± 0.1 91.3 ± 0.1 96.0 ± 0.5 107.6 ± 0.3

91.8 ± 2.1 99.2 ± 2.4 98.2 ± 1.8 105.1 ± 2.4

32.7 35.7 36.6 40.7

1.2 1.2 1.0 1.2

a

Uncertainties calculated from the uncertainties described in eq 11 using the root-sum-square method. bUncertainties calculated from the uncertainties described in eq 12 using the root-sum-square method. cThe differences between the estimated and experimental values are a consequence of the contributions assigned to the formyl group that were derived before from the experimental results of only two compounds.11

of the contributions of this substituent for the referred to above estimation scheme.

ester, seven with cyano, and only two with formyl, and two with methylamino substituents.11 To test the contributions assigned before for these four substituents and also for checking their eventual interactions in the para position, the standard Gibbs energies and enthalpies of sublimation of the methyl benzoates studied were estimated using eq 11 and eq 12 and compared with the results determined experimentally.

■

* Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00978. Table S1 presents the areas and Clausing factors of the effusion orifices used in the Knudsen effusion study; Table S2 reports the effusion vapor pressures of crystalline methyl p-(methylamino)benzoate determined using each of the nine effusion orifices; Table S3 reports heat capacities in the gaseous phase of the four methyl benzoates studied in this work (PDF)

Δcrg Gmo (298.15K)/kJ ·mol−1 = −(11.5 ± 0.7) + (0.056 ± 0.003)(Tfus/K) +

∑ ni ·gi + ∑ nx ·xG(R /R ) + ∑ ny ·yG(R /R ) j

k

j

k

(11)

Δcrg Hmo (298.15K)/kJ ·mol−1

■

= (40.0 ± 1.5) + (0.031 ± 0.005)(Tfus/K) +

∑ ni . hi + ∑ nx ·x H(R /R ) + ∑ ny ·y H(R /R ) j

k

j

ASSOCIATED CONTENT

S

AUTHOR INFORMATION

Corresponding Author

k

*E-mail: [email protected].

(12)

Funding

In eqs 11 and 12, gi and hi correspond to the contribution of each substituent i, respectively, to [Δcrg Gmo (298.15K) − 0.056(Tfus/K)] and to [ΔgcrHom(298.15 K) − 0.031(Tfus/K)], and ni refers to their number. The symbols xG(Rj/Rk) and xH(Rj/Rk) refer to the contributions of eventual interactions between the substituents Rj and Rk in ortho positions, and nx signifies the number of these interactions (in the compounds studied in this work, nx = 0). YG(Rj/Rk), yH(Rj/Rk) and ny have comparable connotations for substituent groups in the para position to each other. Comparison of the experimental and estimated results (with yG(Rj/Rk) = yH(Rj/Rk) = 0) indicates the absence of significant para effects between the methyl ester group and the substituents cyano, nitro, and methylamino. Table 6 presents the experimental and estimated results of standard Gibbs energy and enthalpy of sublimation, at T = 298.15 K, of the methyl p-cyano, p-formyl, p-nitro, and p-(methylamino) benzoates studied in this work. It is possible to notice that, except for methyl p-formylbenzoate, the values of the referred thermodynamic properties estimated by eqs 11 and 12 are in good agreement with the ones determined experimentally in the present work. However, the contributions assigned to the formyl group,11 gi = 14.72 ± 0.88 kJ mol−1 and hi = 23.8 ± 1.8 kJ mol−1, were derived from sublimation results of only two compounds (3- and 4-hydroxybenzaldehyde).38 Considering the discrepancy observed between the experimental and estimated values of methyl p-formylbenzoate it looks necessary to study the sublimation of other substituted benzenes containing the formyl group in order to check the reliability

Thanks are due to Fundaçaõ para a Ciência e Tecnologia (FCT), Lisbon, Portugal, for the financial support to Project UID/QUI/0081/2015 and to FEDER (COMPETE 2020) for the financial support to Project POCI-01-0145-FEDER006980. A.R.R.P.A also thanks FCT, Operational Program and European Union for the award of the postdoctoral fellowship (SFRH/BPD/97046/2013). Notes

The authors declare no competing financial interest.

■

REFERENCES

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Vapor Pressures of Four Methyl Esters of Substituted Benzoic Acids

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