Heat Capacity Measurements of 13 Methyl Esters of n-Carboxylic

caprate and methyl laurate at pressures up to 16.2 MPa. Xiangyang Liu , Chenyang Zhu , Chao Su , Maogang He , Wei Dong , Tansu Shang , Weiping Yan...
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J. Chem. Eng. Data 2004, 49, 1036-1042

Heat Capacity Measurements of 13 Methyl Esters of n-Carboxylic Acids from Methyl Octanoate to Methyl Eicosanoate between 5 K and 350 K Mark J. van Bommel,† Harry A. J. Oonk, and J. Cees van Miltenburg* Chemical Thermodynamics Group, Debye Institute, Utrecht University, Padualaan 8, 3584-CH Utrecht, The Netherlands

Molar heat capacities of 13 methyl esters of the linear carboxylic acids from methyl octanoate to methyl eicosanoate were measured from 5 K to 350 K. The derived thermodynamic functions Sabs,m(T) and Hm(T) - H(0) were calculated. A correlation function for the absolute entropy at 298.15 K was found to be Sabs(n,298.15 K) ) {215.94 + 31.517n} J‚K-1‚mol-1, with n being the number of carbon atoms in the parent carboxylic acid minus one. The heat capacity of the liquid phases in the temperature range of 250 K to 350 K can be described by Cp(n,T) ) {103.16 + 16.273n + 0.04735n(T/K)} J‚K-1‚mol-1, with a mean absolute percentage deviation of 0.3%.

Introduction In this article, we report on the measurement of the molar heat capacity of 13 methyl esters of the normal carboxylic acids with a chain length of 8-20 carbon atoms in the fatty acid group. The measurements were made using adiabatic calorimetry. This work was part of a thesis1 of one of us (van Bommel) who finished this work in 1986. The data collected were only published in the thesis, and in order to make them more generally available, we present here the data in a concise form. The methyl ester of the carboxylic acids form a homologous series which allowed us to look for relations within the series, like the dependence of the absolute entropy and the heat capacity of the liquid phase, on the chain length. The vapor pressure of these liquid esters was published before.2 The methyl esters form an important group of organic compounds that are used in the production of very different derivatives, often they replace fatty acids in the production.3,4 Experimental Section The samples used were purchased from MERCK. The compounds were readily available as they are used as gasliquid chromatography references. Because of the high purity of the samples, no attempt was made to purify them further; the stated purity and the masses used in the calorimeter are given in Table 1. The adiabatic calorimeter used (laboratory design number CALV) was described before.5,6 Samples were transferred to the gold-plated sample container and degassed in a vacuum. Before closing the vessel, a helium pressure of about 5 kPa was admitted in order to improve the heat conduction within the vessel. Temperatures were measured using an automated ASL bridge;7 the thermometer was calibrated by Oxford Instruments to 0.001 K on the International Practical Temperature Scale of 1968. The performance of the calorimeter * To whom correspondence may be addressed. E-mail: miltenb@ chem.uu.nl. † Present address: Philips Research, Jan Campertstraat 5, 6416 SG Heerlen, The Netherlands.

Table 1. Purity of the Compounds as Stated by the Manufacturer and Masses Used in the Calorimetric Experiments compound

purity/mass %

used mass/g

methyl octanoate methyl nonanoate methyl decanoate methyl undecanoate methyl dodecanoate methyl tridecanoate methyl tetradecanoate methyl pentadecanoate methyl hexadecanoate methyl heptadecanoate methyl octadecanoate methyl nonadecanoate methyl eicosanoate

99.8 99.7 99.8 99.5 99.5 99.9 99.5 99.6 99.3 99.0 99.0 99.7 99.1

4.99 5.56 6.83 6.03 4.50 7.67 6.92 6.92 4.61 7.87 3.78 7.41 3.56

was checked with n-heptane and synthetic sapphire;8 no deviations from the recommended values larger than 0.2% were found. The methyl esters of the carboxylic acids do show polymorphic behavior and to exclude or minimize effects caused by the thermal history, all samples were treated in the same way. First they were cooled to about 80 K using liquid nitrogen in the cryostat, and then a slow measurement was made with a mean heating rate of about 1.4 K‚h-1 to (2 or 3) K below the melting point. At that temperature, the samples were equilibrated for 24 h. In this first heating experiment, some metastability, in the form of a slightly higher heat capacity than in the subsequent measurements and some irregularities, could be detected in methyl tridecanoate, methyl pentadecanoate, and methyl heptadecanoate. After equilibrating the samples close to the melting temperature, these effects have disappeared in the following runs. Subsequently the samples were cooled in a period of 36 h to a temperature of 5 K. Below 80 K, a heater on time was used, which resulted in a temperature rise of 2 K per measurement; the stabilization time used was on the order of 600 s. Above 80 K, a stabilization time of 2000 s and an input time of 1500 s were used. Under these measurement conditions, the melting process generally took 24 h.

10.1021/je0499364 CCC: $27.50 © 2004 American Chemical Society Published on Web 06/16/2004

Journal of Chemical and Engineering Data, Vol. 49, No. 4, 2004 1037 Table 2. Thermodynamic Properties of Methyl Octanoate at Selected Temperatures (M ) 158.24 g·mol-1) T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

5 10 20 30 40 50 60 70 80 90 100 110

0.38 3.03 18.19 33.71 50.53 66.36 79.75 92.33 103.39 113.40 122.25 131.10

0.13 1.04 7.36 17.65 29.66 42.67 56.01 69.26 82.28 95.04 107.48 119.57

0.48 7.65 107.6 366 788 1374 2108 2968 3945 5030 6211 7480

120 130 140 150 160 170 180 190 200 210 220 230

138.74 146.18 153.44 160.31 167.13 174.18 181.34 188.84 196.94 205.99 217.68 242.75

131.31 142.71 153.81 164.63 175.20 185.53 195.69 205.69 215.58 225.99 235.24 245.34

8830 10255 11753 13322 14959 16664 18442 20292 22220 24234 26349 28621

240 250 260 270 280 290 300 310 320 330 340 350

301.67 301.39 303.17 305.83 308.83 312.81 316.17 320.13 323.19 327.93 332.21 336.19

366.89 379.17 391.02 402.52 413.69 424.59 435.25 445.67 455.9 465.92 475.77 485.46

57286 60294 63317 66362 69435 72543 75688 78870 82086 85342 88643 91985

Table 3. Thermodynamic Properties of Methyl Nonanoate at Selected Temperatures (M ) 172.27 g·mol-1) T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

5 10 20 30 40 50 60 70 80 90 100 110

0.39 2.96 17.17 34.66 53.39 71.31 86.46 100.55 113.08 123.98 134.32 143.79

0.13 1.03 7.11 17.30 29.83 43.70 58.06 72.47 86.73 100.68 114.30 127.55

0.48 7.69 103.6 361 801 1426 2216 3152 4222 5407 6701 8092

120 130 140 150 160 170 180 190 200 210 220 230

152.28 160.47 168.48 175.96 183.23 190.85 198.49 206.56 215.27 224.62 236.53 265.31

140.43 152.94 165.13 177.01 188.61 199.93 211.06 222.00 232.82 243.54 254.26 265.22

9572 11136 12782 14504 16301 18170 20116 22142 24250 26449 28751 31219

240 250 260 270 280 290 300 310 320 330 340 350

330.80 330.84 333.42 335.90 338.72 342.82 346.27 350.79 354.3 359.10 363.82 368.16

395.87 409.95 422.98 435.62 447.87 459.82 471.49 482.91 494.10 505.08 515.87 526.47

61702 65148 68471 71816 75188 78595 82040 85526 89051 92618 96232 99892

Table 4. Thermodynamic Properties of Methyl Decanoate at Selected Temperatures (M ) 186.29 g·mol-1) T K 5 10 20 30 40 50 60 70 80 90 100 110

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 0.45 3.70 20.01 37.87 57.28 75.63 91.46 105.95 119.09 131.08 141.62 151.65

0.15 1.12 8.17 19.64 33.19 47.99 63.18 78.38 93.41 108.15 122.53 136.52

H(T) - H(0)

T

J‚mol-1

K

0.56 8.36 119.6 408 884 1550 2386 3374 4501 5754 7120 8588

120 130 140 150 160 170 180 190 200 210 220 230

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 160.63 169.23 177.35 185.25 192.99 200.77 209.01 217.44 226.26 234.91 245.06 256.05

150.10 163.30 176.14 188.64 200.86 212.79 224.50 235.02 247.40 258.65 269.81 280.93

H(T) - H(0)

T

J‚mol-1

K

10150 11799 13532 15345 17238 19206 21256 23387 25606 27913 30311 32814

240 250 260 270 280 290 300 310 320 330 340 350

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 269.17 300.63 540.13 361.09 368.72 372.12 376.14 380.31 385.19 389.78 394.95 400.20

292.11 303.61 320.00 465.32 478.68 491.68 504.36 516.77 528.93 540.85 552.56 564.07

H(T) - H(0) J‚mol-1 35440 38258 41290 80090 83762 87467 91208 94992 98821 102695 106620 110592

Table 5. Thermodynamic Properties of Methyl Undecanoate at Selected Temperatures (M ) 200.32 g·mol-1) T K 5 10 20 30 40 50 60 70 80 90 100 110

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 0.42 3.28 18.49 38.09 59.59 80.21 97.96 113.74 128.03 141.39 152.92 163.81

0.14 1.12 7.63 18.72 32.61 48.17 64.37 80.66 96.83 112.68 128.19 143.29

H(T) - H(0)

T

J‚mol-1

K

0.52 8.36 110.9 391 879 1580 2471 3530 4742 6089 7563 9147

120 130 140 150 160 170 180 190 200 210 220 230

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 173.57 182.89 191.72 200.53 209.38 217.78 226.50 235.38 244.52 253.93 264.97 276.95

Results and Discussion In Tables 2-14, the molar heat capacity data, the absolute entropy, and the enthalpy difference with reference to 0 K are given at selected temperatures between 5 K and 350 K. These data were calculated from the total measuring sets by extrapolating the heat capacity values below 15 K according to the Debye low-temperature limit

157.96 172.23 186.11 199.63 212.87 225.81 238.50 250.00 263.29 275.45 287.51 299.55

H(T) - H(0)

T

J‚mol-1

K

10835 12617 14491 16451 18503 20638 22859 25169 27568 30060 32654 35363

240 250 260 270 280 290 300 310 320 330 340 350

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 291.77 320.50 576.88 395.83 398.95 402.95 406.99 411.22 416.08 421.78 426.55 431.52

311.64 324.01 340.00 494.94 509.40 523.47 537.18 550.60 563.73 576.61 589.27 601.73

H(T) - H(0) J‚mol-1 38203 41235 43904 85677 89654 93662 97708 101798 105936 110128 114370 118660

Cp ) RT3 and using the value of R to calculate starting values for a numerical calculation of S and H(T) - H(0). The numerical calculation was performed on a data set obtained from the experimental set by using a cubic spline interpolation method. All compounds showed an increase in the molar heat capacity when nearing the melting point, larger than could be explained by premelting due to impurities. This in-

1038 Journal of Chemical and Engineering Data, Vol. 49, No. 4, 2004

Figure 1. Molar heat capacity of methyl octadecanoate around the melting point showing the anomalous increase of the heat capacity. The solid lines were used as baselines for the calculation of the enthalpy of fusion. See text for the dashed line. Table 6. Thermodynamic Properties of Methyl Dodecanoate at Selected Temperatures (M ) 214.35 g·mol-1) T K 5 10 20 30 40 50 60 70 80 90 100 110

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 0.50 4.31 19.62 40.21 63.08 85.07 103.02 119.02 134.57 148.81 160.46 171.83

0.17 1.33 8.52 20.22 34.91 51.39 68.57 85.73 103.76 119.42 135.69 151.52

H(T) - H(0)

T

J‚mol-1

K

0.62 9.95 122 418 934 1677 2622 3738 5014 6430 7975 9638

120 130 140 150 160 170 180 190 200 210 220 230

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 181.94 191.82 201.16 209.76 218.85 227.97 237.26 246.66 256.21 265.84 277.21 288.57

166.91 181.87 196.43 210.61 224.46 238.00 251.30 264.37 277.27 290.00 302.62 315.19

H(T) - H(0)

T

J‚mol-1

K

11406 13276 15241 17297 19444 21678 24005 26424 28938 31548 34260 37090

240 250 260 270 280 290 300 310 320 330 340 350

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 299.95 315.69 335.52 392.98 428.00 432.76 438.82 443.32 448.38 453.83 460.08 467.86

327.72 340.29 353.03 366.39 535.85 551.59 566.39 580.85 595.01 608.89 622.53 635.95

H(T) - H(0) J‚mol-1 40033 43115 46364 49905 97029 101511 105869 110280 114738 119249 123819 128458

Table 7. Thermodynamic Properties of Methyl Tridecanoate at Selected Temperatures (M ) 228.37 g·mol-1) T K 5 10 20 30 40 50 60 70 80 90 100 110

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 0.53 4.03 19.77 41.39 65.69 89.16 108.80 127.88 144.45 158.95 171.63 183.91

0.16 1.28 8.36 20.31 35.52 52.75 70.79 88.99 107.13 124.91 142.28 159.22

H(T) - H(0)

T

J‚mol-1

K

0.6 10.58 120 422 957 1734 2726 3909 5269 6781 8430 10209

120 130 140 150 160 170 180 190 200 210 220 230

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 195.21 205.64 215.67 225.37 234.95 244.50 254.10 264.04 274.24 284.88 296.06 307.94

crease, leading to a positive second derivative of the heat capacity, started already at about (100 to 50) K below the melting point. In Figure 1, this effect is illustrated for methyl octadecanoate. Similar effects have been reported before, for instance in the n-paraffines,9 the linear carboxylic acids,10,11 and the normal hydrocarbons,12 where it was explained to be due to an increasing randomization of orientation about the stretched length of the molecule. The enthalpy of fusion of the compounds was calculated by using a linear fit of the solid heat capacity between (150 to 100) K before the melting point as a baseline, together with a fit of the heat capacity of the liquid, using data between (10 to 20) K above the melting point. These fits are shown in Figure 1 for methyl octadecanoate as solid lines. The dashed line, the fit of the heat capacity close to the melting point, is discussed in the comparison of the

175.72 191.76 207.37 222.58 237.43 251.96 266.21 280.21 294.01 307.65 321.16 334.58

H(T) - H(0)

T

J‚mol-1

K

12105 14110 16217 18422 20724 23121 25614 28205 30896 33691 36595 39614

240 250 260 270 280 290 300 310 320 330 340

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1

H(T) - H(0) J‚mol-1

321.07 336.07 350.98 371.61

347.96 361.36 374.82 388.43

42759 46044 49476 53083

463.91 469.05 473.89 479.30 485.18 491.82

584.21 600.01 615.47 630.59 645.43 660.01

108019 112680 117394 122159 126981 131868

enthalpies of fusion with the literature data. The result of these calculations and the end temperatures of the fusion are given in Table 15. These temperatures are not the triple-temple temperatures often reported in adiabatic calorimetry. As the plots of the reciprocal of the melted fraction against the equilibrium temperatures in the melt did not result in straight lines, the fractional melting method based on the van’t Hoff relation could not be used. There are two possible explanations for this, one being that the impurity does not form a eutectic system with the main component, the second one being that a possible phase transition is hidden in the melting process. We did not observe any anomaly in the heat capacity curves near the melting point; small exothermic effects however were seen in the stabilization periods at about (2 or 3) K below the end melting point. Aleby13 described phase transitions in

Journal of Chemical and Engineering Data, Vol. 49, No. 4, 2004 1039 Table 8. Thermodynamic Properties of Methyl Tetradecanoate at Selected Temperatures (M ) 242.40 g·mol-1) T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

5 10 20 30 40 50 60 70 80 90 100 110

0.55 4.56 21.34 43.99 69.20 93.62 113.90 133.41 150.35 165.54 179.38 192.06

0.18 1.46 9.38 22.18 38.26 56.37 75.32 94.38 113.34 131.92 150.09 167.80

0.68 10.93 134.7 458 1023 1839 2882 4121 5542 7122 8848 10707

120 130 140 150 160 170 180 190 200 210 220 230

203.55 214.52 224.93 235.23 244.79 254.91 265.19 275.63 286.07 296.67 308.85 321.05

185.01 201.74 218.02 233.89 249.38 264.52 279.39 294.00 308.41 322.62 336.69 350.68

12685 14776 16973 19274 21675 24173 26774 29478 32287 35201 38225 41373

240 250 260 270 280 290 300 310 320 330 340 350

334.49 349.48 368.64 388.14 429.30

364.62 378.57 392.64 406.90 421.61

44650 48067 51655 55435 59480

500.03 504.66 510.00 515.86 522.03 528.04

624.53 641.00 657.11 672.89 688.38 703.60

118932 123954 129028 134156 139345 144580

Table 9. Thermodynamic Properties of Methyl Pentadecanoate at Selected Temperatures (M ) 256.43 g·mol-1) T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

5 10 20 30 40 50 60 70 80 90 100 110

0.50 4.15 21.13 43.92 71.36 97.58 120.37 141.42 159.35 175.80 190.15 203.86

0.17 1.34 8.62 21.10 37.46 56.30 76.10 96.26 116.32 136.02 155.28 174.06

0.63 10.05 125 441 1016 1865 2954 4265 5769 7444 9273 11244

120 130 140 150 160 170 180 190 200 210 220 230

216.45 228.03 239.15 249.97 260.57 272.29 282.10 293.10 304.43 316.28 328.72 341.80

192.35 210.13 227.44 244.31 260.78 276.90 292.71 308.26 323.58 338.72 353.71 368.61

13347 15570 17906 20352 22904 25564 28330 31206 34193 37297 40521 43873

240 250 260 270 280 290 300 310 320 330 340

355.90 371.28 387.35 403.92 432.13 740.09 524.33 534.12 539.26 544.80 551.15

383.45 398.28 413.16 428.06 443.24 458.95 655.54 672.98 690.02 706.70 723.05

47360 50994 54788 58735 62911 67386 125101 130483 135850 141270 146750

Table 10. Thermodynamic Properties of Methyl Hexadecanoate at Selected Temperatures (M ) 270.45 g·mol-1) T K 5 10 20 30 40 50 60 70 80 90 100 110

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 0.66 5.56 23.70 47.98 75.87 104.12 129.69 151.19 167.13 184.19 198.32 213.49

0.22 1.76 10.48 24.47 42.05 62.04 83.35 105.13 126.24 146.91 167.01 186.66

H(T) - H(0)

T

J‚mol-1

K

0.83 13.20 149 503 1120 2021 3194 4610 6193 7949 9858 11921

120 130 140 150 160 170 180 190 200 210 220 230

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 226.50 238.62 250.27 261.54 272.73 284.03 295.27 306.80 318.65 330.97 343.93 357.74

205.81 224.42 242.54 260.19 277.43 294.30 310.85 327.12 343.16 359.00 374.70 390.29

H(T) - H(0)

T

J‚mol-1

K

14123 16449 18894 21453 24125 26908 29804 32814 35941 39189 42564 46072

240 250 260 270 280 290 300 310 320 330 340 350

Cp,m

∆Sm

H(T) - H(0)

J‚K-1‚mol-1 J‚K-1‚mol-1 372.37 388.24 405.39 423.81 448.60 482.70 740.48 570.55 576.47 583.02 590.14 597.66

J‚mol-1

405.82 421.33 436.89 452.54 468.38 484.81 505.58 708.87 727.67 746.08 764.13 781.86

49721 53522 57490 61636 65993 70668 76774 138668 144404 150201 156066 162005

Table 11. Thermodynamic Properties of Methyl Heptadecanoate at Selected Temperatures (M ) 284.48 g·mol-1) T K 5 10 20 30 40 50 60 70 80 90 100 110

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 0.56 4.36 23.27 48.82 77.97 106.88 131.71 154.68 175.53 192.90 208.51 224.09

0.20 1.56 10.05 24.13 42.13 62.67 84.44 106.58 128.63 150.31 171.45 192.08

H(T) - H(0)

T

J‚mol-1

K

0.73 11.70 145 500 1133 2059 3257 4696 6350 8193 10201 12367

120 130 140 150 160 170 180 190 200 210 220 230

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 238.40 252.69 265.74 275.72 284.57 302.09 313.76 326.38 340.04 355.66 367.89 382.88

the methyl esters which he observed using a temperatureprogrammable X-ray powder diffraction camera. If the observed exothermic effect were the onset of a transition to a more stable crystal form, this transition is extremely slow, and in that case, the data reported in this publication were measured on a metastable phase. In practice however, this will be the phase most likely to occur.

212.23 231.88 251.06 269.67 287.87 305.64 323.23 340.53 357.50 374.47 391.26 407.90

H(T) - H(0)

T

J‚mol-1

K

14684 17140 19730 22428 25250 28181 31259 34461 37769 41248 44859 48603

240 250 260 270 280 290 300 310 320 330 340 350

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 399.49 418.37 438.62 456.93 480.24 517.76 980.45 599.17 605.44 609.25 615.40 622.81

424.55 441.22 458.02 474.93 491.94 509.36 528.34 746.03 764.27 782.96 802.10 820.06

H(T) - H(0) J‚mol-1 52514 56600 60882 65363 70042 75007 80605 147001 152746 158820 165221 171411

The melting points clearly show an even-odd effect; in Figure 2, the melting points of the even and odd compounds are plotted. Comparison with the Literature. Literature data for the heat capacity and derived properties of the methyl esters on which we report here are scarce. For methyl octanoate, two sources are available17,18 for the heat

1040 Journal of Chemical and Engineering Data, Vol. 49, No. 4, 2004 Table 12. Thermodynamic Properties of Methyl Octadecanoate at Selected Temperatures (M ) 298.50 g·mol-1) T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

5 10 20 30 40 50 60 70 80 90 100 110

0.82 5.96 26.20 52.72 82.60 112.11 137.80 162.71 182.89 201.46 217.35 234.15

0.28 2.20 12.05 27.52 46.74 68.38 91.14 114.27 137.22 159.90 181.95 203.49

0.93 16.49 168 599 1234 2210 3462 4966 6686 8614 10709 12970

120 130 140 150 160 170 180 190 200 210 220 230

248.17 261.72 274.54 286.99 299.33 312.93 327.18 341.65 354.70 368.18 382.77 397.82

224.83 244.83 264.69 284.06 302.97 321.50 339.81 357.91 375.77 393.93 410.86 428.20

15377 17927 20608 23416 26348 29403 32609 35965 39438 43052 46806 50708

240 250 260 270 280 290 300 310 320 330 340 350

413.11 428.51 446.92 468.64 497.34 541.05 696.62

445.45 462.63 479.77 497.03 514.58 532.70 552.91

54763 58971 63342 67917 72743 77908 83874

639.00 646.44 655.14 664.03

792.61 812.38 831.80 850.92

159212 165638 172153 178743

Table 13. Thermodynamic Properties of Methyl Nonadecanoate at Selected Temperatures (M ) 312.53 g·mol-1) T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

T

Cp,m

∆Sm

H(T) - H(0)

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

K

J‚K-1‚mol-1

J‚K-1‚mol-1

J‚mol-1

5 10 20 30 40 50 60 70 80 90 100 110

0.69 5.10 26.27 55.13 87.37 117.80 143.77 168.98 190.79 210.18 228.66 244.31

0.23 1.85 11.96 27.91 48.15 70.82 94.67 118.77 142.79 166.39 189.53 212.06

0.89 13.90 171 574 1285 2308 3619 5186 6988 8993 11190 13557

120 130 140 150 160 170 180 190 200 210 220 230

259.07 273.22 286.84 300.17 313.53 327.31 339.52 353.20 367.35 380.94 397.52 413.93

233.96 255.26 276.01 296.25 316.04 335.43 354.46 373.18 391.66 409.91 428.02 446.04

16074 18734 21536 24471 27539 30737 34068 37531 41133 44875 48768 52825

240 250 260 270 280 290 300 310 320 330 340 350

432.32 450.65 469.65 491.94 518.01 549.43 586.63

464.04 482.07 500.10 518.24 536.60 555.29 574.53

57053 61470 66067 70874 75924 81252 86928

691.61 677.17 684.76 693.78

829.73 850.79 871.12 891.09

166761 173605 180415 187307

Table 14. Thermodynamic Properties of Methyl Eicosanoate at Selected Temperatures (M ) 326.56 g·mol-1) T K 5 10 20 30 40 50 60 70 80 90 100 110

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 0.75 5.46 28.85 56.97 89.89 122.31 149.98 176.80 199.80 220.14 235.76 255.12

0.25 2.00 13.00 29.60 50.46 74.05 98.89 124.12 149.20 173.90 198.05 221.50

H(T) - H(0)

T

J‚mol-1

K

0.94 15 186 605 1338 2402 3768 5408 7289 9388 11682 14144

120 130 140 150 160 170 180 190 200 210 220 230

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1 271.01 285.48 299.45 313.11 326.52 339.86 353.31 366.99 381.11 395.71 411.05 427.04

capacity at 298.15 K. These values correspond to our value at that temperature to within 0.3%. For methyl tetradecanoate, one value for the heat capacity at 298.15 K was found;18 the correspondence of our value is within 0.25%. For the enthalpy of fusion and or the melting points, three data sources were found.14-16 The values are given in Table 15. While there is generally a good correspondence in the melting points, the enthalpy of fusion data of the literature are all lower than our values. We think that this can be partly explained by an aforementioned anomalous premelting effect in the compounds. The measurements in the literature were started at a much higher temperature; in ref 15, the starting temperature was 291 K for methyl octadecanoate. This implies that the authors used a baseline for the enthalpy calculation, constructed from the fit of the heat capacity data as given in Figure 1 by the dashed line. When we calculated the enthalpy of fusion using the fit given by the dashed line in Figure 1, the calculated enthalpy was 64 200 J‚mol-1, 2 150 J‚mol-1 lower than our value, and very close to the value of ref 15. So a large part of the differences is due to the way the enthalpy of fusion is defined. A second reason for the differences might be

244.38 266.65 288.33 309.46 330.09 350.29 370.09 389.56 408.74 427.69 446.45 465.07

H(T) - H(0)

T

J‚mol-1

K

16774 19558 22483 25547 28745 32077 35543 39144 42884 46767 50801 54991

240 250 260 270 280 290 300 310 320 330 340 350

Cp,m

∆Sm

J‚K-1‚mol-1 J‚K-1‚mol-1

H(T) - H(0) J‚mol-1

443.77 461.58 480.50 501.55 525.09 551.06 585.33 667.58

483.60 502.07 520.55 539.06 557.71 576.59 595.84 616.03

59344 63871 68582 73486 78617 83997 89676 95838

714.47 722.28 732.20

890.20 911.64 932.71

183976 191159 198432

the annealing of the sample close to the melting point we applied. Without this annealing, we would have measured lower values for those compounds that showed metastability in the freshly crystallized samples. The annealing process was not mentioned in the refs 14 and 15, and this could explain, together with the choice of the baseline, the large differences for some of the compounds. Liquid Heat Capacity and a Correlation for the Absolute Entropy at 298.15 K. The data for the liquid heat capacity of these 13 esters do not show an even-odd effect. This effect is restricted to the solid phase as it is caused by differences in molecular packing. The heat capacity of the liquids can be described as a function of temperature and n, where n is the number of carbon atoms in the molecule in the parent carboxylic acid minus one. This implies that the shortest ester, methyl formate, is taken as the start of the series with n being zero. The correlation function found, optimized by using the Solver option of the Excel program was

Cp(n,T) ) {103.16 + 16.273n + 0.04735n(T/K)} J‚K-1‚mol-1

Journal of Chemical and Engineering Data, Vol. 49, No. 4, 2004 1041

Figure 2. Even and odd effect in the melting points (Tf) of the methyl esters. n is the number of carbon atoms in the parent carboxylic acid minus one.

and undercooled liquids at that temperature. The correlation function found was

Table 15. Melting Temperatures and Enthalpies of Fusion of the Methylesters compound

Tfusion/K

236.20 ( 0.02 236.4 ( 0.1 methyl nonanoate 238.72 ( 0.02 238.8 ( 0.1 methyl decanoate 260.33 ( 0.02 260.4 ( 0.1 methyl undecanoate 261.80 ( 0.02 261.8 ( 0.1 methyl dodecanoate 278.18 ( 0.02 278.2 ( 0.1 methyl tridecanoate 279.07 ( 0.02 278.9 ( 0.1 methyl tetradecanoate 292.14 ( 0.02 292.2 ( 0.1 291.5 ( 0.3 methyl pentadecanoate 292.35 ( 0.02 292.2 ( 0.1 methyl hexadecanoate 302.71 ( 0.02 303.70 ( 0.05 302.2 ( 0.2 methyl heptadecanoate 303.09 ( 0.02 302.8 ( 0.5 methyl octadecanoate 311.84 ( 0.02 312.15 ( 0.05 310.9 ( 0.3 methyl nonadecanoate 311.49 ( 0.02 311.6 ( 0.1 311.8 ( 0.3 methyl eicosanoate 319.48 ( 0.02 320 ( 0.1 319.75 ( 0.05 318.5 ( 0.2

methyl octanoate

∆fusH/J‚mol-1

ref

25636 ( 500 25100 ( 1000 27342 ( 500 27600 ( 1100 35917 ( 500 34300 ( 1300 36204 ( 500 35900 ( 1400 43147 ( 500 43100 ( 1700 45566 ( 500 43300 ( 1700 52008 ( 500 50000 ( 2000 44500 54283 ( 500 48000 ( 1900 60039 ( 500 55400

this work 14 this work 14 this work 14 this work 14 this work 14 this work 14 this work 14 15 this work 14 this work 16 15 this work 14 this work 16 15 this work 14 15 this work 14 16 15

63895 ( 500 66354 ( 500 64400 70925 ( 500 62200 78794 ( 500 73700

This function was derived with 85 data points in the temperature range between 250 K and 350 K, the values of n were 7-19, the absolute mean percentage deviation was 0.3%, and the maximum deviation was 1%. As with all correlation functions, one should be careful if the function is used to calculate heat capacity data outside the mentioned temperature range or is used to extrapolate to esters with other chain lengths. We used this correlation function within these limits to calculate the absolute entropy of the compounds at 298.15 K, taking the experimental values at 340 K as starting points. At that temperature the compounds ranging between methylhexadecanoate and methyleicosonate are in the solid phase, the correlation for the entropy at 298.15 K was made for stable

Sabs(298.15 K) ) {215.94 + 31.517n} J‚K-1‚mol-1 The value of n is the same as that used in the correlation function for the heat capacity of the liquid phase. The standard deviation of this fit was 3.3 J‚K-1‚mol-1; this corresponds to about 0.5%. Literature Cited (1) van Bommel, M. J. Thermodynamic Behaviour of Methyl Esters of Long Chain Linear Carboxylic Acids, Thesis, Utrecht University, 1986. (2) Van Genderen, A. C. G.; van Miltenburg, J. C.; Blok, J. G.; van Bommel, M. J.; van Ekeren, P. J.; van den Berg, G. J. K.; Oonk, H. A. J. Liquid-Vapor Equilibria of the Methyl Esters of Alkanoic Acids: Vapor Pressures as a Function of Temperature and Standard Thermodynamic Function Changes. Fluid Phase Equilib. 2002, 202, 109-120. (3) Sonntag, N. O. V. New Developments in the Fatty Acid Industry. J. Am. Oil Chem. Soc. 1979, 56, 861A-864A. (4) Sonntag, N. O. V. New Developments in the Fatty Acid Industry in America. J. Am. Oil Chem. Soc. 1984, 61, 229-232. (5) van Miltenburg, J. C.; van den Berg, G. J. K.; van Bommel, M. J. Construction of an Adiabatic Calorimeter. Measurement of the Molar Heat Capacity of Synthetic Sapphire and of n-Heptane. J. Chem. Thermodyn. 1987, 19, 1129-1137. (6) van Miltenburg, J. C.; van Genderen, A. C. G.; van den Berg, G. J. K. Design Improvements in Adiabatic Calorimetry. The Heat Capacity of Cholesterol Between 10 and 425 K. Thermochim. Acta 1998, 319, 151-162. (7) Automatic System Laboratories, http://www.asltd.co.uk. (8) Archer, D. G. Thermodynamic Properties of Synthetic Sapphire (R-Al2O3), Standard Reference Material 720 and the Effect of Temperature-Scale Differences on Thermodynamic Properties. J. Phys. Chem. Ref. Data 1993, 22, 1441-1453. (9) Finke, H. C.; Gross, M. E.; Waddington, G.; Huffman, H. M. LowTemperature Thermal Data for the Nine Normal Paraffin Hydrocarbons from Octane to Hexadecane. J. Am. Chem. Soc. 1954, 76, 333-341. (10) Schaake, R. C. F.; van Miltenburg, J. C. Thermodynamic Properties of the Normal Alkanoic Acids. I. Molar Heat Capacities of Seven Odd-Numbered Normal Alkanoic Acids. J. Chem. Thermodyn. 1982, 14, 771-778. (11) Schaake, R. C. F.; van Miltenburg, J. C. Thermodynamic Properties of the Normal Alkanoic Acids. II. Molar Heat Capacities of Seven Even-Numbered Normal Alkanoic Acids. J. Chem. Thermodyn. 1982, 14, 763-769. (12) Ubbelohde, A. R. Melting and Crystal Structure; Clarendon Press, Oxford, 1965. (13) Aleby, S.; von Sydow, E. The Crystal Structure of Methyl Stearate. Acta Crystallogr. 1960, 23, 487-492. (14) Adriaanse, N.; Dekker, H.; Coops, J. Some Physical Constants of Normal Saturated Fatty Acids and Their Methyl Esters. Recl. Trav. Chim. Pays-Bas 1964, 83, 557.

1042 Journal of Chemical and Engineering Data, Vol. 49, No. 4, 2004 (15) King, A. M.; Garner, W. E.; The Heats of Crystallization of Methyl and Ethyl Esters of Monobasic Fatty Acids. J. Chem. Soc. 1936, 1372-1376. (16) Francis, F.; Piper, S. H.; The Higher n-Aliphatic Acids and their Methyl and Ethyl Esters. J. Am. Chem. Soc. 1939, 61, 577-581. (17) Pintos, M; Bravo, R; Baluja, M. C.; Paz Andrade, M. I.; RouxDesgranges, G; Grolier, P. E. Thermodynamics of Alkanoate + Alkane Binairy Mixtures. Concentration Dependence of Excess Heat Capacities and Volumes. Can. J. Chem. 1988, 66, 11791186.

(18) Deshpande, D. D.; Patterson, D.; Andreoli-Ball, L.; Costas, M.; Trejo, M. L. Heat Capacities, Self-Association and Complex Formation in Alcohol-Ester Systems. J. Chem. Soc. Faraday Trans. 1991, 87 (8), 1133-1139.

Received for review February 9, 2004. Accepted April 1, 2004.

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