Additivity of Thermodynamic Properties of Organic Compounds in the

Feb 12, 2002 - Measurement and Prediction of Thermochemical Properties: Improved Increments for the Estimation of Enthalpies of Sublimation and Standa...
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J. Chem. Eng. Data 2002, 47, 239-244

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Additivity of Thermodynamic Properties of Organic Compounds in the Crystalline State. 3. Heat Capacities and Related Properties of Urea Phenyl Derivatives Vladimir V. Diky,† Alexander A. Kozyro,‡ and Gennady J. Kabo* Chemistry Faculty and Research Institute for Physical Chemical Problems, Belarusian State University, Leningradskaya 14, Minsk 220050, Belarus

Heat capacities of 1,1-diphenylurea, 1,3-diphenylurea, and 1,1-dimethyl-3-phenylurea in the range (5 to 300) K were measured with an adiabatic calorimeter. Related thermodynamic functions were obtained. These functions were proved to conform to additivity principles. Taking into account the parameters developed earlier for alkylureas, the additive parameters of the phenyl group for calculation of the heat capacity, entropy, and thermal enthalpy of organic compounds in the crystalline state were derived.

Introduction papers1,2

we showed that the heat In two previous capacities and related properties of organic substances (alkanes, alkenes, alkanols, and alkanones) in crystalline state could be predicted by the additive method with a reasonable accuracy (about 5%). However, no way has been found to use the information about the phase transitions that is often available in the absence of any heat capacity data. After the previous publications,1,2 we measured the heat capacities and obtained the related thermodynamic functions for three phenyl urea derivatives: 1,1-diphenylurea (11), 1,3-diphenylurea (13), and 1,1-dimethyl-3-phenylurea (113), that allowed us to derive the additive parameters of the phenyl group for calculations of thermodynamic properties in the crystalline state. Another aim of this work was to check if the knowledge of the values of the temperatures and enthalpies of the solid-to-solid transitions could improve the prediction of the entropies and thermal enthalpies for crystals of organic compounds. Experimental Section Substance 13 was synthesized by heating of aniline hydrochloride with urea in water according to ref 3. The product was treated with water at T ) 373 K to remove any impurity of phenylurea, crystallized from ethyl acetate, and sublimed in a vacuum at T ) 428 K. 11 and 113 were synthesized at the Mendeleev University of Chemical Technology (Moscow) and sublimed twice in a vacuum. The identity of the substances was proved by NMR spectroscopy. The amount of CO2 in the products of combustion (99.93% of theoretical value) was used as an indirect characteristic of purity for 13. 13 was found to be not hygroscopic. However, the samples were kept in a desiccator over P2O5. The density of 13 measured in a pycnometer with isooctane as a pycnometric liquid is 1239 kg‚m-3 at T ) 293 K, in accordance with literature data.4 * To whom correspondence should be addressed. Fax: +375-172203916. E-mail: [email protected]. † Present address: Thermodynamics Research Center, NIST, Mail Code 838.00, 325 Broadway, Boulder, CO 80305-3328. ‡ Deceased.

Heat capacities in the temperature range (5 to 300) K were measured in an adiabatic calorimeter TAU-1 produced by VNIIFTRI (Moscow) and described in detail.5 The temperature scale adopted was ITS-90. The uncertainty of heat capacity measurements was about 2% at T ) 5 K, decreased at higher temperatures, and did not exceed 0.4% at T > 40 K. The reliability of the device was proved by periodical measurements of the heat capacity of benzoic acid (K-1 reference sample). Samples of 11 (0.496 89 g), 13 (0.374 48 g), and 113 (0.861 56 g) were loaded in stainless steel containers sealed by indium rings. Total heat capacities of containers with samples were measured in separate experiments under adiabatic conditions maintained with an electronic device. Temperature increments were 0.2 K near 5 K and up to 5 K near 300 K. Those increments can be roughly estimated by the differences between the mean temperatures of successive experiments (Tables 1-3). The total heat capacity of a container with a sample was calculated in each experiment as the relation of a heat input to a temperature increment corrected for a temperature drift slope in a conventional manner. The heat capacities of the samples were obtained after subtraction of heat capacities of containers measured in separate series and were not less than 50% of the total heat capacities of the samples with containers in the whole temperature range. The enthalpy of the solid-phase transition shown by 11 was measured in two experiments that covered the temperature range of the transition after subtraction of the heat spent for heating of crystal I to the transition temperature and crystal II above Ttr (Table 4). Results and Discussion Among the studied substances, only 11 showed a solidto-solid transition in the range (5 to 300) K (Figure 1). The transition occurred at T ) 287 ( 0.5 K (peak temperature) and had a very small enthalpy ∆trHm ) 19 ( 4 J‚K-1‚mol-1. We cannot explain its nature without crystallographic and spectroscopic studies that were not subjects of the present work. It is evident from the value of ∆trHm that the transition was not caused by formation of plastic crystals.

10.1021/je0155150 CCC: $22.00 © 2002 American Chemical Society Published on Web 02/12/2002

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Journal of Chemical and Engineering Data, Vol. 47, No. 2, 2002

Table 1. Experimental Heat Capacity of 1,1-Diphenylurea

Table 2. Experimental Heat Capacity of 1,3-Diphenylurea

T

Cs

T

Cs

T

Cs

T

Cs

T

Cs

T

Cs

K

J‚K-1‚mol-1

K

J‚K-1‚mol-1

K

J‚K-1‚mol-1

K

J‚K-1‚mol-1

K

J‚K-1‚mol-1

K

J‚K-1‚mol-1

5.25 5.55 5.89 6.27 6.69 7.07 7.48 7.92 8.39 8.87 9.38 9.90 10.38 10.87 11.44 12.02 12.62 13.23 13.92 14.66 15.35 16.03 16.74 17.38 18.04 18.71

0.502 0.599 0.723 0.860 1.030 1.223 1.503 1.807 2.151 2.546 3.011 3.601 4.070 4.646 5.286 6.037 6.871 7.662 8.648 9.717 10.72 11.80 12.91 13.91 14.87 16.03

51.45 53.84 56.07 58.18 60.18 62.15 64.89 67.23 69.45 72.63 76.61 80.35 83.89 87.27 90.51 93.63 97.02 100.66 104.19 107.60 110.93 114.17 117.50 120.94 124.29

63.34 65.66 67.88 69.78 71.71 73.60 75.66 77.61 79.37 81.58 84.60 87.50 89.99 92.56 94.88 97.21 99.41 101.92 104.18 106.59 109.00 111.12 113.43 115.71 117.94

6.62 7.01 7.39 7.73 8.04 8.39 8.77 9.12 9.45 9.86 10.36 10.82 11.24 11.63 12.05

20.44 20.89 21.32 21.87 22.52 23.14 23.73 24.37 25.12 25.89 26.83 27.93 28.95 29.91

20.15 20.86 21.51 22.28 23.32 24.37 25.26 26.28 27.38 28.70 30.09 31.80 33.36 35.04

236.47 241.70 247.32 252.91 258.45 263.95 269.42 275.52 282.24 288.99 295.52 301.97

203.52 207.49 211.99 216.54 220.66 225.28 229.69 234.29 243.10 242.10 248.40 255.06

85.13 87.85 90.48 93.04 95.51 98.57 102.19 105.68 109.08 112.38 115.60 118.75 121.83

90.19 92.52 94.40 96.07 97.99 100.05 102.54 104.96 107.17 109.50 111.65 113.71 115.80

120.77 124.32 128.37 132.90 137.31 141.63 145.86 150.01 154.54 159.46 164.28 169.02 173.68 273.32 276.20 279.08 281.00

115.33 117.74 120.41 123.46 126.44 129.65 132.57 135.64 138.80 142.40 145.99 149.55 153.21 232.84 235.15 238.09 239.95

Series 1 19.44 17.33 20.23 18.59 21.10 20.16 22.17 22.00 23.26 23.86 24.27 25.54 25.36 27.38 26.52 29.39 27.60 31.21 28.61 32.89 29.70 34.75 30.95 36.90 32.43 39.18 34.06 41.82 35.55 44.06 36.93 46.05 38.22 47.97 39.45 49.65 40.60 50.99 41.71 52.60 42.76 53.78 43.80 55.01 45.03 56.45 46.53 58.12 48.05 59.79 49.51 61.36 Series 2 178.27 156.83 182.80 160.11 187.26 163.63 191.67 167.07 196.48 170.80 201.67 175.09 206.81 179.19 211.87 183.50 216.89 187.21 221.85 191.70 226.77 195.52 231.64 199.11 Series 3 282.44 241.36 283.89 242.48 285.33 243.89

287.03 288.57 290.00

256.19 242.50 243.46

Figure 1. Temperature dependence of the heat capacity of crystalline 1,1-diphenylurea.

The smoothed values of heat capacities and the related thermodynamic functions of the studied compounds are

1.456 1.729 2.000 2.335 2.603 2.957 3.246 3.641 4.084 4.501 5.039 5.727 6.283 6.810 7.403

Series 1 12.57 8.176 13.15 9.081 13.69 9.881 14.19 10.60 14.72 11.43 15.27 12.20 15.78 12.98 16.27 13.75 16.73 14.44 17.27 15.27 17.86 16.18 18.43 17.04 18.97 17.86 19.48 18.64 19.97 19.42 Series 2 50.19 60.81 52.13 62.68 54.59 65.10 56.91 67.41 59.08 69.42 61.52 71.55 64.20 73.81 66.74 76.00 69.15 78.00 72.51 80.47 76.27 83.51 79.36 85.99 82.31 88.18

31.87 32.82 33.89 35.07 36.29 37.56 38.76 39.89 41.22 42.72 44.28 45.88 47.39 48.82

37.84 39.35 40.97 42.61 44.39 46.17 47.80 49.28 50.76 52.55 54.43 56.19 57.87 59.47

124.87 128.16 131.75 135.27 138.73 142.13 145.48

118.00 119.87 122.28 124.75 127.10 129.49 132.01

Series 3 148.77 134.38 152.39 136.68 156.65 139.66 161.17 142.95 165.61 146.24 169.99 149.33 174.31 152.50

178.56 182.76 186.91 191.02 195.08 199.11

156.01 158.88 162.06 165.08 168.55 171.54

203.87 209.32 214.70 220.04 225.32 230.55 235.74

174.95 179.52 183.45 187.84 191.80 195.75 199.86

Series 4 240.87 204.20 246.00 207.89 251.08 212.18 256.12 215.91 261.14 220.18 266.14 224.15 271.11 227.84

276.06 280.99 285.91 290.82 295.67 300.48

231.94 235.70 238.92 242.77 246.67 250.20

given in Tables 5-7. The heat capacities were extrapolated below T ) 5 K as cubic functions of temperature. The probable error of such an extrapolation was comparable with the experimental uncertainty of heat capacity measurements, 2% near T ) 5 K, and did not affect the thermodynamic functions at higher temperatures. Formation of stable crystals of the studied compounds and zero residual entropy at T ) 0 K are confirmed by the absence of any glasslike transitions and corresponding anomalies on the heat capacity curves. In our previous study,2 the thermodynamic functions of alkylureas were approximated as sums of an according function of urea and increments corresponding to substitution of N-H by N-CH3 (Pi) or of C-H by C-CH3 (Pj), and to the appearance of each new C-C-C chain (Pk), C-C-N chain (Pl), and N-C-N chain (Pm). Two new parameters are necessary for the compounds studied in this work. The first (PPh) corresponds to substitution of N-H by N-phenyl. The second (PPh,Ph) corresponds to the appearance of a

Journal of Chemical and Engineering Data, Vol. 47, No. 2, 2002 241 new phenyl-N-phenyl chain, for example, during introduction of the second phenyl group to phenylurea, leading to formation of 1,1-diphenylurea. A property of alkylphenylurea PAPU can be calculated as a sum of the corresponding property of urea Purea and additive increments Pindex multiplied by their occurrences nindex:

Table 3. Experimental Heat Capacity of 1,1-Dimethyl-3-phenylurea T

Cs

T

Cs

T

Cs

K

J‚K-1‚mol-1

K

J‚K-1‚mol-1

K

J‚K-1‚mol-1

49.96 53.26 56.88 60.18 63.64 67.27 70.67 74.18 77.82 81.61 85.55 89.30 92.89 96.66 100.60 104.40 108.40 112.57 116.61 120.54

51.54 55.27 59.38 62.98 66.59 70.25 73.41 76.85 80.16 83.26 86.61 89.67 92.51 95.39 98.43 101.17 104.03 106.89 109.71 112.32

244.29 249.23 254.12 259.51 265.52 271.42 277.23 282.97 288.62 294.20 299.71 305.15

187.15 190.05 193.25 196.60 200.57 204.55 208.20 211.70 215.21 218.47 221.87 225.20

5.30 5.80 6.23 6.69 7.18 7.70 8.33 8.95 9.49 10.06 10.65 11.18 11.72 12.28 12.79 13.32 13.96 14.65 15.37 16.25 17.33 118.76 122.94 127.48 131.89 136.20 140.80 145.68 150.45 155.11 159.69 164.18 168.59 173.11

Series 1 18.43 9.806 19.53 11.18 20.76 12.71 21.97 14.32 23.23 15.98 24.54 17.73 25.85 19.58 27.17 21.48 28.38 23.07 29.62 24.94 30.95 26.81 32.41 28.76 34.05 31.07 35.71 33.30 37.36 35.56 39.02 37.82 40.56 40.01 42.16 41.88 44.24 44.60 47.02 47.98

0.333 0.437 0.529 0.670 0.816 1.006 1.241 1.524 1.796 2.128 2.480 2.852 3.209 3.611 4.048 4.519 5.080 5.680 6.429 7.325 8.530

Series 2 177.73 147.35 182.62 150.15 187.77 153.23 192.83 156.31 197.81 159.09 202.71 162.06 207.88 165.00 213.30 168.39 218.64 171.58 223.91 174.84 229.11 178.15 234.23 181.18 239.29 184.22

110.86 113.56 116.51 119.31 122.06 125.04 128.21 130.83 133.78 136.64 139.20 141.84 144.63

PAPU ) Purea +

T2

Q

Qcal

H1

H2

∆trH

∆trHm

K

K

J

J

J

J

J

J‚mol-1

272.44 292.04 42.567 31.563 8.103 2.864 0.037 272.53 292.84 44.150 32.720 8.054 3.324 0.052

indexPindex

where index enumerates the above-mentioned types of contributions to the property. For example, 1-methyl-3,3diphenylurea can be built from urea in the following way:

NH2-CO-NH2 f phenyl-NH-CO-NH2 f phenyl2N-CO-NH2 f phenyl2N-CO-NH-CH3 Its thermodynamic property can be approximated, in accordance with this scheme, by a sum

P ) Purea + PPh + (PPh + PPh,Ph) + Pi ) Purea + 2PPh + PPh,Ph + Pi This result does not depend on the sequence of substitutions leading from urea to the final product. A matrix of coefficients n for the studied compounds is given in Table 8. We checked additivity relations for the thermodynamic functions of phenylureas in two ways. In the first way, we used the parameters Pi to Pm derived in our previous work,2 and calculated the PPh and PPh,Ph parameters by the leastsquares method after subtraction of properties of urea and values of appropriate Pi to Pm increments2 from the properties of 11, 13, and 113 at each temperature (Tables 5-7). We took into account the data for all crystalline phases of compounds showing solid-phase transitions (Tables 13-16 of the preceding paper2).

Table 4. Measurements of the Enthalpy of the Solid Phase Transition for 1,1-Diphenylurea (Mass of the Sample 0.496 89 g)a T1

∑n

The values of the parameters obtained are given in Table 9, and square-averaged deviations of the calculated values of the thermodynamic properties of 11, 13, and 113 from the experimental ones are given in Table 10. The deviations, except for those at the lowest temperatures, do not exceed 5% for the heat capacities and are even much less for other thermodynamic functions. Using the parameters obtained, we calculated the thermodynamic functions for phenylurea not involved in evaluation of the additive

16 22

a T is the initial temperature of the experiment, T is the final 1 2 temperature of the experiment, Q is the energy supplied, Qcal is the energy expended for heating the calorimeter cell from T1 to T2, H1 is the energy necessary for heating the sample in the crystal II state from T1 to Ttr ) 287 K, H2 is the energy necessary for heating the sample in the crystal I state from Ttr to T2, and ∆trH is the enthalpy of the transition cr,II to cr,I.

Table 5. Thermodynamic Functions (in J‚K-1‚mol-1) of 1,1-Diphenylurea T/K

Cp

S

H/T

-G/T

0 5 10 15 20 25 30 35 40 45 50 60

0 0.437 3.68 10.21 18.26 26.79 35.25 43.20 50.29 56.50 61.97 71.37

0 0.146 1.194 3.852 7.860 12.85 18.49 24.53 30.77 37.06 43.30 55.46

0 0.109 0.900 2.857 5.675 9.045 12.71 16.51 20.30 23.98 27.51 34.06

0 0.036 0.294 0.995 2.185 3.806 5.777 8.020 10.47 13.08 15.79 21.39

287 290

240.24 243.18

265.63 268.14

130.11 131.27

135.52 136.87

T/K

Cp

S

H/T

-G/T

T/K

Cp

S

H/T

-G/T

70 80 90 100 110 120 130 140 150 160 170 180

Crystal II 79.63 67.09 87.30 78.23 94.57 88.93 101.49 99.26 108.22 109.25 114.94 118.95 121.65 128.41 128.49 137.68 135.52 146.78 142.78 155.76 150.26 164.64 157.95 173.44

39.99 45.43 50.49 55.25 59.76 64.07 68.24 72.30 76.28 80.21 84.11 88.00

27.10 32.80 38.44 44.01 49.49 54.88 60.17 65.38 70.50 75.55 80.53 85.45

190 200 210 220 230 240 250 260 270 280 287

165.81 173.80 181.85 189.98 198.07 206.13 214.14 222.11 230.00 237.95 243.52

182.19 190.90 199.58 208.22 216.85 225.45 234.02 242.58 251.11 259.62 265.56

91.88 95.78 99.69 103.61 107.54 111.48 115.43 119.38 123.33 127.28 130.04

90.31 95.12 99.89 104.62 109.31 113.97 118.60 123.20 127.78 132.34 135.52

298.15

Crystal I 251.14 274.99

134.43

140.56

300

252.95

276.55

135.16

141.39

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Journal of Chemical and Engineering Data, Vol. 47, No. 2, 2002

Table 6. Thermodynamic Functions (in J‚K-1‚mol-1) of 1,3-Diphenylurea T/K

Cp

S

H/T

-G/T

T/K

Cp

0 5 10 15 20 25 30 35 40 45 50 60 70

0 0.653 4.655 11.83 19.45 27.25 35.12 42.55 49.29 55.29 60.67 70.10 78.50

0 0.218 1.655 4.846 9.298 14.47 20.14 26.11 32.24 38.40 44.51 56.43 67.87

0 0.163 1.230 3.534 6.555 9.907 13.46 17.09 20.70 24.22 27.60 33.91 39.69

0 0.055 0.425 1.312 2.744 4.562 6.680 9.026 11.54 14.19 16.91 22.51 28.18

80 90 100 110 120 130 140 150 160 170 180 190

86.38 93.91 101.12 107.87 114.39 121.15 128.05 135.07 142.22 149.50 156.91 164.44

S Crystal 78.88 89.49 99.76 109.72 119.38 128.80 138.03 147.11 156.05 164.89 173.64 182.33

H/T

-G/T

T/K

Cp

S

H/T

-G/T

45.04 50.06 54.80 59.32 63.64 67.80 71.86 75.84 79.76 83.65 87.51 91.36

33.84 39.43 44.95 50.39 55.74 61.00 66.17 71.27 76.29 81.24 86.13 90.96

200 210 220 230 240 250 260 270 280 290 298.15 300

172.07 179.80 187.61 195.48 203.38 211.28 219.17 227.00 234.74 242.35 248.42 249.78

190.96 199.54 208.08 216.60 225.08 233.55 241.99 250.40 258.80 267.17 273.97 275.51

95.21 99.05 102.90 106.75 110.61 114.48 118.36 122.24 126.12 129.99 133.15 133.86

95.75 100.49 105.18 109.84 114.47 119.06 123.63 128.17 132.68 137.18 140.82 141.65

Table 7. Thermodynamic Functions (in J‚K-1‚mol-1) of 1,1-Dimethyl-3-phenylurea T/K

Cp

S

H/T

-G/T

T/K

Cp

0 5 10 15 20 25 30 35 40 45 50 60 70

0 0.275 2.090 6.024 11.76 18.41 25.41 32.37 39.10 45.52 51.59 62.77 72.82

0 0.092 0.721 2.247 4.734 8.059 12.03 16.47 21.24 26.22 31.33 41.74 52.19

0 0.069 0.539 1.658 3.439 5.756 8.447 11.37 14.42 17.52 20.63 26.74 32.61

0 0.023 0.182 0.589 1.295 2.303 3.586 5.105 6.821 8.698 10.71 15.01 19.57

80 90 100 110 120 130 140 150 160 170 180 190

81.93 90.28 97.99 105.06 111.73 118.22 124.52 130.65 136.69 142.65 148.58 154.50

S Crystal 62.52 72.65 82.57 92.25 101.67 110.88 119.87 128.67 137.29 145.76 154.08 162.27

Table 8. Matrix of the Occurrences of All Kinds of Substitutions and Interactions in the Studied Phenylureas code

compound

phenylurea 11 1,1-diphenylurea 13 1,3-diphenylurea 113 1,1-dimethyl-3-phenylurea

ni nj nk nl nm nPh nPh,Ph 0 0 0 2

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 1

1 2 2 1

0 1 0 0

parameters. Experimental thermodynamic properties of phenylurea were reported for T ) (100, 200, and 300) K.6 As shown in Table 11, the deviations of the additive predictions from the experimental values are within 5% of the latter. In the second way, we used the whole set of alkylureas and alkylphenylureas for evaluation of the phenyl group increments and re-evaluation of the parameters for alkylureas. The alternative parameter set obtained in this way is very similar to the first one. The temperature dependence of the parameters for C-N-C interaction2 shows jumps caused by the phase transitions of tetraalkylureas. These jumps were smoothed by 1-2 J‚K-1‚mol-1 when the second way of evaluation was applied. Approximation of the properties of 11, 13, and 113 by the new parameters is a bit better, but the prediction for phenylurea is, in general, of the same quality as that of the prediction in the first way. The square-averaged deviations of the calculated properties from the experimental values are given in Table 12. Many alkylurea derivatives show phase transitions in the crystalline state. The additive parameters proposed in the previous paper2 and this paper do not allow us to take into account a knowledge of the characteristics of phase transitions during prediction of the entropies and thermal enthalpies for new compounds. That may be done in the following manner. Enthalpies and entropies of phase

H/T

-G/T

T/K

Cp

S

H/T

-G/T

38.22 43.54 48.61 53.42 58.01 62.39 66.60 70.67 74.61 78.43 82.17 85.82

24.30 29.11 33.96 38.82 43.67 48.49 53.27 58.00 62.69 67.33 71.91 76.46

200 210 220 230 240 250 260 270 280 290 298.15 300

160.45 166.43 172.46 178.54 184.69 190.88 197.13 203.40 209.69 215.95 221.03 222.18

170.35 178.32 186.20 194.00 201.73 209.40 217.00 224.56 232.07 239.54 245.60 246.97

89.40 92.93 96.40 99.84 103.25 106.63 109.99 113.33 116.66 119.98 122.67 123.28

80.95 85.40 89.80 94.16 98.48 102.77 107.01 111.23 115.41 119.56 122.92 123.68

Table 9. Additive Parameters (C, S, H, and G in J‚K-1‚mol-1) for Calculations of Thermodynamic Functions (Heat Capacity, Cp, Entropy, S, Enthalpy Function, (H - H(0))/T, and Gibbs Energy Function, (G - H(0))/T, Respectively) of Phenylureas T/K

CPh

CPh,Ph

SPh

SPh,Ph

HPh

HPh,Ph

GPh

GPh,Ph

10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.15 300

1.8 4.2 6.5 8.8 11.0 13.1 15.0 16.6 18.1 20.7 23.1 25.5 27.9 30.2 32.2 34.2 36.3 38.5 40.7 42.8 45.0 47.3 49.7 52.2 54.4 56.6 58.9 61.2 63.5 65.7 68.0 76.4 79.3 81.4 81.8

-0.5 -0.6 0.1 1.0 1.7 2.1 2.4 2.4 2.3 1.9 1.4 1.0 0.6 0.2 0.1 0.3 0.2 0.1 0.1 0.5 1.0 1.6 2.1 2.6 3.5 4.5 5.5 6.3 7.1 7.8 8.5 -3.2 -6.3 -4.7 -4.3

0.7 1.8 3.4 5.0 6.9 8.7 10.6 12.4 14.3 17.8 21.2 24.4 27.5 30.6 33.6 36.4 39.3 42.1 44.8 47.5 50.1 52.8 55.4 57.9 60.5 63.1 65.7 68.2 70.7 73.3 75.8 79.2 82.2 84.4 85.1

-0.3 -0.5 -0.7 -0.5 -0.3 0.1 0.3 0.6 0.9 1.2 1.5 1.6 1.8 1.8 1.8 1.9 1.8 1.8 1.9 1.8 2.0 2.0 2.2 2.4 2.5 2.7 2.9 3.2 3.5 3.8 4.1 2.6 2.0 1.9 1.5

0.5 1.3 2.4 3.4 4.5 5.6 6.6 7.7 8.6 10.4 12.1 13.6 15.1 16.4 17.8 19.1 20.3 21.5 22.7 23.9 25.1 26.2 27.4 28.6 29.7 30.9 32.0 33.1 34.3 35.5 36.6 38.6 40.1 41.3 41.6

-0.2 -0.4 -0.4 -0.2 0.1 0.4 0.6 0.8 0.9 1.1 1.2 1.2 1.1 1.1 1.0 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.9 1.0 1.1 1.3 1.5 1.9 2.0 2.2 2.4 1.1 0.6 0.3 0.1

0.2 0.5 1.0 1.7 2.4 3.1 4.0 4.8 5.6 7.4 9.1 10.8 12.5 14.2 15.8 17.4 19.0 20.5 22.1 23.6 25.0 26.5 27.9 29.4 30.8 32.2 33.6 35.1 36.5 37.8 39.2 40.7 42.1 43.1 43.5

-0.1 -0.2 -0.3 -0.4 -0.4 -0.3 -0.3 -0.2 -0.1 0.1 0.3 0.5 0.6 0.7 0.8 0.9 1.0 1.0 1.0 1.1 1.2 1.2 1.3 1.3 1.3 1.4 1.5 1.4 1.5 1.6 1.7 1.5 1.4 1.6 1.4

Journal of Chemical and Engineering Data, Vol. 47, No. 2, 2002 243 Table 10. Square-Averaged Deviations of the Calculated Properties of the Three Studied Alkylphenylureas from the Experimental Ones T K 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.15 300

Cp

(H - H(0))/T -(G - H(0))/T

S

J‚K-1‚mol-1 J‚K-1‚mol-1 J‚K-1‚mol-1 0.6 1.3 1.7 1.8 2.0 1.9 1.8 1.5 1.3 0.8 0.3 0.1 0.1 0.2 0.3 0.4 0.4 0.5 0.5 0.0 0.3 0.8 0.9 1.1 1.9 2.8 3.8 4.6 5.5 6.3 7.2 8.2 9.2 9.6 9.6

0.2 0.6 1.0 1.5 1.8 2.1 2.3 2.5 2.7 2.8 3.0 2.9 3.0 3.0 2.9 3.0 2.9 2.8 2.8 2.7 2.9 2.9 3.0 3.1 3.2 3.4 3.5 3.7 3.9 4.1 4.3 2.3 1.3 1.1 0.6

K

0.1 0.2 0.4 0.5 0.7 0.9 1.1 1.2 1.4 1.6 1.8 2.0 2.0 2.1 2.2 2.2 2.3 2.3 2.3 2.4 2.4 2.5 2.5 2.5 2.5 2.5 2.6 2.5 2.5 2.6 2.7 2.4 2.3 2.4 2.1

10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.15 300

0.1 0.4 0.7 0.9 1.0 1.2 1.3 1.3 1.3 1.3 1.1 1.0 0.9 0.9 0.7 0.6 0.5 0.5 0.4 0.4 0.5 0.4 0.4 0.6 0.7 0.7 0.9 1.3 1.4 1.6 1.7 0.1 0.9 1.3 1.6

T/K

exp

S calc

exp

H/T calc

exp

calc

100 70.15 71.2 62.57 66.9 36.49 37.7 200 117.7 119.1 125.6 130.6 65.05 66.3 298.15 171.8 174.5 182.5 188.7 91.20 92.9 300 173.1 175.4 183.6 189.9 91.70 93.4

T

J‚K-1‚mol-1

Cp

S

(H - H(0))/T -(G - H(0))/T

J‚K-1‚mol-1 J‚K-1‚mol-1 J‚K-1‚mol-1 0.4 0.9 1.2 1.3 1.4 1.3 1.2 1.1 1.1 1.2 1.4 1.5 1.6 1.6 1.7 1.7 1.8 2.0 2.1 2.3 3.2 3.7 4.1 4.7 5.7 6.7 7.8 9.1 10.3 11.3 12.8 7.0 6.9 7.6 7.9

0.2 0.4 0.7 1.0 1.2 1.4 1.6 1.7 1.8 1.9 2.0 2.1 2.1 2.2 2.2 2.3 2.3 2.3 2.4 2.5 2.6 2.7 2.8 2.5 2.6 2.7 2.8 3.1 3.3 3.5 3.6 3.4 2.4 5.2 4.9

0.1 0.3 0.5 0.6 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.1 1.1 1.2 1.2 2.2 2.2 2.1 2.1 1.7 1.9 2.1 2.2 2.1 1.2 4.1 4.0

J‚K-1‚mol-1 0.04 0.1 0.2 0.3 0.5 0.6 0.7 0.8 0.9 1.1 1.2 1.3 1.4 1.4 1.5 1.5 1.6 1.6 1.7 1.7 1.8 1.8 1.8 1.9 1.8 1.8 1.8 1.6 1.7 1.7 1.7 1.7 1.6 1.8 1.6

Table 13. Square-Averaged Deviations of the Calculated “Jumpless” Properties of the Alkylureas and Alkylphenylureas from the Experimental Values

Table 11. Experimental and Predicted Values of Thermodynamic Properties (in J‚K-1‚mol-1) of Phenylurea Cp

Table 12. Square-Averaged Deviations of the Properties of the Alkylureas and Alkylphenylureas Calculated by the Second Way from the Experimental Values

-G/T exp 26.08 60.55 91.30 91.90

T

calc

K

29.2 64.4 95.8 96.5

10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.15 300

transitions are subtracted from the corresponding thermodynamic properties of alkylureas (or the corresponding thermodynamic functions are obtained by integrating Cp and Cp/T, respectively, ignoring the contributions of the phase transitions). Then additive parameters are developed for such “jumpless” thermodynamic functions. The “jumpless” thermodynamic functions for a new compound can be calculated using “jumpless” additive parameters. To predict the values for the true thermodynamic functions, the known (measured) values of the enthalpies and entropies of the phase transition have to be added to the “jumpless” values. We calculated the “jumpless” additive parameters for alkyl- and phenylureas. However, the average error of approximation of the “jumpless” thermodynamic properties (Table 13) does not substantially differ from the one of the approximation of the true values affected by the phase transitions (Table 12). That is why we concluded the proposed way to take into account the known characteristics of the solid-phase transitions was not effective. Such a conclusion is consistent with a worse additivity of heat capacities among other thermodynamic properties, despite the absence of large jumps of the heat capacities during

Cp

S

(H - H(0))/T -(G - H(0))/T

J‚K-1‚mol-1 J‚K-1‚mol-1 J‚K-1‚mol-1 0.4 0.9 1.2 1.3 1.4 1.3 1.2 1.1 1.1 1.2 1.4 1.5 1.6 1.6 1.7 1.7 1.8 2.0 2.1 2.3 3.2 3.7 4.1 4.7 5.7 6.7 7.8 9.1 10.3 11.3 12.8 7.0 6.9 7.6 7.9

0.2 0.4 0.7 1.0 1.2 1.4 1.6 1.7 1.8 1.9 2.0 2.1 2.1 2.2 2.2 2.3 2.3 2.3 2.4 2.5 2.5 2.6 2.7 2.8 3.0 3.1 3.4 3.5 3.9 4.2 4.6 4.0 4.1 4.4 4.3

0.1 0.3 0.5 0.6 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.1 1.1 1.2 1.3 1.4 1.5 1.7 1.8 2.1 2.4 2.7 3.0 2.6 2.7 2.8 2.8

J‚K-1‚mol-1 0.04 0.1 0.2 0.3 0.5 0.6 0.7 0.8 0.9 1.1 1.2 1.3 1.4 1.4 1.5 1.5 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.8 1.9 1.9 2.0 1.7 1.7 1.8 1.9 1.8 1.8 1.9 1.8

244

Journal of Chemical and Engineering Data, Vol. 47, No. 2, 2002

the solid-to-solid transitions (See figures in our previous publication2). Conclusion The additive parameters for prediction of the heat capacities and the related properties of phenylureas were developed. The expected accuracy of the prediction is 5%. The parameters developed earlier for alkylureas are transferable to alkylphenylureas without essential loss of accuracy. Literature Cited (1) Kabo, G. J.; Kozyro, A. A.; Diky, V. V. Additivity of Thermodynamic Properties of Organic Compounds in the Crystalline State. 1. Additive Calculations for Thermodynamic Properties of Alkanes, Alkenes, Alkanols, and Alkanones. J. Chem. Eng. Data 1995, 40, 160-166.

(2) Kabo, G. J.; Kozyro, A. A.; Diky, V. V.; Simirsky, V. V. Additivity of Thermodynamic Properties of Organic Compounds in Crystalline State. 2. Heat Capacities and Enthalpies of Phase Transition of Alkyl Derivatives of Urea in the Crystalline State. J. Chem. Eng. Data 1995, 40, 371-393. (3) Sintezy Organicheskih Veshchestv; Kazanskii, B. A., Ed.; Khimia: Moscow, 1949. (4) Bellsteins Handbuch der organischen Chemie; Springer-Verlag: Berlin, 1929; Vol. 12, p 346. (5) Pavese, F.; Malyshev, V. M. Routine Measurements of Specific Heat Capacity and Thermal Conductivity of High-Tc Superconducting Materials in the Range 4-300 K Using Modular Equipment. Adv. Cryog. Eng. 1994, 40, 119-124. (6) Kiparisova, E. G.; Kulagina, T. G.; Smirnova, N. N.; Vasil′ev, V. G. Heat Capacity of Phenylurea. Abstracts of 11th All-Union Conf. on Chem. Thermodyn. (USSR) 1986, Vol. 2, 81.

Received for review September 5, 2001. Accepted December 5, 2001.

JE0155150