Position Group Contribution Method for the Prediction of Critical

Apr 1, 2008 - (2) However, most of the group contribution methods have a serious ..... 2-methylhexane, 530.1, 530.1, 0.0, 0.0, 4,4-dimethylheptane, 59...
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J. Chem. Eng. Data 2008, 53, 1103–1109

1103

Position Group Contribution Method for the Prediction of Critical Temperatures of Organic Compounds Qiang Wang,†,‡ Peisheng Ma,*,† Qingzhu Jia,†,‡ and Shuqian Xia† School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, People’s Republic of China, and School of Material Science and Chemical Engineering, Tianjin University of Science and Technology, 13 St. TEDA, Tianjin, 300457, People’s Republic of China

Based on position group contribution additivity, a new simple and reliable method is proposed for the prediction of critical temperatures of organic compounds involving a carbon chain from C2 to C18. Contributions for organic compounds containing oxygen, nitrogen, chlorine, bromine, and sulfur are given. The overall average absolute difference for critical temperature Tc predictions of 467 organic compounds is 6.6 K and 1.1 %, which means absolute relative difference, which is compared to 17.6 K and 3.1 % with the method of Joback and Reid and 13.5 K and 2.3 % with the method of Constantinou and Gani. Owing to the utilization of the position compensation factor, this method demonstrates significant improvements compared to the previously used first- or secondorder method, especially in the capability of distinguishing between isomers. Furthermore, this new position contribution group method with better precision and simplicity is fully predictive.

Introduction Because the experimental measurement of thermophysical properties is an expensive and time-consuming procedure, the alternative is to develop models from which the required properties with the desired accuracy could be obtained. Group contribution methods are widely used to predict a variety of thermodynamic properties (e.g., vapor pressure, critical temperature, critical pressure, boiling point) of organic compounds. A large variety of group contribution methods have been designed in the past years, differing in their field of applicability and in the set of experimental data they are based on.1 According to the complexity of the decomposition used to represent the molecule, the numerous group contribution methods have been classified by Benson as zero-order methods, first-order methods, and secondorder methods.2 However, most of the group contribution methods have a serious problem that they cannot distinguish among structural isomers. To overcome this problem, many researchers have tried to improve group contribution methods. Based on conjugate forms, Constantinou et al. proposed a quite complex estimation technique, which could provide accurate estimations of several properties of pure compounds and allow capturing the differences among isomers.3,4 However, the generation of conjugate forms is a nontrivial issue and requires a symbolic computing environment.5 A less complex method has been proposed by Constantinou and Gani,6 which performs the estimation at two levels: the basic level uses contributions from first-order simple groups, while the second level uses a small set of second-order groups having the firstorder groups as building blocks. The role of the second-order groups is to consider the proximity effects and to distinguish among isomers. Marrero-Morejón and Pardillo-Fontdevilla proposed another technique that considers the contributions of interactions between bonding groups instead of the contributions * To whom correspondence should be addressed. E-mail: mapeisheng@ tju.edu.cn. † Tianjin University. ‡ Tianjin University of Science and Technology.

of simple groups, which allows the distinction between isomers.7 Dalmazzone et al.8 reported a second group contribution method shown as formula (1) to predict the critical temperature of organics based on Benson’s second-order group contribution, where A and B are obtained by summing the contributions obtained for Benson’s groups that compose the molecule: A ) ∑ NiAi and B ) ∑ NiBi. Using this method, the average differences for Tc prediction of the given 381 compounds claimed by these authors is 5.8 K, but for some compounds, the differences are very high. For example, the difference for 1-octene is 0.9 K in their work, but for cis-2-octene and trans2-octene, the differences are up to (70.6 and 65.7) K, respectively. Furthermore, because the value of B is negative, the formula (1) could not be used for the prediction of critical temperature for the cis-3-octene, trans-3-octene, cis-4-octene, and trans-4-octene out of the samples.

Tc ) 5.926A · [0.5503 ln B + 0.6B2]-1

(1)

The objective of this work was to develop a simple and reliable method for estimation of critical temperatures of organic compounds.

Method Proposed in this Work Experimental Data. A total of 467 compounds were used for the determination of group contributions, which includes linear and branched alkanes (153), cycloalkanes (28), alkenes (33), aromatics (26), ketones and aldehydes (36), alcohols (34), acids (12), phenols and ether oxides (22), esters (25), bromoalkanes and chloro (18), amines and anilines (28), nitriles (9), pyridines (10), alkane thiols (16), and thio ethers (17). The sources of experimental data were from a series of critical compilation reviews in the Journal of Chemical and Engineering Data by Tsonopoulos and Ambrose priority,9,10 Daubert and Gude,11,12 and Marsh et al.13,14 Critical data were also obtained from a compilation of organic property data by Ma.15 Position Group Contributions for the Critical Temperature. The critical temperature function is constructed by all groups’ contribution as well as position correction. The position

10.1021/je700641j CCC: $40.75  2008 American Chemical Society Published on Web 04/01/2008

1104 Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008 Table 1. Position Group Contributions for the Prediction of TCa group

A/K

group

A/K

C-(CH3)(H)3 C-(CH2)(H)3 C-(CH)(H)3 C-(C)(H)3 C-(C)2(H)2 C-(C)3(H) C-(C)4 Cd-(H)(O) Cd-(H)2 Cd-(C)(H) C-(Cd)(C)(H)2 C-(Cd)(H)3 Cd-(C)2 C-(Cd)(C)2(H) Cd-(Cd)(H) C-(Cd)(O)(H)2 C-(O)(H)3 C-(CO)(H)3 C-(C)(CO)(H)2 C-(C)2(CO)(H) C-(C)3(CO) C-(C)(O)(H)2 C-(C)2(O)(H) C-(C)3(O) CO-(CH3)(O) CO-(CH2)(O) CO-(CH)(O) CO-(O)(H) CO-(C)(H) CO-(C)2 CO-(Cd)(O) Cb-(H) Cb-(C) C-(Cb)(H)3 C-(Cb)(C)(H)2 C-(Cb)(C)2(H) C-(Cb)(C)3 Cb-(O) O-(Cb)(H) O-(C)(H) O-(C)2 O-(CO)(CH3) O-(CO)(CH2) O-(CO)(CH) O-(CO)(H) TO

8.589 -3.221 -8.890 -14.484 18.079 48.151 83.076 46.012 -27.380 -63.544 51.485 33.191 -162.278 69.961 108.449 89.056 34.841 33.844 63.061 75.234 115.973 49.710 64.062 56.349 338.831 379.870 418.437 448.857 177.738 117.280 715.602 188.476 -99.785 50.436 80.209 103.365 160.621 1508.227 -544.590 307.389 -276.216 -246.748 -258.532 -238.405 167.195 7409.200

C-(C)(Br)(H)2 C-(C)2(Br)(H) C-(C)3(Br) C-(C)(Cl)(H)2 C-(C)2(Cl)(H) C-(C)3(Cl) C-(C)(Cl)2(H) C-(S)(H)3 C-(C)(S)(H)2 C-(C)2(S)(H) C-(C)3(S) Cb-(N) C-(N)(H)3 C-(C)(N)(H)2 C-(C)2(N)(H) C-(C)3(N) C-(C)(CN)(H)2 C-(C)2(CN)(H) C-(C)3(CN) N-(C)(H)2 N-(C)2(H) N-(C)3 N-(Cb)(H)2 N-(Cb)(C)(H) N-(Cb)(C)2 NI-(Cb)2 S-(C)(H) S-(C)2 ortho correctionb meta correctionb cyclopentane correction cyclohexane correction cyclopentane correction cyclohexane correction Cobc Cmbc Cpbc -(CH)< position correction >(C)< position correction double bond position correction hydroxyl position correction trans or cis structure correction carbonyl position correction Phenol position correction a2 a1

66.426 117.880 107.893 58.178 73.200 106.738 77.578 72.873 73.880 94.062 110.884 25.565 14.035 32.301 48.644 60.814 134.543 168.107 195.908 219.661 118.014 -2.076 787.186 828.730 713.458 370.289 96.099 -159.102 10.087 -2.402 -16.667 -5.116 -9.582 15.018 18.704 -9.909 -6.961 0.146 3.971 -0.593 -4.667 0.823 -7.843 0.788 7.723 -6900.452

a Notice: The first symbol represents the element that forms the center of the group. The symbols between parentheses represent the elements to which it is linked. Usual symbols are used to represent the elements in their normal valence state. Elements in other valence states are distinguished by using additional characters; furthermore, different symbols represent multiple bonded carbons, depending on the element at the other end of the multiple bond: Cd, carbon forming a double bond with another carbon; Cb, carbon involved in a benzene or a pyridine ring; CO, CdO group; CN, CtN group; NI, nitrogen of the imide (CdN-) function. Also used for the nitrogen of pyridine derivatives. The pyridine ring is considered as formed of five Cb and one NI. b Ortho and meta corrections consider interactions between alkyl chains through a benzene ring. c Corrections for pyridines: Cob, Cmb, and Cpb pyridine corrections take into account alkyl ligands in positions ortho, meta, and para with respect to the N element, respectively.

corrections were used to take into account longer distance interaction which could distinguish most isomers including the cis- and trans- or Z- and E- structure of organic compounds for their thermodynamics properties. Here, the critical temperature is expressed as

TC - T0 )

∑ AiNi + ∑ Aj tanh(Nj ⁄ N) + ∑ AkPk + i

j

forms the center; N stands for the total number of groups; Pk stands for the position correlation factor; and a1 and a2 are parameters of the model. The set of contributions that allowed us to minimize the residual estimation difference was then computed by regression. T0 is 7409.200 K, and M is molecular weight. Table 1 reports the values computed for the group contributions Ai.

k

a1 exp(1 ⁄ M) + a2 exp(1 ⁄ N) N)

∑ Ni + ∑ Nj i

Results and Discussion (2)

j

Parameter Ai or Aj stands for i or j group contributions; Ni stands for the number of each group for which the carbon element forms the center of the group in the molecular formula; Nj stands for the number of each group for which the noncarbon element

The results of the reference compounds obtained using the new position group contribution method were presented in detail in Table 3, and the prediction computations of the critical temperature examples are shown as appendix A. Table 2 compares the critical temperature predictions obtained using our method and previous methods to experimental data. Also,

Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008 1105 Table 2. Comparison of Tc Predicted with Our Method and with the Methods of Joback and Constantinou for Various Classes of Organic Compoundsa

a

Joback

Constantinou

this work

chemical family

no. of compounds

MD/K

100 δj

MD/K

100 δj

MD/K

j 100 δ

alkanes cycloalkanes alkenes aromatics ketones and aldehydes alcohols acids phenols and ether oxides esters bromo- and chloroalkanes amines and anilines nitriles pyridines alkane thiols thio ethers overall

153 28 33 26 36 34 12 22 25 18 28 9 10 16 17 467

22.8 9.2 16.5 11.5 17.1 17.0 17.7 18.3 8.2 18.4 28.0 15.9 17.2 12.7 17.5 17.6

4.4 1.6 3.2 1.8 3.1 3.0 2.7 3.1 1.5 3.5 5.7 2.6 2.7 2.1 3.1 3.1

19.1 6.8 7.8 9.7 6.3 12.9 8.5 17.2 12.5 11.8 17.3 10.7 23.7 14.2 11.7 13.5

3.5 1.1 1.5 1.5 1.2 2.1 1.2 3.2 2.3 1.7 3.2 1.8 3.6 2.4 2.0 2.3

6.9 6.9 1.9 4.7 8.4 8.5 9.2 5.0 4.6 5.8 6.6 13.6 3.4 8.2 8.3 6.6

1.2 1.2 0.3 0.7 1.4 1.4 1.4 0.8 0.8 1.1 1.3 2.2 0.5 1.5 1.4 1.1

MD is the overall average absolute difference, and δj is the average mean difference.

the overall average absolute difference (MD) between experimental and predicted values for each group of molecules, as well as the overall mean differences δ and the average mean differences δj are summarized in Table 2.

MD )

∑ |Tc,exptl - Tc,pred|

n Tc,exptl - Tc,pred δ) Tc,exptl

|

δ)

1 N

∑| n

|

Tc,exptl - Tc,pred Tc,exptl

(3) (4)

|

than the existing methods that use first- or second-order groups. Hence, using our new position group contribution method, a greater prediction precision could be obtained for organic compounds, and no extra group classification complexity was added in the process.

Appendix A A.1. Example 1. Estimation of the critical temperature of 2,2,4,5-tetramethylhexane:

(5)

Results presented in Table 2 show that the proposed method is more accurate than other methods for the critical temperature. The MD for critical temperature Tc predictions of 467 organic compounds is 6.6 K, and the δj is 1.1 %, which is compared to 17.6 K and 3.1 % with the method of Joback and 13.5 K and 2.3 % with the method of Constantinou and Gani. To test the quality of the regressed parameters of the position group contributions equation, the degree of confidence should be calculated. According to the definition of the F distribution function, the degree of confidence is calculated with the incomplete β function which could be calculated from the γ function. The results show that the correlation coefficient is 0.9896; the value of F distribution is 190.26; and the degree of confidence is 0.9998, which confirms the greater precision of our position group contribution method which can be used for the best estimation of the critical temperature of organic compounds.

Conclusion A new quantitative relationship for estimating critical temperature based on position group contribution method has been proposed. Contributions for compounds containing carbon, hydrogen, oxygen, nitrogen, sulfur, chlorine, and bromine were reported, and that position compensation factor has been developed which could distinguish between the thermodynamic properties of most isomers of organic compounds including cis- and trans- or Z- and E-structures. The predicted results for 467 different organic compounds showed that the position group contribution method is more precise

This compound is decomposed in the position groups as follows

3C-(CH)(H)3 ; 3C-(C)(H)3 ; 1C-(C)2(H)2 ; 2C-(C)3(H); 1C-(C)4 Total number of groups: N ) 10. The position factor: position of (CH) group 4, 5; the compensated factor is P ) 4 + 5 ) 9. Position of (C) group 2; the compensated factor is P ) 2. Molecular weight: M ) 142.285. From the contributions in Table 1, the critical temperature is estimated by eq 2

Tc ) -8.890 · 3 - 14.484 · 3 + 18.079 · 1 + 48.151 · 2 + 83.076 · 1 + 7.723 · exp(1/10) 6900.452 · exp(1/142.285) + 0.1469 · 3.971 · 2 + 7409.200 ) 605.2 K The calculated result is 605.2 K, while the experimental critical temperature is 599.7 K. A.2. Example 2. Estimation of the critical temperature of 2-ethyl hexanoic acid:

1106 Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008 Table 3. Fully Predictive Estimations of Critical Temperature Tca this work

this work

compound

exptl

predict

D

100 δ

compound

exptl

predict

D

100 δ

ethane propane n-butane 2-methylpropane n-pentane 2-methylbutane 2,2-dimethylpropane n-hexane 2-methylpentane 3-methylpentane 2,2-dimethylbutane 2,3-dimethylbutane n-heptane 2-methylhexane 3-methylhexane 3-ethylpentane 2,2-dimethylpentane 2,3-dimethylpentane 2,4-dimethylpentane 3,3-dimethylpentane 2,2,3-trimethylbutane n-octane 2-methylheptane 3-methylheptane 4-methylheptane 3-ethylhexane 2,2-dimethylhexane 2,3-dimethylhexane 2,4-dimethylhexane 2,5-dimethylhexane 3,3-dimethylhexane 3,4-dimethylhexane 2-methyl-3-ethylpentane 3-methyl-3-ethylpentane 2,2,3-trimethylpentane 2,2,4-trimethylpentane 2,3,3-trimethylpentane 2,3,4-trimethylpentane n-nonane 2-methyloctane 4-ethyloctane 2,2-dimethyloctane 2,3-dimethyloctane 2,4-dimethyloctane 2,5-dimethyloctane 2,6-dimethyloctane 2,7-dimethyloctane 3,3-dimethyloctane 3,4-dimethyloctane 3,5-dimethyloctane 3,6-dimethyloctane 4,4-dimethyloctane 4,5-dimethyloctane 4-propylheptane 3-ethyl-2-methylheptane 3-ethyl-3-methylheptane 3-ethyl-4-methylheptane 3-ethyl-5-methylheptane 4-ethyl-2-methylheptane 4-ethyl-3-methylheptane 4-ethyl-4-methylheptane 5-ethyl-2-methylheptane 2,2,3-trimethylheptane 2,2,4-trimethylheptane 2,2,5-trimethylheptane 2,2,6-trimethylheptane 2,3,3-trimethylheptane 2,3,4-trimethylheptane 2,3,5-trimethylheptane 2,3,6-trimethylheptane 2,4,4-trimethylheptane 2,4,5-trimethylheptane 2,4,6-trimethylheptane 2,5,5-trimethylheptane

305.32 369.83 425.12 408.14 469.7 460.39 433.75 507.6 497.5 504.4 488.7 499.9 540.2 530.1 535.2 540.5 520.4 537.3 519.7 536.3 531.1 568.7 559.6 563.6 561.7 565.4 549.8 563.4 553.5 550 562 568.8 567 576.5 563.4 543.9 573.5 566.3 594.6 587 618.2 602 613 600 603 606 604 614.9 619.8 609.4 609.4 614.9 619.8 618.2 619.8 627.4 624.2 613.9 609.4 624.2 627.4 609.4 615.2 598.1 598.9 593.6 623.2 621.3 611 606.5 606.1 611 596.2 606.1

305.3 356.9 428.6 420.7 469.7 467.4 455.0 503.2 500.9 506.7 499.8 498.8 532.4 530.1 535.9 541.6 528.9 533.7 528.1 544.2 526.8 558.9 556.6 562.4 562.5 568.1 555.4 560.1 560.3 554.8 570.6 566.1 565.8 581.9 558.9 553.4 568.4 558.1 583.5 581.2 616.2 597.7 608.1 608.2 608.4 608.5 603.0 618.6 614.0 614.2 614.3 622.6 614.3 616.2 613.7 629.9 619.7 619.9 613.9 619.7 639.4 614.0 606.9 607.0 607.2 601.7 616.3 611.8 611.9 606.4 620.3 612.1 606.5 624.3

0.0 12.9 3.5 12.5 0.0 7.0 21.2 4.4 3.4 2.3 11.1 1.1 7.8 0.0 0.7 1.1 8.5 3.6 8.4 7.9 4.3 9.8 3.0 1.2 0.8 2.7 5.6 3.3 6.8 4.8 8.6 2.7 1.2 5.4 4.5 9.5 5.1 8.2 11.1 5.8 2.0 4.3 4.9 8.2 5.4 2.5 1.0 3.7 5.8 4.8 4.9 7.7 5.5 2.0 6.1 2.5 4.5 6.0 4.5 4.5 12.0 4.6 8.3 8.9 8.3 8.1 6.9 9.5 0.9 0.1 14.2 1.1 10.3 18.2

0.0 3.5 0.8 3.1 0.0 1.5 4.9 0.9 0.7 0.5 2.3 0.2 1.4 0.0 0.1 0.2 1.6 0.7 1.6 1.5 0.8 1.7 0.5 0.2 0.2 0.5 1.0 0.6 1.2 0.9 1.5 0.5 0.2 0.9 0.8 1.8 0.9 1.4 1.9 1.0 0.3 0.7 0.8 1.4 0.9 0.4 0.2 0.6 0.9 0.8 0.8 1.2 0.9 0.3 1.0 0.4 0.7 1.0 0.7 0.7 1.9 0.8 1.3 1.5 1.4 1.4 1.1 1.5 0.1 0.0 2.3 0.2 1.7 3.0

3-methyloctane 4-methyloctane 2-ethylheptane 3-ethylheptane 4-ethylheptane 2,2-dimethylheptane 2,3-dimethylheptane 2,4-dimethylheptane 2,5-dimethylheptane 2,6-dimethylheptane 3,3-dimethylheptane 3,4-dimethylheptane 3,5-dimethylheptane 4,4-dimethylheptane 3-ethyl-2-metylhexane 3-ethyl-3-metylhexane 3-ethyl-4-methylhexane 4-ethyl-2-methylhexane 2,2,3-trimethylhexane 2,2,4-trimethylhexane 2,2,5-trimethylhexane 2,3,3-trimethylhexane 2,3,4-trimethylhexane 2,3,5-trimethylhexane 2,4,4-trimethylhexane 3,3,4-trimethylhexane 3,3-diethylpentane 3-ethyl-2,2-dimethylpentane 3-ethyl-2,3-dimethylpentane 3-ethyl-2,4-dimethylpentane 2,2,3,3-tetramethylpentane 2,2,3,4-tetramethylpentane 2,2,4,4-tetramethylpentane 2,3,3,4-tetramethylpentane n-decane 2-methylnonane 3-methylnonane 4-methylnonane 5-methylnonane 3-ethyloctane 3-ethyl-2,2-dimethylhexane 3-ethyl-2,3-dimethylhexane 3-ethyl-2,4-dimethylhexane 3-ethyl-2,5-dimethylhexane 3-ethyl-3,4-dimethylhexane 4-ethyl-2,2-dimethylhexane 4-ethyl-2,3-dimethylhexane 4-ethyl-2,4-dimethylhexane 4-ethyl-3,3-dimethylhexane 2,2,3,3-tetramethylhexane 2,2,3,4-tetramethylhexane 2,2,3,5-tetramethylhexane 2,2,4,4-tetramethylhexane 2,2,4,5-tetramethylhexane 2,3,3,4-tetramethylhexane 2,3,3,5-tetramethylhexane 2,3,4,4-tetramethylhexane 2,3,4,5-tetramethylhexane 3,3,4,4-tetramethylhexane 3,3-dethyl-2-methylpentane 3-ethyl-2,2,3-trimethylpentane 3-ethyl-2,2,4-trimethylpentane 3-ethyl-2,3,4-trimethylpentane 2,2,3,3,4-pentamethylpentane 2,2,3,4,4-pentamethylpentane n-undecane n-dodecane n-tridecane n-tetradecane n-pentadecane n-hexadecane n-heptadecane n-octadecane cyclopropane

590.15 587.65 594.3 590.45 594.3 576.69 591.4 581 581 577.85 591 595.8 585.5 591.4 595.8 603.5 600.3 585.5 591.3 573.55 569.8 596.05 597.4 579.15 581 602.25 616 595.7 611.8 597.4 607.5 574.6 592.7 607.1 617.7 610 613 610 610 618.2 619.6 635.7 625.8 611 640.1 602.6 625.8 618.6 632.1 623 621.2 606.4 599.3 599.7 635.9 614.4 629.2 622.9 640.9 648.2 640.9 621.2 643.9 636.7 616.6 639 658 675 693 708 723 736 747 397.91

587.0 587.2 586.9 592.7 592.8 580.0 584.7 584.9 585.0 579.5 595.3 590.7 590.9 599.2 590.4 606.5 596.4 590.6 583.6 583.7 578.2 593.0 588.4 582.9 597.0 598.9 595.1 589.2 604.3 588.4 591.8 581.6 584.5 591.0 606.8 604.5 610.3 610.5 610.6 616.0 629.3 633.2 617.4 611.9 633.5 612.7 622.7 631.5 627.9 615.1 610.6 605.1 619.1 605.2 620.0 614.5 623.8 609.9 634.3 609.6 632.0 610.6 625.6 618.8 611.4 629.2 650.9 672.0 692.7 713.0 733.1 752.9 772.6 397.9

3.1 0.5 7.4 2.2 1.5 3.3 6.7 3.9 4.0 1.7 4.3 5.1 5.4 7.8 5.4 3.0 3.9 5.1 7.7 10.2 8.4 3.1 9.0 3.8 16.0 3.3 20.9 6.5 7.5 9.0 15.7 7.0 8.2 16.1 10.9 5.5 2.7 0.5 0.6 2.2 9.7 2.5 8.4 0.9 6.6 10.1 3.1 12.9 4.2 7.9 10.6 1.3 19.8 5.5 15.9 0.1 5.4 13.0 6.6 38.6 8.9 10.6 18.3 17.9 5.2 9.8 7.1 3.0 0.3 5.0 10.1 16.9 25.6 0.0

0.5 0.1 1.2 0.4 0.2 0.6 1.1 0.7 0.7 0.3 0.7 0.9 0.9 1.3 0.9 0.5 0.7 0.9 1.3 1.8 1.5 0.5 1.5 0.6 2.7 0.5 3.4 1.1 1.2 1.5 2.6 1.2 1.4 2.7 1.8 0.9 0.4 0.1 0.1 0.4 1.6 0.4 1.3 0.1 1.0 1.7 0.5 2.1 0.7 1.3 1.7 0.2 3.3 0.9 2.5 0.0 0.9 2.1 1.0 6.0 1.4 1.7 2.8 2.8 0.8 1.5 1.1 0.4 0.0 0.7 1.4 2.3 3.4 0.0

Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008 1107 Table 3. (Continued) this work

this work

compound

exptl

predict

D

100 δ

compound

exptl

predict

D

100 δ

3,3,4-trimethylheptane 3,3,5-trimethylheptane 3,4,4-trimethylheptane 3,4,5-trimethylheptane 3,4-diethylhexane 3,3-diethylhexane cis-1,2-dimethylcyclopentane trans-1,2-dimethylcyclopentane cis-1,3-dimethylcyclopentane trans-1,3-dimethylcyclopentane 1,1-dimethylcyclopentane 1,1-dimethylcyclohexane cis-1,2-dimethylcyclohexane trans-1,2-dimethylcyclohexane cis-1,3-dimethylcyclohexane trans-1,3-dimethylcyclohexane cis-1,4-dimethylcyclohexane trans-1,4-dimethylcyclohexane ethylcyclohexane n-propylcyclopentane n-propylcyclohexane n-butylcyclopentane n-butylcyclohexane n-pentylcyclopentane n-pentylcyclohexane n-hexylcyclopentane n-heptylcyclohexane 1-butene cis-2-butene trans-2-butene 1-pentene cis-2-pentene trans-2-pentene 2-methyl-1-butene 2-methyl-2-butene 3-methyl-1-butene 1-hexene cis-2-hexene trans-2-hexene cis-3-hexene trans-3-hexene 2-methyl-1-hexene 3-methyl-1-hexene 4-methyl-1-hexene 1-heptene cis-2-heptene n-heptylbenzene butanone 2-pentanone 3-pentanone 3-methyl-2-butanone 2-hexanone 3-hexanone 3,3-dimethyl-2-butanone 4-methyl-2-pentanone 2-heptanone 3-heptanone 4-heptanone 2-methyl-3-hexanone 2,4-dimethyl-3-pentanone 2-methyl-3-heptanone 2,5-dimethyl-3-hexanone 5-nonanone 4-nonanone 3-nonanone 2-nonanone 2,6-dimethyl-4-heptanone 6-undecanone 2-undecanone 3-undecanone 4-undecanone 5-undecanone propanal butanal

627.7 609.6 627.7 625.8 639.9 628.7 565.15 553.15 551 553 547 591.15 606.15 596.15 587.7 598 598.15 587.7 609.15 596 639.15 621 667 643.8 669 664.1 682.6 419.5 435.5 428.6 464.8 475 475 465 470 452.7 504 513 513 509 509 538 528 534 537.3 549 714 536.7 561.1 561.5 553 587 582.8 570.9 574.6 611.4 606.6 602 593 579.1 614.9 597.5 641.4 643.7 648.1 652.2 619.4 678.5 688 684.6 680.9 679.4 505 537

622.3 622.4 626.1 606.5 625.4 641.1 564.4 562.7 564.5 562.9 560.7 599.1 602.7 601.1 602.9 601.2 603.0 601.4 604.2 604.2 628.9 617.4 652.4 640.9 674.9 663.4 685.1 420.0 431.2 429.6 466.9 476.0 474.4 462.5 472.9 452.7 504.2 514.1 512.5 510.5 508.9 537.4 528.0 539.7 536.0 546.6 706.6 528.9 556.8 556.9 536.8 582.5 582.5 570.9 617.2 605.7 605.9 598.1 585.6 565.8 646.3 606.3 634.5 642.3 650.1 650.1 638.3 668.3 691.7 691.8 684.0 676.1 508.8 535.9

5.4 12.8 1.6 19.3 14.5 12.4 0.8 9.6 13.5 9.9 13.7 7.9 3.4 4.9 15.2 3.2 4.9 13.7 5.0 8.2 10.2 3.6 14.6 2.9 5.9 0.7 2.5 0.5 4.3 1.0 2.1 1.0 0.6 2.5 2.9 0.0 0.2 1.1 0.5 1.5 0.1 0.6 0.0 5.7 1.3 2.4 7.4 7.8 4.3 4.6 16.2 4.5 0.3 0.0 42.6 5.7 0.7 3.9 7.4 13.3 31.4 8.8 6.9 1.4 2.0 2.1 18.9 10.2 3.7 7.2 3.1 3.3 3.8 1.1

0.9 2.1 0.3 3.1 2.3 2.0

cyclobutane cyclopentane cyclohexane methylcyclopentane methylcyclohexane ethylcyclopentane trans-2-heptene cis-3-heptene trans-3-heptene 1-octene cis-2-octene trans-2-octene cis-3-octene trans-3-octene cis-4-octene trans-4-octene 1-nonene 1-decene 1-undecene 1-dodecene 1,3-butadiene benzene methylbenzene 1,4-dimethylbenzene 1,2-dimethylbenzene 1,3-dimethylbenzene ethylbenzene 1,2,3-trimethylbenzene 1,2,4-trimethylbenzene 1,3,5-trimethylbenzene 1,2,3,4-tetramethylbenzene 1,2,3,5-tetramethylbenzene 1,2,4,5-tetramethylbenzene 1-methyl-2-ethylbenzene 1-methyl-3-ethylbenzene 1-methyl-4-ethylbenzene n-propylbenzene isopropylbenzene 1-methyl-2-isopropylbenzene 1-methyl-3-isopropylbenzene 1-methyl-4-isopropylbenzene n-butylbenzene sec-butylbenzene tert-butylbenzene n-pentylbenzene n-hexylbenzene 1-butanol 2-butanol 2-methyl-1-propanol 2-methyl-2-propanol 1-pentanol 2-pentanol 3-pentanol 2-methyl-1-butanol 3-methyl-1-butanol 2-methyl-2-butanol 3-methyl-2-butanol 1,2-butanedial 1,3-butanedial 1-hexanol 2-hexanol 3-hexanol 2-methyl-1-pentanol 4-methyl-1-pentanol 2-methyl-2-pentanol 2-methyl-3-pentanol 4-methyl-2-pentanol 1-heptanol 2-heptanol 3-heptanol 4-heptanol 1-octanol 2-octanol 3-octanol

459.93 511.6 553.5 532.79 572.19 569.5 543 545 540 566.65 572 577 569 574 568 573 594 617 638 658 425 562.05 591.75 616.2 630.3 617 617.15 664.5 649.1 637.3 693 679 675.15 647.2 637.2 640.2 635.38 631.05 653.5 649 652 660.5 664.54 660 679.9 698 563.05 536.05 547.78 506.21 588.15 560.3 559.6 575.4 579.4 545 556.1 680 676 610.3 585.9 582.4 604.4 603.5 559.5 576 603.5 632.6 608.3 605.4 602.6 652.5 637 628.5

459.9 492.8 538.8 530.4 571.7 565.8 544.9 543.0 541.3 564.4 575.5 573.9 571.9 570.3 571.3 569.7 590.5 614.9 638.2 660.8 425.0 572.5 594.2 615.7 625.8 613.3 621.3 657.3 647.2 632.3 692.2 679.7 682.1 654.1 641.6 644.0 638.9 629.4 663.7 651.2 653.6 656.0 652.2 660.0 672.8 689.7 563.1 545.8 560.8 505.8 586.0 568.7 574.9 598.1 595.7 549.1 584.0 654.3 644.0 607.5 590.3 591.3 610.9 605.6 555.9 558.9 588.3 628.3 611.0 612.0 607.4 648.5 631.2 632.2

0.0 18.8 14.7 2.3 0.5 3.7 1.9 2.0 1.3 2.2 3.5 3.1 2.9 3.7 3.3 3.3 3.5 2.1 0.2 2.8 0.0 10.5 2.5 0.5 4.5 3.7 4.2 7.2 1.9 5.0 0.8 0.7 6.9 6.9 4.4 3.8 3.5 1.7 10.2 2.2 1.6 4.5 12.4 0.0 7.1 8.3 0.1 9.8 13.1 0.4 2.2 8.4 15.3 22.7 16.3 4.1 27.9 25.7 32.0 2.8 4.4 8.9 6.5 2.1 3.6 17.1 15.2 4.3 2.7 6.6 4.8 4.0 5.8 3.7

0.0 3.7 2.7 0.4 0.1 0.6 0.4 0.4 0.2 0.4 0.6 0.5 0.5 0.7 0.6 0.6 0.6 0.3 0.0 0.4 0.0 1.9 0.4 0.1 0.7 0.6 0.7 1.1 0.3 0.8 0.1 0.1 1.0 1.1 0.7 0.6 0.5 0.3 1.6 0.3 0.2 0.7 1.9 0.0 1.0 1.2 0.0 1.8 2.4 0.1 0.4 1.5 2.7 3.9 2.8 0.7 5.0 3.8 4.7 0.5 0.7 1.5 1.1 0.3 0.6 3.0 2.5 0.7 0.4 1.1 0.8 0.6 0.9 0.6

1.0 1.5 0.8 0.8 2.9 0.8 0.0 0.0 7.4 0.9 0.1 0.7 1.2 2.3 5.1 1.5 1.1 0.2 0.3 0.3 3.1 1.5 0.5 1.1 0.5 0.5 0.8 0.2

1108 Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008 Table 3. (Continued) this work

this work

compound

exptl

predict

D

100 δ

compound

exptl

predict

D

100 δ

1-pentanal 1-hexanal 1-heptanal 1-octanal 1-nonanal 1-decanal 2-methylpropanal 2-methylhexanal 3-methylhexanal ethanol 1-propanol 2-propanol 3,5-xylenol 3-ethylphenol 2-ethylphenol 4-ethylphenol diethyl ether isopropyl methyl ether ethyl n-propyl ether butyl methyl ether methyl pentyl ether butyl ethyl ether dipropyl ether diisopropyl ether methyl formiate methyl acetate ethyl formiate propyl formiate ethyl acetate methyl propionate propyl acetate isopropyl acetate methyl butanoate methyl isobutanoate 2-propenyl acetate 2-ethenyl acetate ethyl propionate butyl acetate propyl propionate ethyl butanoate n-propyl butyrate ethyl isobutanoate methyl pentanoate ethyl pentanoate propyl pentanoate diphenyl ether methylamine dimethylamine ethylamine propylamine isopropylamine trimethylamine decanenitrile chloroethane 1-chloropropane 2-chloropropane 1-chlorobutane 2-chlorobutane 2-chloro-2-methylpropane 1-chloropentane 2-chloropentane 1-chloro-3-methylbutane 1,1-dichloroethane bromoethane 1-bromopropane 2-bromopropane 1-bromobutane 1-bromo-2-methylpropane 2-bromo-2-methylpropane 1-bromopentane methylthio ethane 1-methylthio propane 2-methylthio propane 1-methylthio butane

567 592 617 639 659 674 507 592 595 513.92 536.78 508.3 715.6 718.8 703 716.4 466.7 464.2 500.2 512.7 546.5 531 530.6 500.3 487.2 506.5 508.4 538 523.3 530.7 549.7 531 554.5 540.7 552.2 525 546 579 578 566 600 553.6 567 570 613 766.8 430.05 437 456.4 497 471.8 433.3 693.2 460.35 503.1 482.4 542 520.6 507 568 556.8 560 523.4 503.9 536.9 556 571.1 567.2 540.5 590 553 574.1 549.5 591.3

560.8 584.2 606.5 628.0 648.8 669.2 515.7 604.2 610.0 508.8 538.1 515.1 710.9 714.3 713.5 715.0 462.9 451.1 504.6 511.0 546.2 539.7 539.7 503.2 495.5 500.4 510.1 520.3 519.9 536.8 546.0 531.0 553.3 547.1 552.2 525.0 552.8 570.2 576.1 568.2 590.5 555.6 568.5 582.6 604.1 766.8 411.2 430.8 464.5 501.9 485.6 442.5 730.1 468.6 504.1 486.5 534.8 522.9 507.0 562.3 550.4 560.2 520.1 521.1 544.5 574.9 567.5 565.2 540.5 589.8 532.0 571.5 559.0 604.8

6.2 7.8 10.5 11.0 10.2 4.8 8.7 12.2 15.0 5.2 1.3 6.8 4.8 4.5 10.5 1.4 3.8 13.1 4.4 1.7 0.3 8.7 9.1 2.9 8.3 6.1 1.7 17.7 3.4 6.1 3.7 0.0 1.2 6.4 0.0 0.0 6.8 8.8 1.9 2.2 9.5 2.0 1.5 12.6 8.9 0.0 18.8 6.2 8.1 4.9 13.8 9.2 36.9 8.3 1.0 4.1 7.2 2.3 0.0 5.7 6.4 0.2 3.3 17.2 7.6 18.9 3.6 2.0 0.0 0.2 21.0 2.6 9.5 13.5

1.1 1.3 1.7 1.7 1.5 0.7 1.7 2.1 2.5 1.0 0.2 1.3 0.7 0.6 1.5 0.2 0.8 2.8 0.9 0.3 0.1 1.6 1.7 0.6 1.7 1.2 0.3 3.3 0.6 1.2 0.7 0.0 0.2 1.2 0.0 0.0 1.2 1.5 0.3 0.4 1.6 0.4 0.3 2.2 1.4 0.0 4.4 1.4 1.8 1.0 2.9 2.1 5.3 1.8 0.2 0.9 1.3 0.4 0.0 1.0 1.2 0.0 0.6 3.4 1.4 3.4 0.6 0.4 0.0 0.0 3.8 0.5 1.7 2.3

4-octanol 1-nonanol 2-nonanol phenol o-cresol m-cresol p-cresol 2,3-xylenol 2,4-xylenol 2,5-xylenol 2,6-xylenol 3,4-xylenol butylamine isobutylamine sec-butylamine tert-butylamine diethylamine pentylamine cyclopentylamine hexylamine butyl ethylamine isopropyl propylamine triethylamine dipropylamine diisopropylamine cyclohexylamine dibutylamine benzenamine 2-methylbenzenamine 3-methylbenzenamine N-methylbenzenamine N-ethylbenzenamine N,N-dimethylbenzenamine N,N-diethylbenzenamine pyridine 2-methylpyridine 3-methylpyridine 4-methylpyridine 2,3-dimethylpyridine 2,4-dimethylpyridine 2,5-dimethylpyridine 2,6-dimethylpyridine 3,4-dimethylpyridine 3,5-dimethylpyridine propanenitrile butanenitrile 2-methylpropanenitrile pentanenitrile 3-methylbutanenitrile 2,2-dimethylpropanenitrile hexanenitrile octanenitrile 2-propanethiol 1-butanethiol 2-butanethiol 2-methyl-1-propanethiol 2-methyl-2-propanethiol 1-pentanethiol 2-methyl-1-butanethiol 3-methyl-1-butanethiol 2-methyl-2-butanethiol 3-methyl-2-butanethiol 2,2-dimethyl-1-propanethiol cyclopentanethiol 1-hexanethiol 2-methyl-2-pentanethiol 2,3-dimethyl-2-butanethiol cyclohexanethiol 1-heptanethiol acetic acid n-propanoic acid acrylic acid n-butyric acid n-pentanoic acid

625.1 668.9 649.5 694.25 697.6 705.7 704.5 722.8 707.6 706.9 701 729.8 526.8 528.5 514.3 483.9 496.6 555 582.15 584 547.1 520 535 550 523.1 615 602.3 699 694.15 709.15 698.2 698 687 689.2 620 621 645 645.7 655.7 647 644.2 623.8 683.8 667.2 561.3 585.4 569.28 610.3 591.62 587.61 633.8 674.4 517 570.1 554 559 530 597.7 591.7 589.3 570.1 576.4 574.9 633.5 620.5 586.3 599.3 664.2 646 590.7 604 615 615.2 643

627.5 668.3 651.0 696.3 698.7 699.5 700.3 721.0 709.3 712.5 710.9 722.6 531.8 529.7 521.2 483.9 504.6 557.8 576.9 581.7 551.5 542.5 519.1 548.9 505.2 612.8 596.0 696.0 703.0 703.7 700.0 696.0 687.9 688.1 619.8 619.7 644.3 648.0 648.3 651.9 648.3 623.7 676.5 672.9 526.4 568.4 569.3 602.6 606.2 587.6 632.4 684.0 527.3 567.0 560.2 564.8 527.6 592.1 595.5 578.8 564.0 583.2 588.6 615.6 615.7 587.5 585.4 651.0 638.1 600.2 618.7 615.0 625.3 636.3

2.4 0.6 1.5 2.0 1.1 6.2 4.2 1.8 1.7 5.6 9.9 7.2 5.0 1.2 6.9 0.0 8.0 2.8 5.2 2.3 4.4 22.5 15.9 1.1 17.9 2.2 6.3 3.0 8.8 5.4 1.8 2.0 0.9 1.1 0.2 1.3 0.7 2.3 7.4 4.9 4.1 0.1 7.3 5.7 34.9 17.0 0.0 7.7 14.6 0.0 1.4 9.6 10.3 3.1 6.2 5.8 2.4 5.6 3.8 10.5 6.1 6.8 13.7 17.9 4.8 1.2 13.9 13.2 7.9 9.5 14.7 0.0 10.1 6.7

0.4 0.1 0.2 0.3 0.2 0.9 0.6 0.3 0.2 0.8 1.4 1.0 0.9 0.2 1.3 0.0 1.6 0.5 0.9 0.4 0.8 4.3 3.0 0.2 3.4 0.4 1.0 0.4 1.3 0.8 0.3 0.3 0.1 0.2 0.0 0.2 0.1 0.4 1.1 0.8 0.6 0.0 1.1 0.8 6.2 2.9 0.0 1.3 2.5 0.0 0.2 1.4 2.0 0.5 1.1 1.0 0.4 0.9 0.6 1.8 1.1 1.2 2.4 2.8 0.8 0.2 2.3 2.0 1.2 1.6 2.4 0.0 1.6 1.0

Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008 1109 Table 3. (Continued) this work

this work

compound

exptl

predict

D

100 δ

compound

exptl

predict

D

100 δ

2-methyl-2-methylthio propane 1-ethylthio propane 2-ethylthio propane 1-ethylthio butane 2-ethylthio butane 2-ethylthio-2-methyl propane methylthio cyclopentane 1,2-dibromopropane 1,1,2-trichloroethane methylthio methane ethanethiol 1-propanethiol

569.8 583.9 571.2 609.2 599.5 549 651.3 679.6 602 470 499.15 536

565.4 584.5 572.0 602.6 590.2 574.6 658.0 660.7 605.3 469.2 509.1 539.7

4.4 0.6 0.8 6.6 9.3 25.6 6.7 18.9 3.3 0.8 10.0 3.7

0.8 0.1 0.1 1.1 1.5 4.7 1.0 2.8 0.6 0.2 2.0 0.7

2-ethyl butyric acid 2-ethyl hexanoic acid n-hexanoic acid n-heptanoic acid n-octanoic acid n-nonanoic acid n-decanoic acid isobutyl acetate isobutyl acrylate isobutyl butyrate isobutyl formate

655 674 655 678 693 711 726 560.8 587 610.4 551.35

646.3 675.6 649.7 664.5 680.1 696.4 713.0 567.6 587.0 609.4 553.6

8.7 1.6 5.3 13.5 12.9 14.6 13.0 6.8 0.0 1.0 2.3

1.3 0.2 0.8 2.0 1.9 2.1 1.8 1.2 0.0 0.2 0.4

a

D is the absolute difference. D ) |Tc,exptl - Tc,pred|.

This compound is decomposed in the position groups as follows

2C-(CH2)(H)3 ; 4C-(C)2(H)2 ; 1C-(C)2(CO)(H); 1CO-(CH)(O); 1O-(CO)(H) Total number of groups: N ) 9. The position of -(CH)< group; the compensated factor is P ) 2. Molecular weight: M ) 144.214. From the contributions in Table 1, the critical temperature is estimated by eq 2

Tc ) -3.221 · 2 + 18.079 · 4 + 75.234 · 1 + 418.437 · tanh(1/ 9) · 1 + 167.195 · tanh(1/ 9) · 1 + 7.723 · exp(1/9) - 6900.452 · exp(1/144.214) + 0.146 · 2 + 7409.200 ) 675.6 K Therefore, the calculated result is 675.6 K, while the experimental critical temperature is 674 K. A.3. Example 3. Estimation of the critical temperature of trans-1,3-dimethylcyclohexane

This compound could be decomposed in the position groups as follows

2C-(CH)(H)3 ; 4C-(C)2(H)2 ; 2C-(C)3(H) Total number of groups: N ) 8. The position factor: position of (CH3) group 1, 3; the compensated factor is P ) 1 + 3 ) 4. The position of the trans-structure compensated factor is -1. One cyclohexane correction. Molecular weight: M ) 112.215. From the contributions in Table 1, the critical temperature is estimated by eq 2

Tc ) -8.890 · 2 + 18.079 · 4 + 48.151 · 2 - 5.116 + 0.146 · 4 + (-1) · 0.823 + 7.723 · exp(1/8) 6900.452 · exp(1/112.215) + 7409.200 ) 601.2 K So, the calculated result is 601.2 K, while the experimental critical temperature is 598 K.

Literature Cited (1) Joback, K. G.; Reid, R. C. Estimation of Pure-Component Properties from Group-Contributions. Chem. Eng. Commun. 1987, 57, 233–243. (2) Benson, S. W. Thermochemical Kinetics, 2nd ed.; John Wiley and Sons: New York, 1976. (3) Constantinou, L.; Prickett, S. E.; Mavrovouniotis, M. L. Estimation of Thermodynamic and Physical Properties of Acyclic Hydrocarbons using ABC Approach and Conjugation Operators. Ind. Eng. Chem. Res. 1993, 32, 1734–1746. (4) Constantinou, L.; Prickett, S. E.; Mavrovouniotis, M. L. Estimation of Properties of Acyclic Organic Compounds Using Conjugation Operators. Ind. Eng. Chem. Res. 1994, 33, 395–402. (5) Prickett, S. E.; Constantinou, L.; Mavrovouniotis, M. L. Computational Identification of conjugate paths for estimation of properties of organic components. Mol. Simul. 1993, 11, 205–228. (6) Constantinou, L.; Gani, R. New group contribution method for estimating properties of pure compounds. AIChE J. 1994, 40, 1697– 1710. (7) Marrero-Morejón, J.; Pardillo-Fontdevilla, E. Estimation of pure compound properties using group-interaction contribution. AIChE J. 1999, 45, 615–621. (8) Dalmazzone, D.; Salmon, A.; Guella, S. A second order group contribution method for the prediction of critical temperatures and enthalpies of vaporization of organic compounds. Fluid Phase Equilib. 2006, 242, 29–42. (9) Kudchadker, A. P.; Ambrose, D.; Tsonopoulos, C. Vapor-liquid critical properties of elements and compounds 7.Oxygen compounds other than alkanols and cycloalkanols. J. Chem. Eng. Data 2001, 46, 457– 479. (10) Tsonopoulos, C.; Ambrose, D. Vapor-liquid critical properties of elements and compounds 8-Organic sulfur, silicen and tin. J. Chem. Eng. Data 2001, 46, 480–485. (11) Daubert, T. E. Vapor-liquid critical properties of branched alkanes and cycloalkanes. J. Chem. Eng. Data 1996, 41, 365–372. (12) Gude, M.; Teja, A. S. Vapor-liquid critical properties of elements and compounds. 4. Aliphatic alkanols. J. Chem. Eng. Data 1995, 40, 1025– 1036. (13) Marsh, K. N.; Abramson, A; Ambrose, D.; Nikitin, E.; Tsonopoulos, C.; Young, C. L. Vapor-Liquid Critical Properties of Elements and Compounds. 10. Organic Compounds Containing Halogens. J. Chem. Eng. Data 2007, 52, 1509–1538. (14) Marsh, K. N.; Young, C. L.; Morton, D. W.; Ambrose, D.; Tsonopoulos, C. Vapor-Liquid Critical Properties of Elements and Compounds. 9. Organic Compounds Containing Nitrogen. J. Chem. Eng. Data 2006, 51, 305–314. (15) Ma, P. Sh.; Handbook of property data of organic compounds; Chemical Engineering Press: Beijing, 2006.

Received for review November 3, 2007. Accepted March 7, 2008.

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