Prediction of the Liquid Molar Volume and the Latent Heat of Vaporization. for Aliphatic Hydrocarbons by the Group Contribution Method

Transcription

1 Prediction of the Liquid Molar Volume and the Latent Heat of Vaporization for Aliphatic Hydrocarbons by the Group Contribution Method Daisuke HOSHINO* Kunio NAGAHAMA* and Mitsuho HIRATA* vaporization of 384 aliphatic hydrocarbons at the normal boiling points were successfully predicted by the group contribution method. This method is very simple and requires only the knowledge of the structural formula of the molecule. By this method, the liquid molar volume and the latent heat of vaporization were predicted within the maximum errors of 4.8% and 4.6%, respectively. 1. Introduction The liquid molar volume is calculated from the known value of molecular weight and liquid density, and is one of the basic and important physical properties used to calculate vapor-liquid equilibria9), solubility parameters5), critical temperatures4) and viscosities11). Especially, the liquid molar nologically but also can be used as a basic datum to estimate the liquid molar volume at any desired temperature13). On the other hand, the latent heat of vaporization is essential for the processes in which thermal effects are considered. Especially, the latent heat of vaporization at the normal boiling point is highly important, and is utilized in calculating critical properties7), vapor pressures8), and the latent heat of vaporization at any desired temperature3). Recently, Fedors2) used the group contribution method to estimate the liquid molar volume at heat of vaporization at the normal boiling point groups which have various specific values. In the present paper, two different methods were used to estimate the liquid molar volume of ali- method of Fedors which makes use of the newly determined values of functional groups to increase the accuracy of estimation. The other method considers the effect of the position of a functional group, because each position has a different value. The latent heat of vaporization of aliphatic hydrocarbons was estimated by the same method that was used to estimate the liquid molar volume Received May 23, * Department of Industrial Chemistry, Faculty of Engineering, Tokyo Metropolitan Setagaya-ku, Tokyo 158) University (2-1-1, Fukazawa, For the structural formula of the molecule, the IUPAC nomenclature was used. 2. The Group Contribution Method The group contribution method was already successfully used to estimate physical properties and critical constants7). And, it can be said that it is one of the reasonable methods to predict the physical properties of a fluid when no data are available. The basic advantage of this method is that the physical properties of thousands of compounds are calculated by the summation of a much smaller number of functional groups which constitute those compounds. Also, using a minimum amount of experimental data, values of those functional groups can be determined. Thus, by the group contribution method, the the i-th functional group for the liquid molar tion at the normal boiling point, respectively. 3. The Determination of the Group Increments Aliphatic hydrocarbons are made up from 10 kinds of functional groups as [-CH3], [-CH2-],

2 33 For the calculation of the liquid molar volume, the following two methods were used to determine the group increments. One treatment (Method I) is an improved Fedors' method. In this method, the group increments of [-CH3], [-CH2-] and [-CH-] have the same values for the functional groups on the main chain and those on the side chains. Fedors used no distinction between the saturated and unsaturated aliphatic hydrocarbons for [-CH-] and [-C-] functional groups. But, in this work, [-CH-] and [-C-] functional groups have different values for the saturated and unsaturated aliphatic hydrocarbons, also, the group increments of [=C=] were determined but they were not in Fedors' work. The other method (Method II) represents that the group increments of [-CH3 ], [-CH2-] and [-CH-] have different values whether they consist of the functional groups on the main chain or on the side chains. In addition, the values of the increments on the main chain have different values depending on their positions. Moreover, following functional groups on the main chain [-CH2-], [-CH-] and [-C-], and [-CH2-] and [-CH-] functional groups on the side chains, have different values for the saturated and unsaturated aliphatic hydro- a: Alkane. *: Position number of functional groups on the main chain. a: Alkane, n-a: n-alkane, b-a: Branched alkane.

3 carbons. In the calculation of the latent heat of vaporization, the basic idea of the latter method for calculating the liquid molar volume was used. The increments for unsaturated aliphatic hydrocarbons were determined based on the saturated aliphatic hydrocarbon increments which were reported in a previous study6). The group increments of [-CH3], [-CH2-] and [-CH-] functional groups take different values if they belong to the main chain or to the side chains. The increment of [-CH2-] functional group on the main chain has the same value for branched alkanes, branched alkenes, alkadienes and alkynes, but that value was different from the values for n-alkanes and n-1-alkenes. In addition, the value for n-alkane is different from that for n-1- alkene. The group increments determined for calculation of the liquid molar volume for aliphatic hydro- Table 3 Group Contributions for Calculation of the Latent Heat of Vaporization for Aliphatic Hydrocarbons at the Normal Boiling Point *: Position number of functional groups on the main chain, **: End group. n-a: n-alkane, n-1-a: n-1-alkene.

4 35 Table 1 shows the Fedors' group increments and the improved ones, namely they are determined by method I. Table 2 shows those increments determined by method II. The data of API10) was used to determine the values of the individual group increments. Table 3 shows the group increments determined for the latent heat of vaporization for aliphatic hydrocarbons at the normal boiling points. To determine the values of almost all the individual group increments, the data of Wilhoit and Zwolinski14) were used. But, the values of [-CH2-] group increments for n-alkanes (from C21H44 to C40H82) and n-1-alkenes (from C21H42 to C40H80) were determined from the data of Dreisbach1) because the relevant data were not included in the work of Wilhoit and Zwolinski. 4. Calculations and Results Examples of calculations of the liquid molar of aliphatic hydrocarbons at the normal boiling points were shown in the Appendix. The results calculated in this work and the experimental data obtained are compared, and a summary of errors for the liquid molar volume at heat of vaporization is shown in Table 5. For liquid molar volume calculations, the two methods Table 4 A Summary of Errors in the Calculation of Liquid Molar Volumes of Aliphatic Hydro- Table 5 A Summary of Errors in the Calculation of were used as shown. These methods were used for 303 aliphatic hydrocarbons which included 141 alkanes (C5H12 to C10H22), 151 alkenes (C5H10 to C10H20), 5 alkadienes (C5H8) and 4 alkynes (C4H6 and C5H8). The relative average error and maximum error for method I were found to be 1.1% and 4.8% for 2-methyl-3,3-diethylpentane, respectively. For method II, they were 0.7% and 3.0% for 4,5-dimethyloctane, respectively. Fedors' increments were also examined for 300 aliphatic hydrocarbons which included 141 alkanes (C5H12 to C10H22), 151 alkenes (C5H10 to C10H20), 2 alkadienes (C5H8) and 4 alkynes (C4H6 and C5H8). The relative average error and maximum error were 1.7% and 6.7% for 3,3,4,4-tetramethylhexane, respectively. The latent heat of vaporization for 384 aliphatic hydrocarbons were calculated. These hydrocarbons included 180 alkanes (CH4 to C40H82), 189 alkenes (C2H4 to C40H80), 8 alkadienes (C3H4 to C5H8) and 7 alkynes (C2H2 to C5H8). The relative average error of 1.3% was found with the maximum error of 4.6% for 2-ethyl-1-butene. 180 alkanes found in a previous study6) were here culated by treating the methane molecule as 1.1 interaction [-CH3] (functional group on the main chain) groups. 5. Conclusions The group contribution method is simple and convenient because it requires only the knowledge of the structural formula of the molecule. The application of this method to the prediction of the vaporization of aliphatic hydrocarbons at the normal boiling points showed good agreement between the experimental data and the predicted values. Appendix the Latent Heat of Vaporization of Aliphatic Hydrocarbons at the Normal Boiling Points The use of Tables 1 to 3 is shown by calculat- heat of vaporization at the normal boiling point

5 of 2-ethyl-3-methyl-1-butene as follows: 2-ethyl-3-methyl-1-butene Subscripts cal=calculated exp=experimental [Table 3] (for the latent heat of vaporization the normal boiling point) at References 1) Dreisbach, R. R., "Physical Properties of Chemical Compounds", Advances in Chem. Ser., ACS Monograph 22 (1959). 2) Fedors, R. F., Poly. Eng. Sci., 14, 147 (1974). 3) Fishtine, S. H., Hydrocarbon Process. Petrol. Refiner, 42, (10), 143 (1963). 4) Hakuta, T., Matsushita, K., Shono, H., Hirata, M., Bull. Japan Petrol. Inst., 12, 146 (1970). 5) Hildebrand, J. H., Scott, R. L., "Solubility of Nonelectrolytes", Reinhold (1950). 6) Hoshino, D., Nagahama, K., Hirata, M., J. Chem. Eng. Japan, 5, 403 (1978). 7) Lydersen, A. L., "Estimation of Critical Properties of Organic Compounds", Coll. Eng. Univ. Wisconsin, Eng. Expt. Sta, Rept. 3, Madison, Wis., April (1955). 8) Miller, D. G., Ind. Eng. Chem., 56, 46 (1964). 9) Prausnitz, J. M., Eckert, C. A., Orey, R. V., O'Connell, J. P., "Computer Calculation for Multicomponent Vapor-Liquid Equilibria", Prentice-Hall (1967). 10) "Technical Data Book-Petroleum Refining", Am. Petrol. Inst., (1966), New York. 11) Thomas, L. H., J. Chem. Soc., 573 (1946). 12) Verma, K. K., Doraiswamy, L. K., Ind. Eng. Chem. Fundamentals, 4, 389 (1965). 13) Yamada, T., Gunn, R. D., J. Chem. Eng. Data, 18, 234 (1973). 14) Wilhoit, R. C., Zwolinski, B. J., "Handbook of Vapor Pressure and Heats of Vaporization of Hydrocarbons and Related Compounds", API-TRC Publication No. 101 (1971). Nomenclature E=relative error [%]

6 Keyword Aliphatic hydrocarbon, Group contribution method, Latent heat vaporization, Molar volume liquid