Abstract
In this chapter, physical and chemical transformations are considered as a route from a less stable to a more stable equilibrium state. Initially, only physical transformations are considered describing the first and second thermodynamic laws and thermodynamic properties like internal energy, enthalpy, and entropy. Next, thermodynamic equilibrium in chemically reacting systems is considered, defining “chemical potential” as the driving force for reactions and examining in detail chemical equilibrium conditions. Equilibrium reactions between gases at different pressures are considered and the fugacity concept to describe the behavior of real gases is introduced. Different methods for determining and fugacity are described. Equilibrium reactions between reactants in the liquid phase are also considered, introducing the concept of activity. Different methods for determining activity coefficients are described. Several examples of equilibrium calculations are reported. Matlab code associated with these examples is available online. Finally, vapor–liquid equilibrium is examined in detail considering its applications in a flash-unit and a tray-distillation column.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abrams, D., Prausnitz, J.M.: Statistical thermodynamics of liquid mixtures. A new expression for the excess Gibbs energy of partly and completely miscible systems. AIChE J. 21, 116–128 (1975)
Ambrose, D.: Correlation and estimation of vapor-liquid critical properties I. Critical temperatures of organic compounds. NPL Rep. Chem. 92, National Physical Laboratory, Teddington, UK (1978)
Ambrose, D.: Vapor-liquid critical properties II. Critical pressure and critical volume. NPL Rep. Chem. 107, National Physical Laboratory, Teddington, UK (1980)
Anderson, J.W., Beyer, G.H., Watson, K.M.: Natl. Petrol News 36, R476–R483 (1944)
Bertucco, A., Barolo, M., Soave, G.: Estimation of chemical equilibria in high-pressure gaseous systems by a modified Redlich-Kwong-Soave equation of state. Ind. Eng. Chem. Res. 34(9), 3159–3165 (1995)
Bodenstein, M.: Zersetzung und Bildung von Jodwasserstoff; Z. Physik. Chem., 22 (1897)
Carrà, S.: La Produzione Chimica: Processi e Operazioni Unitarie; ISEDI, Enciclopedia della Chimica (1977)
Constantinou, L., Gani, R.: New group contribution method for estimating properties of pure compounds. AIChE J. 40(10), 1697–1710 (1994)
Debye, P., Hückel, E.: Zur Theorie der Elektrolyte. Phys. Z. 24, 185–206 (1923)
Dyson, D.C., Simon, J.M.: A kinetic expression with diffusion correction for ammonia synthesis on industrial catalyst. Ind. Eng. Chem. Fundam. 7(4), 605 (1986)
Flory, P.J.: Thermodynamics of high polymer solutions. J. Chem. Phys. 10, 51–61 (1942)
Francis, A.W.: The free energies of some hydrocarbons. Ind. Eng. Chem. 20(3), 277–282 (1928)
Franklin, J.L.: Prediction of heat and free energies of organic compounds. Ind. Eng. Chem. 41, 1070–1076 (1949)
Fredenslund, A.A., Russell, L.J., Prausnitz, J.M.: Group-contribution estimation of activity coefficients in nonideal liquid mixtures. AIChE J. 21(6), 1086–1099 (1975)
Fredenslund, A.A., Gmehling, J., Rasmussen, P.: Vapor-Liquid equilibria using UNIFAC, a group contribution method. Elsevier Scientific Pu. Co., Amsterdam (1977)
Gerasimov, Y.A., Dreving, V., Eremin, E., Kiselev, A., Lebedev, V., Panchenkov, G., Shlygin, A.: Physical Chemistry, Vol. I. MIR Publisher, Moscow (1974)
Gillespie, L.J., Beattie, J.A.: The thermodynamic treatment of chemical equilibria in systems composed of real gases. I. An approximate equation for the mass action function applied to the existing data on the Haber equilibrium. Phys. Rev. 36, 743 (1930)
Glasstone, S.: Thermodynamics for Chemistry. Van Nostrand, New York (1947)
Guéret, C., Daroux, M., Billaud, F.: Methane pyrolysis: thermodynamics. Chem. Eng. Sci. 52(5), 815–827 (1997)
Hayden, J.G., O’Connel, J.P.: A generalized method for predicting second virial coefficients. Ind. Eng. Chem. Proc. Des. Dev. 14(3), 209–216 (1975)
Hildebrand, J.H., Prausnitz, J.M., Scott, R.L.: Regular and Related Solutions. Van Nostrand Reinhold Co., New York (1970)
Hougen, O.A., Watson, K.M.: Chemical Process Principles, Part Two: Thermodynamics. Wiley, New York (1947)
Huggins, M.L.: Solutions of long-chain compounds. J. Chem. Phys. 9, 440 (1941)
Joback, K.G., Reid, R.C.: Estimation of pure-component properties from group contributions. Chem. Eng. Commun. 57, 233–243 (1987)
Kammerlingh Onnes, H.: Expression of the equation of state of gases and liquids by means of serie. Communications from the Physical Laboratory of the University of Leiden 71, pp. 3–25 (1901)
Kay, W.B.: Density of hydrocarbon. Ind. Eng. Chem. 28, 1014 (1936)
Kojima, K., Tochigi, K.: Prediction of Vapor-Liquid Equilibria by the ASOG Method. Kodanska ltd, Elsevier (1979)
Larson, A.T.: The ammonia equilibrium at high pressure. J. Am. Chem. Soc. 46, 367–372 (1924)
Lee, B.I., Kesler, M.G.: A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE J. 21(3), 510–527 (1975)
Lewis, G.N.: The law of physico-chemical change. Proc. Am. Acad. Arts Sci. 37(4), 49–69 (1901)
Lewis, G.N., Randall, M.: Thermodynamics, 2nd edn (Revised by Pitzer, K.S., Brewer, L.). Mc Graw-Hill, New York (1961)
Lowry, T.M.: The Uniqueness of hydrogen. J. Soc. Chem. Ind. 42(3), 43–47 (1923)
Lydersen, A.L.: Estimation of critical properties of organic compounds. Coll. Eng. Univ. Wisconsin, Engineering Experimental Station Rept. 3, Madison, WI (1955)
Margules M.: Über die Zusammensetzung der gesättigten Dämpfe von ischungen. Sitzungsberichte der Kaiserliche Akadamie der Wissenschaften Wien Mathematisch-Naturwissenschaftliche Klasse II. 104, 1243–1278 (1895)
Mc Cann, D.W., Danner, R.P.: Prediction of second virial coefficients of organic compounds by a group contribution method 23(3), 529–533 (1984)
Neumann, B., Kohler, G.: Die Gleichgewitchtsverhaltnisse bei der Wassergasreaktion im Temperaturbereich von 300 bis 1000°. Z. Elektrochem. 34, 218–237 (1928)
Peneloux, A., Rauzy, E., Fréze, R.: A consistent correction for Redlich-Kwong-Soave volumes. Fluid Phase Equilib. 8(1): 7–23 (1982)
Peng, D.Y., Robinson, D.B.: A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15(1), 59–64(1976)
Pitzer, K.S.: The volumetric and thermodynamic properties of fluids. I. Theoretical basis and virial coefficients. J. Am. Chem. Soc. 77, 3427–3433 (1955)
Redlich, O., Kwong, J.N.S.: On the thermodynamics of solutions. V. An equation of state. Fugacities of gaseous solutions. Rev. Chem. 44(1), 233–244 (1949)
Reid, R.C., Prausnitz, J.M., Poling, B.E.: The Properties of Gases & Liquids. Mc Graw Hill, New York (1987)
Renon, H., Prausnitz, J.M.: Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 14(1), 135–144 (1968)
Rihani, D.N., Doraiswamy, L.K.: Estimation of heat capacity of organic compounds from group contributions. Ind. Eng. Chem. Fundam. 4(1), 17–21 (1965)
Rossini, F.D, Pitzer, K.S., Arnett, R.L., Braun, R.M., Pimentel, G.C.: API Project 44, Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds. Carnegie Press, Pittsburg (1953)
Scatchard, G.: Equilibrium in non-electrolyte mixtures. Chem. Rev. 44(1), 7–35 (1949)
Scott, R.L.: Corresponding states treatment of nonelectrolyte solutions. J. Chem. Phys. 25, 193 (1956)
Smith, B.D.: Thermodynamic excess property measurements for acetonitrile-benzene-n-heptane system at 45°C. J. Chem. Eng. Data 17, 71–76 (1972)
Soave, G.: Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 27(6), 1197–1203 (1972)
Soave, G., Barolo, M., Bertucco, A.: Estimation of high-pressure fugacity coefficients of pure gaseous fluids by a modified SRK equation of state. Fluid Phase Equilib. 91, 87–100 (1993)
Standing, M.B., Katz, D.L.: Density of natural gases. Trans. AIME 146, 140–149 (1942)
Stull, D.R., Westrum, E.F., Sinke, G.C.: The Chemical Thermodynamics of Organic Compounds. Wiley, New York (1969)
Su, G.J.: Modified law of corresponding states for real gases. Ind. Eng. Chem. 38, 803–806 (1946)
Tsonopoulos, C.: An empirical correlation of second virial coefficients. A.I.Ch.E. J. 20, 263 (1974)
Vancini, C.A.: Synthesis of Ammonia. The Macmillan Press, London (1971)
Van Krevelen, D.W., Chermin, H.A.: Estimation of the free enthalpy (Gibbs free energy) of formation of organic compounds from group contributions. Chem. Eng. Sci. 1, 66–80 (1951)
Van Laar, J.J.: The vapor pressure of binary mixtures. Z. Phys. Chem. 72, 723 (1910)
Van Ness, H.C., Abbott M.M.: Classical Thermodynamics of Nonelectrolyte Solutions. Mc Graw-Hill, New York (1982)
Verma, K.K., Doraiswamy, L.K.: Estimation of heats of formation of organic compounds. Ind. Eng. Chem. Fundamen. 4(4), 389–396 (1965)
Wallace, F.J., Linning, W.A.: Basic Engineering Thermodynamics. Pitman Paperbacks (1970)
Wilson, G.M.: Vapor-liquid equilibrium. xi. a new expression for the excess free energy of mixing. J. Am. Chem. Soc. 86(2), 127–130 (1964)
Wisniak, Y.: Émile-Hilaire Amagat and the laws of fluids. Educacion Quimica 17(1), 86–96 (2005)
Author information
Authors and Affiliations
Corresponding author
2.1 Electronic Supplementary Material
Below is the link to the electronic supplementary material.
Appendices
Appendix 1: Lydersen’s Method: Increments for the Calculation of the Critical Variables
Functional groups | ΔT | ΔP | ΔV |
|---|---|---|---|
Increments for groups not in a ring | |||
\( - {\text{CH}}_{ 3} \) | 0.020 | 0.227 | 55 |
| 0.020 | 0.227 | 55 |
| 0.012 | 0.210 | 51 |
| 0.000 | 0.210 | 41 |
\( {\text{ = CH}}_{ 2} \) | 0.018 | 0.198 | 45 |
| 0.018 | 0.198 | 45 |
| 0.000 | 0.198 | 36 |
\( {\text{ = C = }} \) | 0.000 | 0.198 | 36 |
\( \equiv {\text{CH}} \) | 0.005 | 0.153 | (36) |
\( \equiv C - \) | 0.005 | 0.153 | (36) |
Increments for groups inside a ring | |||
\( - {\text{CH}}_{2} - \) | 0.013 | 0.184 | 44.5 |
| 0.012 | 0.192 | 46 |
| (−0.007) | (0.154) | (31) |
| 0.011 | 0.154 | 37 |
| 0.011 | 0.154 | 36 |
\( = {\text{C}} = \) | 0.011 | 0.154 | 36 |
Increments for alogens | |||
\( - {\text{F}} \) | 0.018 | 0.224 | 18 |
\( - {\text{Cl}} \) | 0.017 | 0.320 | 49 |
\( - {\text{Br}} \) | 0.010 | (0.50) | (70) |
\( - {\text{I}} \) | 0.012 | (0.83) | (95) |
Increments for groups containing oxygen | |||
\( - {\text{OH}} \) (alcohol) | 0.082 | 0.06 | (18) |
\( - {\text{OH}} \) (phenol) | 0.031 | (−0.02) | (3) |
\( - {\text{O}} - \) (not in a ring) | 0.021 | 0.16 | 20 |
\( - {\text{O}} - \) (in a ring) | (0.014) | (0.12) | (8) |
(not in a ring) | 0.040 | 0.29 | 60 |
(in a ring) | (0.033) | (0.2) | (50) |
(aldehyde) | 0.048 | 0.33 | 73 |
\( - {\text{COOH}} \) (acid) | 0.085 | (0.4) | 80 |
\( - {\text{COO}} - \) (ester) | 0.047 | 0.47 | 80 |
\( {\text{ = O}} \) (different from previous cases) | (0.02) | (0.12) | (11) |
Increments for groups containing nitrogen | |||
\( - {\text{NH}}_{ 2} \) | 0.031 | 0.095 | 28 |
(not in a ring) | 0.031 | 0.135 | (37) |
(in a ring) | (0.024) | (0.09) | (27) |
(not in a ring) | 0.014 | 0.17 | (42) |
(in a ring) | (0.007) | (0.13) | (32) |
\( - {\text{CN}} \) | (0.060) | (0.36) | (80) |
\( - {\text{NO}}_{ 2} \) | (0.055) | (0.42) | (78) |
Increments for groups containing sulphur | |||
\( - {\text{SH}} \) | 0.015 | 0.27 | 55 |
\( - {\text{S}} - \) (not in a ring) | 0.015 | 0.27 | 55 |
\( - {\text{S}} - \) (in a ring) | (0.008) | (0.24) | (45) |
\( = {\text{S}} \) | (0.003) | (0.24) | (47) |
Other functional groups | |||
| 0.03 | (0.54) | – |
| (0.03) | – | – |
Appendix 2: Group Contributions for Estimating \( C_{\text{p}}^{0} \),\( {\Delta} H_{\text{f,298K}}^{0} \), and \( {\Delta} G_{\text{f}}^{0} \)
Part 1 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
Groups | Heat-capacity constants | \( {\Delta} H_{\text{f}}^{0} \) (298 K) | Constants for determining Gibbs free energy | ||||||
300–600 K | 600–1500 K | ||||||||
a | b × 102 | c × 104 | d × 106 | A | B × 102 | A | B × 102 | ||
\( - {\text{CH}}_{ 3} \) | 0.6087 | 2.1433 | –0.0852 | 0.1135 | 10.25 | –10.943 | 2.215 | –12.310 | 2.436 |
\( - {\text{CH}}_{ 2} - \) | 0.3945 | 2.1363 | –0.1197 | 0.2596 | –4.94 | –5.193 | 2.430 | –5.830 | 2.544 |
| –3.5232 | 3.4158 | –0.2816 | 0.8015 | –1.29 | –0.705 | 2.910 | –0.705 | 2.910 |
| –5.8307 | 4.4541 | –0.4208 | 1.263 | 0.62 | 1.958 | 3.735 | 4.385 | 3.350 |
| 0.2773 | 3.4580 | –0.1918 | 0.4130 | 15.02 | 13.737 | 1.655 | 12.465 | 1.762 |
| –0.4173 | 3.8857 | –0.2783 | 0.7364 | 20.50 | 16.467 | 1.915 | 16.255 | 1.966 |
(cis) | –3.1210 | 3.0860 | –0.2359 | 0.5504 | 17.96 | 17.663 | 1.965 | 16.180 | 2.116 |
(trans) | 0.9377 | 2.9904 | –0.1749 | 0.3918 | 17.83 | 17.187 | 1.915 | 15.815 | 2.062 |
| –1.4714 | 3.3842 | –0.2371 | 0.6063 | –20.10 | 20.217 | 2.295 | 19.584 | 2.354 |
| 0.4736 | 3.5183 | –0.3150 | 0.9205 | 30.46 | 25.135 | 2.573 | 25.135 | 2.573 |
| 2.2400 | 4.2896 | –0.2566 | 0.5908 | 49.47 | 49.377 | 1.035 | 48.170 | 1.208 |
| 2.6308 | 4.1658 | –0.2845 | 0.7277 | 51.30 | 51.084 | 1.474 | 51.084 | 1.474 |
| –3.1249 | 6.6843 | –0.5766 | 1.743 | 55.04 | 52.460 | 1.483 | 52.460 | 1.483 |
\( \equiv {\text{CH}} \) | – | – | – | – | 27.10 | 27.048 | –0.765 | 26.700 | –0.704 |
\( \equiv {\text{C}} - \) | – | – | – | – | 27.38 | 26.938 | –0.525 | 26.555 | –0.550 |
Part 2 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
Groups | Heat-capacity constants | \( {\Delta} H_{\text{f}}^{0} \) (298 K) | Constants for determining Gibbs free energy | ||||||
300–600 K | 600–1500 K | ||||||||
a | b × 102 | c × 104 | d × 106 | A | B × 102 | A | B × 102 | ||
Groups for conjugated alkenes | |||||||||
| – | – | – | – | (10.1) | 5.437 | 0.675 | 4.500 | 0832 |
| – | – | – | – | (12) | 7.407 | 1.035 | 6.980 | 1.088 |
| – | – | – | – | – | 9.152 | 1.505 | 10.370 | 1.308 |
| –1.4572 | 1.9147 | –0.1233 | 0.2985 | 3.27 | 3.047 | 0.615 | 2.505 | 0.706 |
| –1.3883 | 1.5159 | –0.0690 | 0.2659 | 5.55 | 4.675 | 1.150 | 5.010 | 0.988 |
| 0.1219 | 1.2170 | –0.0855 | 0.2122 | 4.48 | 3.513 | 0.568 | 3.998 | 0.485 |
Corrections for cycloparafine rings | |||||||||
Three-atom rings | –3.5320 | –0.0300 | 0.0747 | –0.5514 | 24.13 | 23.458 | –3.045 | 22.915 | –2.966 |
Four-atom rings | –8.6550 | 1.0780 | 0.0425 | 0.0250 | 18.45 | 10.73 | –2.65 | 10.60 | –2.50 |
Five-atom rings (pentane) | –12.285 | 1.8609 | –0.1037 | 0.2145 | 5.44 | 4.275 | –2.350 | 2.665 | –2.182 |
Five-atom rings (pentene) | –6.8813 | 0.7818 | –0.0345 | 0.0591 | – | –3.657 | –2.395 | –3.915 | –2.150 |
Six-atom rings (hexane) | –13.3923 | 2.1392 | –0.0429 | –0.1865 | –0.76 | –1.128 | –1.635 | –1.930 | –1.504 |
Six-atom rings (hexene) | –8.0238 | 2.2239 | –0.1915 | 0.5473 | – | –9.102 | –2.045 | –8.810 | –2.071 |
Branched parafines | |||||||||
Side chain with ≥ 2 atoms | – | – | – | – | 0.80 | 1.31 | 0 | 1.31 | 0 |
| – | – | – | – | –1.2 | –2.13 | 0 | 2.12 | 0 |
| – | – | – | – | 0.6 | 1.80 | 0 | 1.80 | 0 |
| – | – | – | – | (5.4) | 2.58 | 0 | 2.58 | 0 |
Part 3 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
Groups | Heat-capacity constants | \( {\Delta} H_{\text{f}}^{0} \) (298 K) | Constants for determining Gibbs free energy | ||||||
300–600 K | 600–1500 K | ||||||||
a | b × 102 | c × 104 | d × 106 | A | B × 102 | A | B × 102 | ||
Branching in cycles with 5 atoms | |||||||||
Single branching | – | – | – | – | 0 | –1.04 | 0 | –1.69 | 0 |
Double branching | |||||||||
Position 1,1 | – | – | – | – | 0.30 | –1.85 | 0 | –1.19 | –0.16 |
Position cis-1,2 | – | – | – | – | 0.70 | –0.38 | 0 | –0.38 | 0 |
Position trans-1,2 | – | – | – | – | –1.10 | –2.55 | 0 | –0.945 | –0.266 |
Position cis-1,3 | – | – | – | – | –0.30 | –1.20 | 0 | –0.370 | –0.166 |
Position trans-1,3 | – | – | – | – | –0.90 | –2.35 | 0 | –0.800 | –0.264 |
Branching in cycles with 6 atoms | |||||||||
Single branching | – | – | – | – | 0 | –0.93 | 0 | 0.230 | –0.192 |
Double branching | |||||||||
Position 1,1 | – | – | – | – | 2.44 | 0.835 | –0.367 | 1.745 | –0.556 |
Position cis-1,2 | – | – | – | – | –0.20 | –0.19 | 0 | 1.470 | –0.276 |
Position trans-1,2 | – | – | – | – | –2.69 | –2.41 | 0 | 0.045 | –0.398 |
Position cis-1,3 | – | – | – | – | –2.98 | –2.70 | 0 | –1.647 | –0.185 |
Position trans-1,3 | – | – | – | – | –0.48 | –1.60 | 0 | 0.260 | –0.290 |
Position cis-1,4 | – | – | – | – | –0.48 | –1.11 | 0 | –1.11 | 0 |
Position trans-1,4 | – | – | – | – | –2.98 | –2.80 | 0 | –0.995 | –0.245 |
Branching in aromatic rings | |||||||||
Double branching | |||||||||
Position 1,2 | – | – | – | – | 0.94 | 1.02 | 0 | 1.02 | 0 |
Position 1,3 | – | – | – | – | 0.38 | –0.31 | 0 | –0.31 | 0 |
Position 1,4 | – | – | – | – | 0.58 | 0.93 | 0 | 0.93 | 0 |
Triple branching | |||||||||
Position 1,2,3 | – | – | – | – | 1.80 | 1.91 | 0 | 2.10 | 0 |
Position 1,2,4 | – | – | – | – | 0.44 | 1.10 | 0 | 1.10 | 0 |
Position 1,3,5 | – | – | – | – | 0.44 | 0 | 0 | 0 | 0 |
Groups containing oxygen | |||||||||
\( -{\text{OH}} \)(primary) | 6.5128 | –0.1347 | 0.0414 | –0.1623 | –41.2 | –41.56 | 1.28 | –41.56 | 1.28 |
\( - {\text{OH}} \)(secondary) | 6.5128 | –0.1347 | 0.0414 | –0.1623 | –43.8 | –41.56 | 1.28 | –41.56 | 1.28 |
\( - {\text{OH}} \)(tertiary) | 6.5128 | –0.1347 | 0.0414 | –0.1623 | –47.6 | –41.56 | 1.28 | –41.56 | 1.28 |
\( - {\text{OH}} \)(quaternary) | 6.5128 | –0.1347 | 0.0414 | –0.1623 | –45.1 | –41.56 | 1.28 | –41.56 | 1.28 |
\( - {\text{O}}- \) | 2.8461 | –0.0100 | 0.0454 | –0.2728 | –24.2 | –15.79 | –0.85 | – | – |
\( - {\text{CHO }}- \) | 3.5184 | 0.9437 | 0.0614 | –0.6978 | –29.71 | –29.28 | 0.77 | –30.15 | 0.83 |
| 1.0016 | 2.0763 | –0.1636 | 0.4494 | –31.48 | –28.08 | 0.91 | –28.08 | 0.91 |
\( - {\text{COOH}} \) | 1.4055 | 3.4632 | –0.2557 | 0.6886 | –94.68 | –98.39 | 2.86 | –98.83 | 2.93 |
\( - {\text{COO}}- \) | 2.7350 | 1.0751 | 0.0667 | –0.9230 | (–79.8) | –92.62 | 2.61 | –92.62 | 2.61 |
| –3.7344 | 1.3727 | –0.1265 | 0.3789 | –21.62 | –18.37 | 0.80 | –16.07 | 0.40 |
Part 4 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
Groups | Heat capacity constants | \( {\Delta} H_{\text{f}}^{0} \) (298 K) | Constants for determining Gibbs free energy | ||||||
300–600 K | 600–1500 K | ||||||||
a | b × 102 | c × 104 | d × 106 | A | B × 102 | A | B × 102 | ||
Groups containing nitrogen | |||||||||
\( - {\text{C }}\equiv {\text{N}} \) | 4.5104 | 0.5461 | 0.0269 | –0.3790 | 36.82 | 30.75 | –0.72 | 30.75 | –0.72 |
\( - {\text{N = C}} \) | 5.0860 | 0.3492 | 0.0259 | –0.2436 | (44.4) | 46.32 | –0.89 | 46.32 | –0.89 |
\( - {\text{NO}}_{2} \) | 1.0898 | 2.6401 | –0.1871 | 0.4750 | –7.94 | –9.0 | 3.70 | –14.19 | 4.38 |
\( - {\text{NH}}_{2} \)(aliphatic) | 4.1783 | 0.7378 | 0.0679 | –0.7310 | 3.21 | 2.82 | 2.71 | –6.78 | 3.98 |
\( - {\text{NH}}_{2} \)(aromatic) | 4.1783 | 0.7378 | 0.0679 | –0.7310 | –1.27 | 2.82 | 2.71 | –6.78 | 3.98 |
(aliphatic) | –1.2530 | 2.1932 | –0.1604 | 0.4237 | 13.47 | 12.93 | 3.16 | 12.93 | 3.16 |
(aromatic) | –1.2530 | 2.1932 | –0.1604 | 0.4237 | 8.50 | 12.93 | 3.16 | 12.93 | 3.16 |
(aliphatic) | –3.4677 | 2.9433 | –0.2673 | 0.7828 | 18.94 | 19.46 | 3.82 | 19.46 | 3.82 |
(aromatic) | –3.4677 | 2.9433 | –0.2673 | 0.7828 | 8.50 | 19.46 | 3.82 | 19.46 | 3.82 |
| 2.4458 | 0.3436 | 0.0171 | –0.2719 | – | 11.32 | 1.11 | 12.26 | 0.96 |
Groups containing sulphur | |||||||||
\( - {\text{SH}} \) | 2.5597 | 1.3347 | –0.1189 | 0.3820 | 4.60 | –10.68 | 1.07 | –10.68 | 1.07 |
\( - {\text{S }}- \) | 4.2256 | 0.1127 | –0.0026 | –0.0072 | 11.17 | –3.32 | 1.42 | –3.32 | 1.44 |
| 4.0824 | –0.0001 | 0.0731 | –0.6081 | (7.8) | –0.97 | 0.51 | –0.65 | 0.44 |
Groups containing alogens | |||||||||
\( - {\text{F}} \) | 1.4382 | 0.3452 | –0.0106 | –0.0034 | – | –45.10 | 0.20 | – | – |
\( - {\text{Cl}} \) | 3.0660 | 0.2122 | –0.0128 | 0.0276 | – | –8.25 | 0 | –8.25 | 0 |
\( - {\text{Br}} \) | 2.7605 | 0.4731 | –0.0455 | 0.1420 | – | –1.62 | –0.26 | –1.62 | –0.26 |
\( - {\text{I}} \) | 3.2651 | 0.4901 | –0.0539 | 0.1782 | – | 7.80 | 0 | 7.80 | 0 |
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Santacesaria, E., Tesser, R. (2018). Thermodynamics of Physical and Chemical Transformations. In: The Chemical Reactor from Laboratory to Industrial Plant. Springer, Cham. https://doi.org/10.1007/978-3-319-97439-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-97439-2_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-97438-5
Online ISBN: 978-3-319-97439-2
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)