Physics:Lydersen method
The Lydersen method[1] is a group contribution method for the estimation of critical properties temperature (Tc), pressure (Pc) and volume (Vc). The Lydersen method is the prototype for and ancestor of many new models like Joback,[2] Klincewicz,[3] Ambrose,[4] Gani-Constantinou[5] and others.
The Lydersen method is based in case of the critical temperature on the Guldberg rule which establishes a relation between the normal boiling point and the critical temperature.
Equations
Critical temperature
- [math]\displaystyle{ T_c=\frac{T_b}{0.567+\sum G_i-\left(\sum G_i\right)^2} }[/math]
Guldberg has found that a rough estimate of the normal boiling point Tb, when expressed in kelvins (i.e., as an absolute temperature), is approximately two-thirds of the critical temperature Tc. Lydersen uses this basic idea but calculates more accurate values.
Critical pressure
- [math]\displaystyle{ P_c=\frac{M}{\left(0.34+\sum G_i\right)^2} }[/math]
Critical volume
- [math]\displaystyle{ V_c\,=\,40+\sum G_i }[/math]
M is the molar mass and Gi are the group contributions (different for all three properties) for functional groups of a molecule.
Group contributions
| Group | Gi (Tc) | Gi (Pc) | Gi (Vc) | Group | Gi (Tc) | Gi (Pc) | Gi (Vc) |
|---|---|---|---|---|---|---|---|
| -CH3,-CH2- | 0.020 | 0.227 | 55.0 | >CH | 0.012 | 0.210 | 51.0 |
| -C< | - | 0,210 | 41.0 | =CH2,#CH | 0.018 | 0,198 | 45.0 |
| =C<,=C= | - | 0.198 | 36.0 | =C-H,#C- | 0.005 | 0.153 | 36.0 |
| -CH2-(Ring) | 0.013 | 0.184 | 44.5 | >CH-(Ring) | 0.012 | 0.192 | 46.0 |
| >C<(Ring) | -0.007 | 0.154 | 31.0 | =CH-,=C<,=C=(Ring) | 0.011 | 0.154 | 37.0 |
| -F | 0.018 | 0.224 | 18.0 | -Cl | 0.017 | 0.320 | 49.0 |
| -Br | 0.010 | 0.500 | 70.0 | -I | 0.012 | 0.830 | 95.0 |
| -OH | 0.082 | 0.060 | 18.0 | -OH(Aromat) | 0.031 | -0.020 | 3.0 |
| -O- | 0.021 | 0.160 | 20.0 | -O-(Ring) | 0.014 | 0.120 | 8.0 |
| >C=O | 0.040 | 0.290 | 60.0 | >C=O(Ring) | 0.033 | 0.200 | 50.0 |
| HC=O- | 0.048 | 0.330 | 73.0 | -COOH | 0.085 | 0.400 | 80.0 |
| -COO- | 0.047 | 0.470 | 80.0 | -NH2 | 0.031 | 0.095 | 28.0 |
| >NH | 0.031 | 0.135 | 37.0 | >NH(Ring) | 0.024 | 0.090 | 27.0 |
| >N | 0.014 | 0.170 | 42.0 | >N-(Ring) | 0.007 | 0.130 | 32.0 |
| -CN | 0.060 | 0.360 | 80.0 | -NO2 | 0.055 | 0.420 | 78.0 |
| -SH,-S- | 0.015 | 0.270 | 55.0 | -S-(Ring) | 0.008 | 0.240 | 45.0 |
| =S | 0.003 | 0.240 | 47.0 | >Si< | 0.030 | 0.540 | - |
| -B< | 0.030 | - | - |
Example calculation
Acetone is fragmented in two different groups, one carbonyl group and two methyl groups. For the critical volume the following calculation results:
Vc = 40 + 60.0 + 2 * 55.0 = 210 cm3
In the literature (such as in the Dortmund Data Bank) the values 215.90 cm3,[6] 230.5 cm3 [7] and 209.0 cm3 [8] are published.
References
- ↑ Lydersen, a.L.. "Estimation of Critical Properties of Organic Compounds". Engineering Experiment Station Report (Madison, Wisconsin: University of Wisconsin College Engineering) 3.
- ↑ Joback, K.G.; Reid, R.C. (1987). "Estimation of pure-component properties from group-contributions". Chemical Engineering Communications (Informa UK Limited) 57 (1–6): 233–243. doi:10.1080/00986448708960487. ISSN 0098-6445.
- ↑ Klincewicz, K. M.; Reid, R. C. (1984). "Estimation of critical properties with group contribution methods". AIChE Journal (Wiley) 30 (1): 137–142. doi:10.1002/aic.690300119. ISSN 0001-1541.
- ↑ Ambrose, D. (1978). Correlation and Estimation of Vapour-Liquid Critical Properties. I. Critical Temperatures of Organic Compounds. National Physical Laboratory Reports Chemistry. 92. p. 1-35.
- ↑ Constantinou, Leonidas; Gani, Rafiqul (1994). "New group contribution method for estimating properties of pure compounds". AIChE Journal (Wiley) 40 (10): 1697–1710. doi:10.1002/aic.690401011. ISSN 0001-1541.
- ↑ Campbell, A. N.; Chatterjee, R. M. (1969-10-15). "The critical constants and orthobaric densities of acetone, chloroform, benzene, and carbon tetrachloride". Canadian Journal of Chemistry (Canadian Science Publishing) 47 (20): 3893–3898. doi:10.1139/v69-646. ISSN 0008-4042.
- ↑ Herz, W.; Neukirch, E. (1923). "Zur Kenntnis kritischer Grössen". Z.Phys.Chem.(Leipzig) 104: S.433-450. doi:10.1515/zpch-1923-10429.
- ↑ Kobe, Kenneth A.; Crawford, Horace R.; Stephenson, Robert W. (1955). "Industrial Design Data—Critical Properties and Vapor Presesures of Some Ketones". Industrial & Engineering Chemistry (American Chemical Society (ACS)) 47 (9): 1767–1772. doi:10.1021/ie50549a025. ISSN 0019-7866.
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