Lydersen method explained

The Lydersen method^[1] is a group contribution method for the estimation of critical properties temperature (T_c), pressure (P_c) and volume (V_c). 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

T _{c = (T _{b})/(0 . 567+ \sum G _{i-\left(\sum} G ^{2} _{i\right)})}

Guldberg has found that a rough estimate of the normal boiling point T_b, when expressed in kelvins (i.e., as an absolute temperature), is approximately two-thirds of the critical temperature T_c. Lydersen uses this basic idea but calculates more accurate values.

Critical pressure

P _{c = (M)/(\left( 0 . 34+ \sum G ^{2} _{i\right)})}

Critical volume

V _{c=40+\sum} G _{i}

M is the molar mass and G_i 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)
bgcolor="#f0f0f0"	-CH3,-CH2-	0.020	0.227	55.0	>CH	0.012	0.210	51.0
bgcolor="#f0f0f0"	-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
bgcolor="#f0f0f0"	-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
bgcolor="#f0f0f0"	-F	0.018	0.224	18.0	bgcolor="#f0f0f0"	-Cl	0.017	0.320	49.0
bgcolor="#f0f0f0"	-Br	0.010	0.500	70.0	bgcolor="#f0f0f0"	-I	0.012	0.830	95.0
bgcolor="#f0f0f0"	-OH	0.082	0.060	18.0	bgcolor="#f0f0f0"	-OH(Aromat)	0.031	-0.020	3.0
bgcolor="#f0f0f0"	-O-	0.021	0.160	20.0	bgcolor="#f0f0f0"	-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	bgcolor="#f0f0f0"	-COOH	0.085	0.400	80.0
bgcolor="#f0f0f0"	-COO-	0.047	0.470	80.0	bgcolor="#f0f0f0"	-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
bgcolor="#f0f0f0"	-CN	0.060	0.360	80.0	bgcolor="#f0f0f0"	-NO2	0.055	0.420	78.0
bgcolor="#f0f0f0"	-SH,-S-	0.015	0.270	55.0	bgcolor="#f0f0f0"	-S-(Ring)	0.008	0.240	45.0
=S	0.003	0.240	47.0	>Si<	0.030	0.540	-
bgcolor="#f0f0f0"	-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:

V_c = 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 cm^{3 [7]} and 209.0 cm^{3 [8]} are published.

References

1. Lydersen . a.L.. Estimation of Critical Properties of Organic Compounds. University of Wisconsin College Engineering. Engineering Experiment Station Report . 3. Madison, Wisconsin.
2. Joback . K.G. . Reid . R.C. . Estimation of pure-component properties from group-contributions . Chemical Engineering Communications . Informa UK Limited . 57 . 1–6 . 1987 . 0098-6445 . 10.1080/00986448708960487 . 233–243.
3. Klincewicz . K. M. . Reid . R. C. . Estimation of critical properties with group contribution methods . AIChE Journal . Wiley . 30 . 1 . 1984 . 0001-1541 . 10.1002/aic.690300119 . 137–142.
4. Book: Ambrose, D.. Correlation and Estimation of Vapour-Liquid Critical Properties. I. Critical Temperatures of Organic Compounds. National Physical Laboratory Reports Chemistry . 92. 1-35. 1978.
5. Constantinou . Leonidas . Gani . Rafiqul . New group contribution method for estimating properties of pure compounds . AIChE Journal . Wiley . 40 . 10 . 1994 . 0001-1541 . 10.1002/aic.690401011 . 1697–1710.
6. Campbell . A. N. . Chatterjee . R. M. . The critical constants and orthobaric densities of acetone, chloroform, benzene, and carbon tetrachloride . Canadian Journal of Chemistry . Canadian Science Publishing . 47 . 20 . 1969-10-15 . 0008-4042 . 10.1139/v69-646 . 3893–3898. free .
7. Herz . W.. Neukirch . E.. Zur Kenntnis kritischer Grössen . Z.Phys.Chem.(Leipzig). 104. S.433-450. 1923. 10.1515/zpch-1923-10429 . 99833350 .
8. Kobe . Kenneth A. . Crawford . Horace R. . Stephenson . Robert W. . Industrial Design Data—Critical Properties and Vapor Presesures of Some Ketones . Industrial & Engineering Chemistry . American Chemical Society (ACS) . 47 . 9 . 1955 . 0019-7866 . 10.1021/ie50549a025 . 1767–1772.