Lydersen method

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

$T_c=\frac{T_b}{0.567+\sum G_i-\left(\sum G_i\right)^2}$

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

$P_c=\frac{M}{\left(0.34+\sum G_i\right)^2}$

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)
-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:

V_c = 40 + 60.0 + 2 * 55.0 = 210 cm³

In the literature^[6] the values 215.90 cm³,^[7] 230.5 cm^{3 [8]} and 209.0 cm^{3 [9]} are published.

References

1. Lydersen a.L., “Estimation of Critical Properties of Organic Compounds“, University of Wisconsin College Engineering, Eng. Exp. Stn. Rep. 3, Madison, Wisconsin
2. Joback K.G., Reid R.C., “Estimation of pure-component properties from group-contributions”, Chem.Eng.Commun., 57, 233-243, 1987
3. Klincewicz K. M., Reid R. C., "Estimation of Critical Properties with Group Contribution Methods", AIChE Journal, 30(1), 137-142, 1984
4. Ambrose D., “Correlation and Estimation of Vapour-Liquid Critical Properties. I. Critical Temperatures of Organic Compounds”, Nat.Phys.Lab.Rep.Chem., Rep.No. 92, 1-35, 1978
5. Constantinou L., Gani R., “New Group Contribution Method for Estimating Properties of Pure Compounds”, AIChE J., 40(10), 1697-1710, 1994
6. Dortmund Data Bank
7. Campbell A.N., Chatterjee R.M., Can.J.Chem., 47(20), S. 3893-3898, 1969
8. Herz W., Neukirch E., Z.Phys.Chem.(Leipzig), 104, S.433-450, 1923
9. Kobe K.A., Crawford H.R., Stephenson R.W., Ind.Eng.Chem., 47(9), S. 1767-1772, 1955