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.

1 Equations
2 Group contributions
3 Example calculation
4 References

Equations

Critical temperature

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

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

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

Critical volume

$V_c\,=\,40%2B\sum G_i$

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	G_i (T_c)	G_i (P_c)	G_i (V_c)	Group	G_i (T_c)	G_i (P_c)	G_i (V_c)
-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 cm³ ^[8] and 209.0 cm³ ^[9] are published.

References

^ Lydersen a.L., “Estimation of Critical Properties of Organic Compounds“, University of Wisconsin College Engineering, Eng. Exp. Stn. Rep. 3, Madison, Wisconsin
^ Joback K.G., Reid R.C., “Estimation of pure-component properties from group-contributions”, Chem.Eng.Commun., 57, 233-243, 1987
^ Klincewicz K. M., Reid R. C., "Estimation of Critical Properties with Group Contribution Methods", AIChE Journal, 30(1), 137-142, 1984
^ 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
^ Constantinou L., Gani R., “New Group Contribution Method for Estimating Properties of Pure Compounds”, AIChE J., 40(10), 1697-1710, 1994
^ Dortmund Data Bank
^ Campbell A.N., Chatterjee R.M., Can.J.Chem., 47(20), S. 3893-3898, 1969
^ Herz W., Neukirch E., Z.Phys.Chem.(Leipzig), 104, S.433-450, 1923
^ Kobe K.A., Crawford H.R., Stephenson R.W., Ind.Eng.Chem., 47(9), S. 1767-1772, 1955