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# 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

${\displaystyle T_{c}={\frac {T_{b}}{0.567+\sum G_{i}-\left(\sum G_{i}\right)^{2}}}}$

Guldberg has found that a rough estimate of the normal boiling point 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

${\displaystyle P_{c}={\frac {M}{\left(0.34+\sum G_{i}\right)^{2}}}}$

### Critical volume

${\displaystyle V_{c}\,=\,40+\sum G_{i}}$

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[6] the values 215.90 cm3,[7] 230.5 cm3 [8] and 209.0 cm3 [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

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