Lydersen method
# Lydersen method

The Lydersen method 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, Klincewicz, Ambrose, Gani-Constantinou 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 | $G_i$ $(T_c)$ | $G_i$ $(P_c)$ | $G_i$ $(V_c)$ | 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 $cm^3$

In the literature (such as in the Dortmund Data Bank) the values 215.90 $cm^3,$ 230.5 $cm^3$ and 209.0 $cm^3$ are published.

