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	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 (such as in the Dortmund Data Bank) the values 215.90 cm³,^[6] 230.5 cm³ ^[7] and 209.0 cm³ ^[8] are published.

References

^ Lydersen, a.L. "Estimation of Critical Properties of Organic Compounds". Engineering Experiment Station Report. 3. Madison, Wisconsin: University of Wisconsin College Engineering.
^ Joback, K.G.; Reid, R.C. (1987). "Estimation of pure-component properties from group-contributions". Chemical Engineering Communications. 57 (1–6). Informa UK Limited: 233–243. doi:10.1080/00986448708960487. ISSN 0098-6445.
^ Klincewicz, K. M.; Reid, R. C. (1984). "Estimation of critical properties with group contribution methods". AIChE Journal. 30 (1). Wiley: 137–142. Bibcode:1984AIChE..30..137K. doi:10.1002/aic.690300119. ISSN 0001-1541.
^ Ambrose, D. (1978). Correlation and Estimation of Vapour-Liquid Critical Properties. I. Critical Temperatures of Organic Compounds. National Physical Laboratory Reports Chemistry. Vol. 92. p. 1-35.
^ Constantinou, Leonidas; Gani, Rafiqul (1994). "New group contribution method for estimating properties of pure compounds". AIChE Journal. 40 (10). Wiley: 1697–1710. Bibcode:1994AIChE..40.1697C. doi:10.1002/aic.690401011. ISSN 0001-1541.
^ Campbell, A. N.; Chatterjee, R. M. (1969-10-15). "The critical constants and orthobaric densities of acetone, chloroform, benzene, and carbon tetrachloride". Canadian Journal of Chemistry. 47 (20). Canadian Science Publishing: 3893–3898. doi:10.1139/v69-646. ISSN 0008-4042.
^ Herz, W.; Neukirch, E. (1923). "Zur Kenntnis kritischer Grössen". Zeitschrift für Physikalische Chemie. 104: S.433-450. doi:10.1515/zpch-1923-10429. S2CID 99833350.
^ Kobe, Kenneth A.; Crawford, Horace R.; Stephenson, Robert W. (1955). "Industrial Design Data—Critical Properties and Vapor Presesures of Some Ketones". Industrial & Engineering Chemistry. 47 (9). American Chemical Society (ACS): 1767–1772. doi:10.1021/ie50549a025. ISSN 0019-7866.

[1] Lydersen, a.L. "Estimation of Critical Properties of Organic Compounds". Engineering Experiment Station Report. 3. Madison, Wisconsin: University of Wisconsin College Engineering.

[2] Joback, K.G.; Reid, R.C. (1987). "Estimation of pure-component properties from group-contributions". Chemical Engineering Communications. 57 (1–6). Informa UK Limited: 233–243. doi:10.1080/00986448708960487. ISSN 0098-6445.

[3] Klincewicz, K. M.; Reid, R. C. (1984). "Estimation of critical properties with group contribution methods". AIChE Journal. 30 (1). Wiley: 137–142. Bibcode:1984AIChE..30..137K. doi:10.1002/aic.690300119. ISSN 0001-1541.

[4] Ambrose, D. (1978). Correlation and Estimation of Vapour-Liquid Critical Properties. I. Critical Temperatures of Organic Compounds. National Physical Laboratory Reports Chemistry. Vol. 92. p. 1-35.

[5] Constantinou, Leonidas; Gani, Rafiqul (1994). "New group contribution method for estimating properties of pure compounds". AIChE Journal. 40 (10). Wiley: 1697–1710. Bibcode:1994AIChE..40.1697C. doi:10.1002/aic.690401011. ISSN 0001-1541.

[6] Campbell, A. N.; Chatterjee, R. M. (1969-10-15). "The critical constants and orthobaric densities of acetone, chloroform, benzene, and carbon tetrachloride". Canadian Journal of Chemistry. 47 (20). Canadian Science Publishing: 3893–3898. doi:10.1139/v69-646. ISSN 0008-4042.

[7] Herz, W.; Neukirch, E. (1923). "Zur Kenntnis kritischer Grössen". Zeitschrift für Physikalische Chemie. 104: S.433-450. doi:10.1515/zpch-1923-10429. S2CID 99833350.

[8] Kobe, Kenneth A.; Crawford, Horace R.; Stephenson, Robert W. (1955). "Industrial Design Data—Critical Properties and Vapor Presesures of Some Ketones". Industrial & Engineering Chemistry. 47 (9). American Chemical Society (ACS): 1767–1772. doi:10.1021/ie50549a025. ISSN 0019-7866.

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