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| The '''Lydersen method'''<ref>Lydersen a.L., “Estimation of Critical Properties of Organic Compounds“, University of Wisconsin College Engineering, Eng. Exp. Stn. Rep. 3, Madison, Wisconsin</ref> is a [[group contribution method]] for the estimation of critical properties temperature ([[Critical temperature|T<sub>c</sub>]]), pressure ([[Critical pressure|P<sub>c</sub>]]) and volume (V<sub>c</sub>). The Lydersen method is the prototype for and ancestor of many new models like [[Joback method|Joback]],<ref>Joback K.G., Reid R.C., “Estimation of pure-component properties from group-contributions”, Chem.Eng.Commun., 57, 233-243, 1987
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| </ref> [[Klincewicz method|Klincewicz]],<ref>Klincewicz K. M., Reid R. C., "Estimation of Critical Properties with Group Contribution Methods", AIChE Journal, 30(1), 137-142, 1984</ref>
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| Ambrose,<ref>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
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| </ref>
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| Gani-Constantinou<ref>Constantinou L., Gani R., “New Group Contribution Method for Estimating Properties of Pure Compounds”, AIChE J., 40(10), 1697-1710, 1994
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| </ref> and others.
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| 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]].
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| == Equations ==
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| === Critical temperature ===
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| <math>T_c=\frac{T_b}{0.567+\sum G_i-\left(\sum G_i\right)^2}</math>
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| Guldberg has found that a rough estimate of the [[normal boiling point]] ''T''<sub>b</sub>, when expressed in [[kelvins]] (i.e., as an [[absolute temperature]]), is approximately two-thirds of the critical temperature ''T''<sub>c</sub>. Lydersen uses this basic idea but calculates more accurate values.
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| === Critical pressure ===
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| <math>P_c=\frac{M}{\left(0.34+\sum G_i\right)^2}</math>
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| === Critical volume === | |
| <math>V_c\,=\,40+\sum G_i</math>
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| M is the [[molar mass]] and G<sub>i</sub> are the group contributions (different for all three properties) for [[functional group]]s of a [[molecule]].
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| == Group contributions ==
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| {| cellpadding="4" rules="all" style="margin: 1em 0em; background: #ffffff; border: 2px solid #aaa;"
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| |- align="center" bgcolor="#f0f0f0"
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| !Group
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| !G<sub>i</sub> (T<sub>c</sub>)
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| !G<sub>i</sub> (P<sub>c</sub>)
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| !G<sub>i</sub> (V<sub>c</sub>)
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| !Group
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| !G<sub>i</sub> (T<sub>c</sub>)
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| !G<sub>i</sub> (P<sub>c</sub>)
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| !G<sub>i</sub> (V<sub>c</sub>)
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| |- align="center"
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| | bgcolor="#f0f0f0" |-CH3,-CH2- ||0.020 ||0.227 ||55.0
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| | bgcolor="#f0f0f0" |>CH ||0.012 ||0.210 ||51.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |-C< ||- ||0,210 ||41.0
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| | bgcolor="#f0f0f0" |=CH2,#CH ||0.018 ||0,198 ||45.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |=C<,=C= ||- ||0.198 ||36.0
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| | bgcolor="#f0f0f0" |=C-H,#C- ||0.005 ||0.153 ||36.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |-CH2-(Ring) ||0.013 ||0.184 ||44.5
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| | bgcolor="#f0f0f0" |>CH-(Ring) ||0.012 ||0.192 ||46.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |>C<(Ring) ||-0.007 ||0.154 ||31.0
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| | bgcolor="#f0f0f0" |=CH-,=C<,=C=(Ring)||0.011 ||0.154 ||37.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |-F ||0.018 ||0.224||18.0
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| | bgcolor="#f0f0f0" |-Cl ||0.017||0.320 ||49.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |-Br ||0.010||0.500||70.0
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| | bgcolor="#f0f0f0" |-I ||0.012 ||0.830||95.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |-OH ||0.082||0.060||18.0
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| | bgcolor="#f0f0f0" |-OH(Aromat)||0.031||-0.020||3.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |-O- ||0.021||0.160||20.0
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| | bgcolor="#f0f0f0" |-O-(Ring) ||0.014||0.120||8.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |>C=O ||0.040||0.290||60.0
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| | bgcolor="#f0f0f0" |>C=O(Ring) ||0.033||0.200||50.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |HC=O- ||0.048||0.330||73.0
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| | bgcolor="#f0f0f0" |-COOH ||0.085||0.400||80.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |-COO- ||0.047||0.470||80.0
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| | bgcolor="#f0f0f0" |-NH2 ||0.031||0.095||28.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |>NH ||0.031||0.135||37.0
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| | bgcolor="#f0f0f0" |>NH(Ring) ||0.024||0.090||27.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |>N ||0.014 ||0.170||42.0
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| | bgcolor="#f0f0f0" |>N-(Ring) ||0.007||0.130||32.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |-CN ||0.060||0.360||80.0
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| | bgcolor="#f0f0f0" |-NO2 ||0.055||0.420||78.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |-SH,-S- ||0.015||0.270||55.0
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| | bgcolor="#f0f0f0" |-S-(Ring) ||0.008||0.240||45.0
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| |- align="center"
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| | bgcolor="#f0f0f0" |=S ||0.003||0.240||47.0
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| | bgcolor="#f0f0f0" |>Si< ||0.030||0.540||-
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| |- align="center"
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| | bgcolor="#f0f0f0" |-B< ||0.030||-||-
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| | bgcolor="#f0f0f0" | || || ||
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| |}
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| == Example calculation ==
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| [[File:AcetonGruppen.PNG|Group assignment for Acetone]]
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| [[Acetone]] is fragmented in two different groups, one carbonyl group and two methyl groups. For the critical volume the following calculation results:
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| V<sub>c</sub> = 40 + 60.0 + 2 * 55.0 = 210 cm<sup>3</sup>
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| In the literature<ref>[[Dortmund Data Bank]]</ref> the values 215.90 cm<sup>3</sup>,<ref>Campbell A.N., Chatterjee R.M., Can.J.Chem., 47(20), S. 3893-3898, 1969</ref> 230.5 cm<sup>3</sup> <ref>Herz W., Neukirch E., Z.Phys.Chem.(Leipzig), 104, S.433-450, 1923</ref> and 209.0 cm<sup>3</sup> <ref>Kobe K.A., Crawford H.R., Stephenson R.W., Ind.Eng.Chem., 47(9), S. 1767-1772, 1955</ref> are published.
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| == References ==
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| <references/>
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| [[Category:Thermodynamic models]]
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