Barlow's law: Difference between revisions

Revision as of 05:01, 20 March 2013

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^[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

[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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+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
+</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>
+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
+</ref>
+Gani-Constantinou<ref>Constantinou L., Gani R., “New Group Contribution Method for Estimating Properties of Pure Compounds”, AIChE J., 40(10), 1697-1710, 1994
+</ref> 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 ===
+<math>T_c=\frac{T_b}{0.567+\sum G_i-\left(\sum G_i\right)^2}</math>
+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.
+=== Critical pressure ===
+<math>P_c=\frac{M}{\left(0.34+\sum G_i\right)^2}</math>
+=== Critical volume ===
+<math>V_c\,=\,40+\sum G_i</math>
+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]].
+== Group contributions ==
+{| cellpadding="4" rules="all" style="margin: 1em 0em; background: #ffffff; border: 2px solid #aaa;"
+|- align="center" bgcolor="#f0f0f0"
+!Group
+!G<sub>i</sub> (T<sub>c</sub>)
+!G<sub>i</sub> (P<sub>c</sub>)
+!G<sub>i</sub> (V<sub>c</sub>)
+!Group
+!G<sub>i</sub> (T<sub>c</sub>)
+!G<sub>i</sub> (P<sub>c</sub>)
+!G<sub>i</sub> (V<sub>c</sub>)
+|- align="center"
+| bgcolor="#f0f0f0" |-CH3,-CH2-	||0.020	||0.227	||55.0
+| bgcolor="#f0f0f0" |>CH	||0.012	||0.210	||51.0
+|- align="center"
+| bgcolor="#f0f0f0" |-C<	||-	||0,210	||41.0
+| bgcolor="#f0f0f0" |=CH2,#CH	||0.018	||0,198	||45.0
+|- align="center"
+| bgcolor="#f0f0f0" |=C<,=C=	||-	||0.198	||36.0
+| bgcolor="#f0f0f0" |=C-H,#C-	||0.005	||0.153	||36.0
+|- align="center"
+| bgcolor="#f0f0f0" |-CH2-(Ring)	||0.013	||0.184	||44.5
+| bgcolor="#f0f0f0" |>CH-(Ring)	||0.012	||0.192	||46.0
+|- align="center"
+| bgcolor="#f0f0f0" |>C<(Ring)	||-0.007	||0.154	||31.0
+| bgcolor="#f0f0f0" |=CH-,=C<,=C=(Ring)||0.011	||0.154	||37.0
+|- align="center"
+| bgcolor="#f0f0f0" |-F	||0.018	||0.224||18.0
+| bgcolor="#f0f0f0" |-Cl	||0.017||0.320	||49.0
+|- align="center"
+| bgcolor="#f0f0f0" |-Br	||0.010||0.500||70.0
+| bgcolor="#f0f0f0" |-I	||0.012	||0.830||95.0
+|- align="center"
+| bgcolor="#f0f0f0" |-OH	||0.082||0.060||18.0
+| bgcolor="#f0f0f0" |-OH(Aromat)||0.031||-0.020||3.0
+|- align="center"
+| bgcolor="#f0f0f0" |-O-	||0.021||0.160||20.0
+| bgcolor="#f0f0f0" |-O-(Ring)	||0.014||0.120||8.0
+|- align="center"
+| bgcolor="#f0f0f0" |>C=O	||0.040||0.290||60.0
+| bgcolor="#f0f0f0" |>C=O(Ring)	||0.033||0.200||50.0
+|- align="center"
+| bgcolor="#f0f0f0" |HC=O-	||0.048||0.330||73.0
+| bgcolor="#f0f0f0" |-COOH	||0.085||0.400||80.0
+|- align="center"
+| bgcolor="#f0f0f0" |-COO-	||0.047||0.470||80.0
+| bgcolor="#f0f0f0" |-NH2	||0.031||0.095||28.0
+|- align="center"
+| bgcolor="#f0f0f0" |>NH	||0.031||0.135||37.0
+| bgcolor="#f0f0f0" |>NH(Ring)	||0.024||0.090||27.0
+|- align="center"
+| bgcolor="#f0f0f0" |>N	||0.014	||0.170||42.0
+| bgcolor="#f0f0f0" |>N-(Ring)	||0.007||0.130||32.0
+|- align="center"
+| bgcolor="#f0f0f0" |-CN	||0.060||0.360||80.0
+| bgcolor="#f0f0f0" |-NO2	||0.055||0.420||78.0
+|- align="center"
+| bgcolor="#f0f0f0" |-SH,-S-	||0.015||0.270||55.0
+| bgcolor="#f0f0f0" |-S-(Ring)	||0.008||0.240||45.0
+|- align="center"
+| bgcolor="#f0f0f0" |=S	||0.003||0.240||47.0
+| bgcolor="#f0f0f0" |>Si<	||0.030||0.540||-
+|- align="center"
+| bgcolor="#f0f0f0" |-B<	||0.030||-||-
+| bgcolor="#f0f0f0" |           ||      ||      ||
+|}
+== Example calculation ==
+[[File:AcetonGruppen.PNG|Group assignment for Acetone]]
+[[Acetone]] is fragmented in two different groups, one carbonyl group and two methyl groups. For the critical volume the following calculation results:
+V<sub>c</sub> = 40 + 60.0 + 2 * 55.0 = 210&nbsp;cm<sup>3</sup>
+In the literature<ref>[[Dortmund Data Bank]]</ref> the values 215.90&nbsp;cm<sup>3</sup>,<ref>Campbell A.N., Chatterjee R.M., Can.J.Chem., 47(20), S. 3893-3898, 1969</ref> 230.5&nbsp;cm<sup>3</sup> <ref>Herz W., Neukirch E., Z.Phys.Chem.(Leipzig), 104, S.433-450, 1923</ref> and 209.0&nbsp;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.
+== References ==
+<references/>
+[[Category:Thermodynamic models]]

Barlow's law: Difference between revisions

Revision as of 05:01, 20 March 2013

Contents

Equations

Critical temperature

Critical pressure

Critical volume

Group contributions

Example calculation

References

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Barlow's law: Difference between revisions

Revision as of 05:01, 20 March 2013

Equations

Critical temperature

Critical pressure

Critical volume

Group contributions

Example calculation

References

Navigation menu

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