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 method is named after Aksel Lydersen who published it in 1955.{{cite journal |last=Lydersen |first=a.L. |title=Estimation of Critical Properties of Organic Compounds |journal=Engineering Experiment Station Report |location=Madison, Wisconsin |publisher=University of Wisconsin College Engineering |volume=3}} The Lydersen method is the prototype for and ancestor of many new models like Joback,{{cite journal | last1=Joback | first1=K.G. | last2=Reid | first2=R.C. | title=Estimation of pure-component properties from group-contributions | journal=Chemical Engineering Communications | publisher=Informa UK Limited | volume=57 | issue=1–6 | year=1987 | issn=0098-6445 | doi=10.1080/00986448708960487 | pages=233–243}} Klincewicz,{{cite journal | last1=Klincewicz | first1=K. M. | last2=Reid | first2=R. C. | title=Estimation of critical properties with group contribution methods | journal=AIChE Journal | publisher=Wiley | volume=30 | issue=1 | year=1984 | issn=0001-1541 | doi=10.1002/aic.690300119 | pages=137–142| bibcode=1984AIChE..30..137K }}

Ambrose,{{cite book|last=Ambrose|first=D.|title=Correlation and Estimation of Vapour-Liquid Critical Properties. I. Critical Temperatures of Organic Compounds|series= National Physical Laboratory Reports Chemistry |volume=92|page=1-35|year=1978}}

Gani-Constantinou{{cite journal | last1=Constantinou | first1=Leonidas | last2=Gani | first2=Rafiqul | title=New group contribution method for estimating properties of pure compounds | journal=AIChE Journal | publisher=Wiley | volume=40 | issue=10 | year=1994 | issn=0001-1541 | doi=10.1002/aic.690401011 | pages=1697–1710| bibcode=1994AIChE..40.1697C }} 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

cellpadding="4" rules="all" style="margin: 1em 0em; background: #ffffff; border: 2px solid #aaa;"
align="center" bgcolor="#f0f0f0" !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)
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

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_c = 40 + 60.0 + 2 * 55.0 = 210 cm³

In the literature (such as in the Dortmund Data Bank) the values 215.90 cm³,{{cite journal | last1=Campbell | first1=A. N. | last2=Chatterjee | first2=R. M. | title=The critical constants and orthobaric densities of acetone, chloroform, benzene, and carbon tetrachloride | journal=Canadian Journal of Chemistry | publisher=Canadian Science Publishing | volume=47 | issue=20 | date=1969-10-15 | issn=0008-4042 | doi=10.1139/v69-646 | pages=3893–3898| doi-access=free }} 230.5 cm³ {{cite journal|last1=Herz |first1=W.|last2=Neukirch |first2=E.|title=Zur Kenntnis kritischer Grössen |journal= Zeitschrift für Physikalische Chemie|volume= 104|page= S.433-450|year=1923|doi=10.1515/zpch-1923-10429 |s2cid=99833350 }} and 209.0 cm³ {{cite journal | last1=Kobe | first1=Kenneth A. | last2=Crawford | first2=Horace R. | last3=Stephenson | first3=Robert W. | title=Industrial Design Data—Critical Properties and Vapor Presesures of Some Ketones | journal=Industrial & Engineering Chemistry | publisher=American Chemical Society (ACS) | volume=47 | issue=9 | year=1955 | issn=0019-7866 | doi=10.1021/ie50549a025 | pages=1767–1772}} are published.

References

Category:Physical chemistry

Category:Thermodynamic models