Girolami method

The Girolami method is a method for estimating the densities of pure liquid substances at room temperature . The focus of this model is the simple estimation of the consistency and not its high accuracy.

Procedure

The method uses purely additive volume contributions for individual atoms and an additional correction factor for substances with special functional groups that cause a volume contraction and thus a higher density. The method is thus a mixture of an atomic and a group contribution method .

Nuclear contributions

The method uses the following contributions for the different atoms:

element	Relative volume V _i
hydrogen	1
Lithium to fluorine	2
Sodium to chlorine	4th
Potassium to bromine	5
Rubidium to iodine	7.5
Cesium and bismuth	9

A scaled molecular volume is now over

${\ displaystyle V_ {S} = \ sum _ {i} V_ {i}}$

and then the density over

${\ displaystyle d = {\ frac {M} {5 \ cdot V_ {S}}}}$

determined with the molar mass M. The factor 5 is used to obtain the density in g · cm ⁻³ .

Group contributions

For some substances Girolami found that their volume is lower and their density is greater than that calculated using the formula given. For components with

a hydroxy function ( alcohols )
a carboxy function ( carboxylic acids )
a primary or secondary amino function ( amines )
an amide group (including amides substituted on nitrogen )

a sulfoxide group ( sulfoxides )

a sulfone ( Sulfone )

a ring (not fused )

it is sufficient to increase the density, which has been determined from the main determining equation, by 10% for each occurrence. For sulphone groups, double the factor is to be used (20%).

Another special case are substances with fused ring systems such as naphthalene . The density of these substances must be increased by 7.5% per ring, for naphthalene by 15%.

If several of these corrections are necessary, they must be added, but not beyond a total of 130%.

Sample calculations

material	M [g / mol]	Volume V _S	corrections	Calculated density [g · cm ⁻³ ]	Exp. Density [g · cm ⁻³ ]
Cyclohexanol	100	${\ displaystyle (6 \ cdot 2) + (12 \ cdot 1) + (1 \ cdot 2) = 26}$	One ring and one hydroxy group = 120%	${\ displaystyle d = {\ frac {1 {,} 2 \ cdot 100} {5 \ cdot 26}} = 0 {,} 92}$	0.962
Dimethylethylphosphine	90	${\ displaystyle (4 \ cdot 2) + (11 \ cdot 1) + (1 \ cdot 4) = 23}$	No corrections	${\ displaystyle d = {\ frac {90} {5 \ cdot 23}} = 0 {,} 78}$	0.76
Ethylenediamine	60	${\ displaystyle (2 \ cdot 2) + (8 \ cdot 1) + (2 \ cdot 2) = 16}$	Two primary amine groups = 120%	${\ displaystyle d = {\ frac {1 {,} 2 \ cdot 60} {5 \ cdot 16}} = 0 {,} 90}$	0.899
Sulfolane	120	${\ displaystyle (4 \ cdot 2) + (8 \ cdot 1) + (2 \ cdot 2) + (1 \ cdot 4) = 24}$	One ring and two S = O bonds = 130%	${\ displaystyle d = {\ frac {1 {,} 3 \ cdot 120} {5 \ cdot 24}} = 1 {,} 30}$	1.262
1-bromonaphthalene	207	${\ displaystyle (10 \ cdot 2) + (7 \ cdot 1) + (1 \ cdot 5) = 32}$	Two fused rings = 115%	${\ displaystyle d = {\ frac {1 {,} 15 \ cdot 207} {5 \ cdot 32}} = 1 {,} 49}$	1.483

quality

The author gives a mean square error (RMS) of 0.049 g · cm ⁻³ for 166 tested components . Only for two components ( acetonitrile and dibromochloromethane) was an error greater than 0.1 g · cm ⁻³ found.

Web links

Online calculator for the Girolami model

literature

↑ Gregory S. Girolami, A Simple "Back of the Envelope" Method for Estimating the Densities and Molecular Volume of Liquids and Volumes, J. of Chemical Education, 71 (11), 962-964 (1994)

[1] Gregory S. Girolami, A Simple "Back of the Envelope" Method for Estimating the Densities and Molecular Volume of Liquids and Volumes, J. of Chemical Education, 71 (11), 962-964 (1994)