Girolami method

The Girolami method,[1] named after Gregory Girolami, is a predictive method for estimating densities of pure liquid components at room temperature. The objective of this method is the simple prediction of the density and not high precision.

Procedure

The method uses purely additive volume contributions for single atoms and additional correction factors for components with special functional groups which cause a volume contraction and therefore a higher density. The Girolami method can be described as a mixture of an atom and group contribution method.

Atom 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	4
Potassium to Bromine	5
Rubidium to Iodine	7.5
Cesium to Bismuth	9

A scaled molecular volume is calculated by

V_{S}\,=\,\sum _{i}V_{i}

and the density is derived by

d\,=\,{\frac {M}{5\cdot V_{S}}}

with the molecular weight M. The scaling factor 5 is used to obtain the density in g·cm⁻³.

Group contribution

For some components Girolami found smaller volumes and higher densities than calculated solely by the atom contributions. For components with

a hydroxylic function (Alcohols)
a carboxylic function (Carboxylic acids)
a primary or secondary amine function
an amide group (incl. amides substituted at the nitrogen)
a sulfoxide group
a sulfone group
a ring (non-condensed),

it is sufficient to add 10% to the density obtained by the main equation. For sulfone groups it is necessary to use this factor twice (20%).

Another specific case are condensed ring systems like Naphthalene. The density has to increased by 7.5% for every ring; for Naphthalene the resulting factor would be 15%.

If multiple corrections are needed their factors have to be added but not over 130% in total.

Example calculation

Component	M [^g/_mol]	Volume V_S	Corrections	Calculated density [g·cm⁻³]	Exp. density [g·cm⁻³]
Cyclohexanol	100	(6×2)+(13×1)+(1×2)=26	One ring and a hydroxylic group = 120%	d=^1.2*100/_5×26=0.92	0.962
Dimethylethylphosphine	90	(4×2)+(11×1)+(1×4)=23	No corrections	d=⁹⁰/_5×23=0.78	0.76
Ethylenediamine	60	(2×2)+(8×1)+(2×2)=16	Two primary amine groups = 120%	d=^1.2×60/_5×16=0.90	0.899
Sulfolane	120	(4×2)+(8×1)+(2×2)+(1×4)=24	One ring and two S=O bonds = 130%	d=^1.3×120/_5×24=1.30	1.262
1-Bromonaphthalene	207	(10×2)+(7×1)+(1×5)=32	Two condensed rings = 115%	d=^1,15×207/_5×32=1.49	1.483

Quality

The author has given a mean quadratic error (RMS) of 0.049 g·cm⁻³ for 166 checked components. Only for two components (acetonitrile and dibromochloromethane) has an error greater than 0.1 g·cm ⁻³ been found.

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References

Girolami, Gregory S. (1994). "A Simple "Back of the Envelope" Method for Estimating the Densities and Molecular Volumes of Liquids and Solids". Journal of Chemical Education. 71 (11): 962–964. doi:10.1021/ed071p962.

External links

Online calculator for the Girolami model

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[1] Girolami, Gregory S. (1994). "A Simple "Back of the Envelope" Method for Estimating the Densities and Molecular Volumes of Liquids and Solids". Journal of Chemical Education. 71 (11): 962–964. doi:10.1021/ed071p962.