Girolami method

Short description: Method of estimating liquid densities

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.

## Contents

* 1 Procedure
* 1.1 Atom contributions
* 1.2 Group contribution
* 2 Example calculation
* 3 Quality
* 4 References
* 5 External links

## 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

|

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

VS=∑iVi

and the density is derived by

d=M5⋅VS

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 VS | 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.

## References

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.

## External links

* Online calculator for the Girolami model

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