World Library  
Flag as Inappropriate
Email this Article

Girolami method

Article Id: WHEBN0021099256
Reproduction Date:

Title: Girolami method  
Author: World Heritage Encyclopedia
Language: English
Subject: Density
Publisher: World Heritage Encyclopedia

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.


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

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

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
Volume VS Corrections Calculated density
Exp. density
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


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.


  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)

External links

  • Online calculator for the Girolami model
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.