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| The '''Girolami method''',<ref>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)</ref> named after Gregory Girolami, is a predictive method for estimating [[Density|densities]] of pure [[liquid]] components at [[room temperature]]. The objective of this method is the simple prediction of the density and not high precision.
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| == Procedure ==
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| The method uses purely additive volume contributions for single atoms and additional correction factors for components with special [[functional group]]s 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]].
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| === Atom contributions ===
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| The method uses the following contributions for the different atoms:
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| {| class="wikitable"
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| ! Element !! Relative volume <br />V<sub>i</sub>
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| |-
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| | [[Hydrogen]] || 1
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| |-
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| | [[Lithium]] to [[Fluorine]] || 2
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| |-
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| | [[Sodium]] to [[Chlorine]] || 4
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| |-
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| | [[Potassium]] to [[Bromine]] || 5
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| |-
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| | [[Rubidium]] to [[Iodine]] || 7.5
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| |-
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| | [[Cesium]] to [[Bismuth]] || 9
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| |}
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| A scaled molecular volume is calculated by
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| :<math>V_S \,=\, \sum_i V_i</math> | |
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| and the density is derived by
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| :<math>d \,=\, \frac{M}{5 \cdot V_S}</math> | |
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| with the [[molecular weight]] M. The scaling factor '''5''' is used to obtain the density in g·cm<sup>−3</sup>.
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| === Group contribution ===
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| For some components Girolami found smaller volumes and higher densities than calculated solely by the atom contributions. For components with
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| * a hydroxylic function ([[Alcohol]]s)
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| * a carboxylic function ([[Carboxylic acid]]s)
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| * a primary or secondary [[amine]] function
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| * an [[amide]] group (incl. amides substituted at the [[nitrogen]])
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| * a [[sulfoxide]] group
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| * a [[sulfone]] group
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| * a ring (non-condensed),
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| 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%).
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| 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%.
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| If multiple corrections are needed their factors have to be added but not over 130% in total.
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| == Example calculation ==
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| {| class="wikitable"
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| ! Component
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| ! M<br />[<sup>g</sup>/<sub>mol</sub>]
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| ! Volume V<sub>S</sub>
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| ! Corrections
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| ! Calculated density<br />[g·cm<sup>−3</sup>]
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| ! Exp. density<br />[g·cm<sup>−3</sup>]
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| |-
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| | [[Cyclohexanol]]
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| | 100
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| | (6×2)+(13×1)+(1×2)=26
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| | One ring and a hydroxylic group = 120%
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| | d=<sup>1.2*100</sup>/<sub>5×26</sub>=0.92
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| | 0.962
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| |-
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| | Dimethylethylphosphine
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| | 90
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| | (4×2)+(11×1)+(1×4)=23
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| | No corrections
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| | d=<sup>90</sup>/<sub>5×23</sub>=0.78
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| | 0.76
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| |-
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| | [[Ethylenediamine]]
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| | 60
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| | (2×2)+(8×1)+(2×2)=16
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| | Two primary amine groups = 120%
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| | d=<sup>1.2×60</sup>/<sub>5×16</sub>=0.90
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| | 0.899
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| |-
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| | [[Sulfolane]]
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| | 120
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| | (4×2)+(8×1)+(2×2)+(1×4)=24
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| | One ring and two S=O bonds = 130%
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| | d=<sup>1.3×120</sup>/<sub>5×24</sub>=1.30
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| | 1.262
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| |-
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| | [[1-Bromonaphthalene]]
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| | 207
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| | (10×2)+(7×1)+(1×5)=32
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| | Two condensed rings = 115%
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| | d=<sup>1,15×207</sup>/<sub>5×32</sub>=1.49
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| | 1.483
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| |}
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| == Quality ==
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| The author has given a mean quadratic error (RMS) of 0.049 g·cm<sup>−3</sup> for 166 checked components. Only for two components ([[acetonitrile]] and [[dibromochloromethane]]) has an error greater than 0.1 g·cm <sup>−3</sup> been found.
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| ==References==
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| <references />
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| == External links ==
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| * [http://www.aim.env.uea.ac.uk/aim/density/density.php Online calculator for the Girolami model]
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| {{DEFAULTSORT:Girolami Method}}
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| [[Category:Thermodynamic models]]
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