Girolami method

<h2 id="procedure">Procedure</h2>
<p>The method uses purely additive volume contributions for single atoms and additional correction factors for components with special <a href="/facts/Functional_group/GXkSPsjM">functional groups</a> which cause a volume contraction and therefore a higher density. The Girolami method can be described as a mixture of an atom and <a href="/facts/Group_contribution_method/29UR7szr">group contribution method</a>.
</p>
<h3>Atom contributions</h3>
<p>The method uses the following contributions for the different atoms:
</p>
<table><tbody><tr><th>Element</th><th>Relative volume Vi</th></tr><tr><td><a href="/facts/Hydrogen/BoYHjl0J">Hydrogen</a></td><td>1</td></tr><tr><td><a href="/facts/Lithium/7vXX6BWA">Lithium</a> to <a href="/facts/Fluorine/YUV0Fb8m">Fluorine</a></td><td>2</td></tr><tr><td><a href="/facts/Sodium/eYuSPu2V">Sodium</a> to <a href="/facts/Chlorine/y27UwYBM">Chlorine</a></td><td>4</td></tr><tr><td><a href="/facts/Potassium/FWPwS7Rj">Potassium</a> to <a href="/facts/Bromine/oLfj3C7D">Bromine</a></td><td>5</td></tr><tr><td><a href="/facts/Rubidium/KDHSe2HM">Rubidium</a> to <a href="/facts/Iodine/JlfMecMf">Iodine</a></td><td>7.5</td></tr><tr><td><a href="/facts/Cesium/dXKN1S5k">Cesium</a> to <a href="/facts/Bismuth/75FLjkoX">Bismuth</a></td><td>9</td></tr></tbody></table>
<p>A scaled molecular volume is calculated by
</p>

V
          
            S
          
        
        
        =
        
        
          ∑
          
            i
          
        
        
          V
          
            i
          
        
      
    
    {\displaystyle V_{S}\,=\,\sum _{i}V_{i}}

<p>and the density is derived by
</p>

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

<p>with the <a href="/facts/Molecular_weight/FWueGMed">molecular weight</a> M. The scaling factor 5 is used to obtain the density in g·cm−3.
</p>
<h3>Group contribution</h3>
<p>For some components Girolami found smaller volumes and higher densities than calculated solely by the atom contributions. For components with
</p>
<ul><li>a hydroxylic function (<a href="/facts/Alcohol_(chemistry)/Y0SCTDkh">Alcohols</a>)</li>
<li>a carboxylic function (<a href="/facts/Carboxylic_acid/U4xuMosy">Carboxylic acids</a>)</li>
<li>a primary or secondary <a href="/facts/Amine/JvfYJfP6">amine</a> function</li>
<li>an <a href="/facts/Amide/C6kCzYEA">amide</a> group (incl. amides substituted at the <a href="/facts/Nitrogen/Nf1QpGDz">nitrogen</a>)</li>
<li>a <a href="/facts/Sulfoxide/Stk3Vnj9">sulfoxide</a> group</li>
<li>a <a href="/facts/Sulfone/LJLP1RcT">sulfone</a> group</li>
<li>a ring (non-condensed),</li></ul>
<p>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%).
</p><p>Another specific case are condensed ring systems like <a href="/facts/Naphthalene/RU2sV8mN">Naphthalene</a>. The density has to increased by 7.5% for every ring; for Naphthalene the resulting factor would be 15%.
</p><p>If multiple corrections are needed their factors have to be added but not over 130% in total.
</p>
<h2 id="example-calculation">Example calculation</h2>
<table><tbody><tr><th>Component</th><th>M[g/mol]</th><th>Volume VS</th><th>Corrections</th><th>Calculated density[g·cm−3]</th><th>Exp. density[g·cm−3]</th></tr><tr><td><a href="/facts/Cyclohexanol/kHdlHrys">Cyclohexanol</a></td><td>100</td><td>(6×2)+(13×1)+(1×2)=26</td><td>One ring and a hydroxylic group = 120%</td><td>d=1.2*100/5×26=0.92</td><td>0.962</td></tr><tr><td>Dimethylethylphosphine</td><td>90</td><td>(4×2)+(11×1)+(1×4)=23</td><td>No corrections</td><td>d=90/5×23=0.78</td><td>0.76</td></tr><tr><td><a href="/facts/Ethylenediamine/VDX8VfFv">Ethylenediamine</a></td><td>60</td><td>(2×2)+(8×1)+(2×2)=16</td><td>Two primary amine groups = 120%</td><td>d=1.2×60/5×16=0.90</td><td>0.899</td></tr><tr><td><a href="/facts/Sulfolane/oFKPToMK">Sulfolane</a></td><td>120</td><td>(4×2)+(8×1)+(2×2)+(1×4)=24</td><td>One ring and two S=O bonds = 130%</td><td>d=1.3×120/5×24=1.30</td><td>1.262</td></tr><tr><td><a href="/facts/1-Bromonaphthalene/nf6e9aDH">1-Bromonaphthalene</a></td><td>207</td><td>(10×2)+(7×1)+(1×5)=32</td><td>Two condensed rings = 115%</td><td>d=1,15×207/5×32=1.49</td><td>1.483</td></tr></tbody></table>
<h2 id="quality">Quality</h2>
<p>The author has given a mean quadratic error (RMS) of 0.049 g·cm−3 for 166 checked components. Only for two components (<a href="/facts/Acetonitrile/fNpbvRp6">acetonitrile</a> and <a href="/facts/Dibromochloromethane/rqjzc5v4">dibromochloromethane</a>) has an error greater than 0.1 g·cm −3 been found.[<i>original research?</i>]
</p>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.aim.env.uea.ac.uk/aim/density/density.php">Online calculator for the Girolami model</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>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. <a href="/wiki/Journal_of_Chemical_Education" target="_blank">/wiki/Journal_of_Chemical_Education</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Girolami method open-in-new

Girolami method