Free-energy relationship

<h2 id="chemical-and-physical-properties">Chemical and physical properties</h2>
<p class="note">Main article: <a href="/facts/LFER_solvent_coefficients_(data_page)/Eb3dFhpX">LFER solvent coefficients (data page)</a></p>
<p>A typical LFER relation for predicting the equilibrium concentration of a compound or solute in the vapor phase to a condensed (or solvent) phase can be defined as follows (following <a href="/facts/Michael_Abraham_(chemist)/B0FPKQNt">M.H. Abraham</a> and co-workers):<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a>
</p>

log
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        e
        
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          S
        
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          A
        
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        b
        
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        l
        
          L
        
      
    
    {\displaystyle \log \mathrm {SP} =c+e\mathrm {E} +s\mathrm {S} +a\mathrm {A} +b\mathrm {B} +l\mathrm {L} }

<p>where SP is some <a href="/facts/Gibbs_free_energy/bvenDuzh">free-energy</a> related property, such as an <a href="/facts/Adsorption/ARH9peYM">adsorption</a> or absorption constant, log K, anesthetic potency, etc. The lowercase letters (e, s, a, b, l) are system constants describing the contribution of the <a href="/facts/Aerosol/X1jXFLp2">aerosol</a> phase to the <a href="/facts/Sorption/nWDhtFkL">sorption</a> process.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> The capital letters (E, S, A, B, L) are <a href="/facts/Solute/MGchhMQV">solute</a> descriptors representing the complementary properties of the compounds. Specifically,
</p>
<ul><li>L is the gas–liquid partition constant on <a href="/facts/N-hexadecane/r39R2agQ"><i>n</i>-hexadecane</a> at 298 K;</li>
<li>E = the excess <a href="/facts/Molar_refractivity/fgssh9Aq">molar refraction</a> (E = 0 for <i>n</i>-alkanes).</li>
<li>S = the ability of a solute to stabilize a neighbouring <a href="/facts/Dipole/G1vRqruD">dipole</a> by virtue of its capacity for orientation and induction interactions;</li>
<li>A = the solute's effective <a href="/facts/Hydrogen_bond/85V86IIg">hydrogen bond</a> <a href="/facts/Acidity/FySU18n1">acidity</a>; and</li>
<li>B = the solute's effective hydrogen-bond <a href="/facts/Basicity/M9wA7qeM">basicity</a>.</li></ul>
<p>The complementary system constants are identified as
</p>
<ul><li>l = the contribution from cavity formation and dispersion interactions;</li>
<li>e = the contribution from interactions with solute <a href="/facts/Lone_pair/Q6kEAC4g">n-electrons</a> and <a href="/facts/Pi_electron/3Q6LAGYK">pi electrons</a>;</li>
<li>s = the contribution from dipole-type interactions;</li>
<li>a = the contribution from hydrogen-bond basicity (because a basic <a href="/facts/Sorbent/C56A0ASK">sorbent</a> will interact with an acidic solute); and</li>
<li>b = the contribution from hydrogen-bond acidity to the transfer of the solute from air to the aerosol phase.</li></ul>
<p>Similarly, the correlation of solvent–solvent partition coefficients as log SP, is given by
</p>

log
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          S
          P
        
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        c
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        e
        
          E
        
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        s
        
          S
        
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        a
        
          A
        
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        b
        
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        v
        
          V
        
      
    
    {\displaystyle \log \mathrm {SP} =c+e\mathrm {E} +s\mathrm {S} +a\mathrm {A} +b\mathrm {B} +v\mathrm {V} }

<p>where V is McGowan's characteristic molecular volume in cubic centimeters per mole divided by 100.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Br%25C3%25B8nsted_catalysis_equation/SLTrp3xh">Brønsted catalysis equation</a></li>
<li><a href="/facts/Hammett_equation/14lHVD7D">Hammett equation</a></li>
<li><a href="/facts/Taft_equation/XfQNWeU3">Taft equation</a></li>
<li><a href="/facts/Swain%25E2%2580%2593Lupton_equation/fhX4jsmj">Swain–Lupton equation</a></li>
<li><a href="/facts/Grunwald%25E2%2580%2593Winstein_equation/uD3UW4nN">Grunwald–Winstein equation</a></li>
<li><a href="/facts/Yukawa%25E2%2580%2593Tsuno_equation/tQwSAy6B">Yukawa–Tsuno equation</a></li>
<li><a href="/facts/Edwards_equation/u6fLkT7A">Edwards equation</a></li>
<li><a href="/facts/Marcus_equation/NK9uRuz7">Marcus equation</a></li>
<li><a href="/facts/Bell%25E2%2580%2593Evans%25E2%2580%2593Polanyi_principle/Ube9pP6G">Bell–Evans–Polanyi principle</a></li>
<li><a href="/facts/Quantitative_structure%25E2%2580%2593activity_relationship/6RDyCQDD">Quantitative structure–activity relationship</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="/facts/International_Union_of_Pure_and_Applied_Chemistry/2AV6myCK">IUPAC</a>, <i><a href="/facts/IUPAC_books/1lpll88F">Compendium of Chemical Terminology</a></i>, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "<a href="https://goldbook.iupac.org/terms/view/L03551.html">linear free-energy relation</a>". <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1351%2Fgoldbook.L03551">10.1351/goldbook.L03551</a></li></ul>

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

<ol>
<li id="fn:1"><p>IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "linear free-energy relation". doi:10.1351/goldbook.L03551 <a href="/wiki/International_Union_of_Pure_and_Applied_Chemistry" target="_blank">/wiki/International_Union_of_Pure_and_Applied_Chemistry</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Lassila JK, Zalatan JG, Herschlag D (2011-06-15). "Biological phosphoryl-transfer reactions: understanding mechanism and catalysis". Annual Review of Biochemistry. 80 (1): 669–702. doi:10.1146/annurev-biochem-060409-092741. PMC 3418923. PMID 21513457. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3418923" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3418923</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "linear free-energy relation". doi:10.1351/goldbook.L03551 <a href="/wiki/International_Union_of_Pure_and_Applied_Chemistry" target="_blank">/wiki/International_Union_of_Pure_and_Applied_Chemistry</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Abraham MH, Ibrahim A, Zissimos AM, Zhao YH, Comer J, Reynolds DP (October 2002). "Application of hydrogen bonding calculations in property based drug design". Drug Discovery Today. 7 (20): 1056–63. doi:10.1016/s1359-6446(02)02478-9. PMID 12546895. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Poole CF, Atapattu SN, Poole SK, Bell AK (October 2009). "Determination of solute descriptors by chromatographic methods". Analytica Chimica Acta. 652 (1–2): 32–53. doi:10.1016/j.aca.2009.04.038. PMID 19786169. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Bradley JC, Abraham MH, Acree WE, Lang AS (2015). "Predicting Abraham model solvent coefficients". Chemistry Central Journal. 9: 12. doi:10.1186/s13065-015-0085-4. PMC 4369285. PMID 25798192. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4369285" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4369285</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
</ol>

Free-energy relationship open-in-new

Free-energy relationship