Free-energy relationship

In physical organic chemistry, a free-energy relationship or Gibbs energy relation relates the logarithm of a reaction rate constant or equilibrium constant for one series of chemical reactions with the logarithm of the rate or equilibrium constant for a related series of reactions.^[1] Free energy relationships establish the extent at which bond formation and breakage happen in the transition state of a reaction, and in combination with kinetic isotope experiments a reaction mechanism can be determined. Free energy relationships are often used to calculate equilibrium constants since they are experimentally difficult to determine.^[2]

The most common form of free-energy relationships are linear free-energy relationships (LFER). The Brønsted catalysis equation describes the relationship between the ionization constant of a series of catalysts and the reaction rate constant for a reaction on which the catalyst operates. The Hammett equation predicts the equilibrium constant or reaction rate of a reaction from a substituent constant and a reaction type constant. The Edwards equation relates the nucleophilic power to polarisability and basicity. The Marcus equation is an example of a quadratic free-energy relationship (QFER).^{[citation needed]}

IUPAC has suggested that this name should be replaced by linear Gibbs energy relation, but at present there is little sign of acceptance of this change.^[1] The area of physical organic chemistry which deals with such relations is commonly referred to as 'linear free-energy relationships'.

Chemical and physical properties

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 M.H. Abraham and co-workers):^[3]^[4]

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

where $SP$ is some free-energy related property, such as an adsorption or absorption constant, $log K$ , anesthetic potency, etc. The lowercase letters ( $e$ , $s$ , $a$ , $b$ , $l$ ) are system constants describing the contribution of the aerosol phase to the sorption process.^[5] The capital letters ( $E$ , $S$ , $A$ , $B$ , $L$ ) are solute descriptors representing the complementary properties of the compounds. Specifically,

$L$ is the gas–liquid partition constant on n-hexadecane at 298 K;
$E$ = the excess molar refraction ( $E = 0$ for n-alkanes).
$S$ = the ability of a solute to stabilize a neighbouring dipole by virtue of its capacity for orientation and induction interactions;
$A$ = the solute's effective hydrogen bond acidity; and
$B$ = the solute's effective hydrogen-bond basicity.

The complementary system constants are identified as

$l$ = the contribution from cavity formation and dispersion interactions;
$e$ = the contribution from interactions with solute n-electrons and pi electrons;
$s$ = the contribution from dipole-type interactions;
$a$ = the contribution from hydrogen-bond basicity (because a basic sorbent will interact with an acidic solute); and
$b$ = the contribution from hydrogen-bond acidity to the transfer of the solute from air to the aerosol phase.

Similarly, the correlation of solvent–solvent partition coefficients as $log SP$ , is given by

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

where $V$ is McGowan's characteristic molecular volume in cubic centimeters per mole divided by 100.

References

^ ^a ^b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "linear free-energy relation". doi:10.1351/goldbook.L03551
^ 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.
^ 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.
^ 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.
^ 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.

External links

IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "linear free-energy relation". doi:10.1351/goldbook.L03551

[GoldBookL03551-1] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "linear free-energy relation". doi:10.1351/goldbook.L03551

[2] 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.

[3] 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.

[4] 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.

[Bradley_2015-5] 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.

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Chemical and physical properties

See also

References

External links