Free-energy relationship

Short description: Relation between the equilibrium/reaction rate constants of two chemical reactions

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).

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'.

## Contents

* 1 Chemical and physical properties
* 2 See also
* 3 References
* 4 External links

## Chemical and physical properties

Main article: Chemistry:LFER solvent coefficients (data page)

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⁡SP=c+eE+sS+aA+bB+lL

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⁡SP=c+eE+sS+aA+bB+vV

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

## See also

* Brønsted catalysis equation
* Hammett equation
* Taft equation
* Swain–Lupton equation
* Grunwald–Winstein equation
* Yukawa–Tsuno equation
* Edwards equation
* Marcus equation
* Bell–Evans–Polanyi principle
* Quantitative structure–activity relationship

## References

1. ↑ 1.0 1.1 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. ↑ "Biological phosphoryl-transfer reactions: understanding mechanism and catalysis". Annual Review of Biochemistry 80 (1): 669–702. 2011-06-15. doi:10.1146/annurev-biochem-060409-092741. PMID 21513457.
3. ↑ "Application of hydrogen bonding calculations in property based drug design". Drug Discovery Today 7 (20): 1056–63. October 2002. doi:10.1016/s1359-6446(02)02478-9. PMID 12546895.
4. ↑ "Determination of solute descriptors by chromatographic methods.". Analytica Chimica Acta 652 (1–2): 32–53. October 2009. doi:10.1016/j.aca.2009.04.038. PMID 19786169.
5. ↑ "Predicting Abraham model solvent coefficients". Chemistry Central Journal 9: 12. 2015. doi:10.1186/s13065-015-0085-4. 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

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