Free-energy relationship

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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]

Contents

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]

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,

The complementary system constants are identified as

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

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

See also

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  1. Between the logarithm of the pre-exponential factors and the activation energies where the series of closely related reactions are indicated by the index i, Ai are the preexponential factors, Ea,i are the activation energies, R is the gas constant, and α, β are constants.
  2. Between enthalpies and entropies of activation where H
    i
    are the enthalpies of activation and S
    i
    are the entropies of activation.
  3. Between the enthalpy and entropy changes of a series of similar reactions where Hi are the enthalpy changes and Si are the entropy changes.

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This page provides supplementary data and solvent coefficients for linear free-energy relationships.

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Michael H Abraham was an English chemist. He mainly worked in the area of physical organic chemistry, with his research interests being hydrogen bonding, solvation, linear free energy relationships (LFER), quantitative structure-activity relationships (QSAR) and solute-solvent interactions. A faculty member of University College London since 1988, Abraham was known within his field for creating the Abraham General Solvation Model.

References

  1. 1 2 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.
  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.