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).Template:Cn
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 Template:Math is some free-energy related property, such as an adsorption or absorption constant, Template:Math, anesthetic potency, etc. The lowercase letters (Template:Mvar, Template:Mvar, Template:Mvar, Template:Mvar, Template:Mvar) are system constants describing the contribution of the aerosol phase to the sorption process.[5] The capital letters (Template:Math, Template:Math, Template:Math, Template:Math, Template:Math) are solute descriptors representing the complementary properties of the compounds. Specifically,
- Template:Math is the gas–liquid partition constant on n-hexadecane at 298 K;
- Template:Math = the excess molar refraction (Template:Math for n-alkanes).
- Template:Math = the ability of a solute to stabilize a neighbouring dipole by virtue of its capacity for orientation and induction interactions;
- Template:Math = the solute's effective hydrogen bond acidity; and
- Template:Math = the solute's effective hydrogen-bond basicity.
The complementary system constants are identified as
- Template:Mvar = the contribution from cavity formation and dispersion interactions;
- Template:Mvar = the contribution from interactions with solute n-electrons and pi electrons;
- Template:Mvar = the contribution from dipole-type interactions;
- Template:Mvar = the contribution from hydrogen-bond basicity (because a basic sorbent will interact with an acidic solute); and
- Template:Mvar = 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 Template:Math, is given by
where Template:Math 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