Free-energy relationship
Encyclopedia
In physical organic chemistry
, a free-energy relationship or linear Gibbs energy relation relates the logarithm
of a reaction rate constant or equilibrium constant for one series of reactions with the logarithm of the rate or equilibrium constant for a related series of reactions. Establishing free-energy relationships helps in the understanding of the reaction mechanism
for a chemical reaction
and allows the prediction of reaction rates and equilibrium constants.
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.
It has been suggested that this name should be replaced by linear Gibbs energy relation, but at present there is little sign of acceptance of this change.
The area of physical organic chemistry which deals with such relations is commonly referred to as 'Linear Free-Energy Relationships'.
For example, a typical LFER relation for predicting solubility
can be defined as follows:
log SP = eE + sS +aA + bB + lL +c
where SP is some free energy
related property, such as an adsorption
or absorption constant. The lower case letters (e, s, a, b, l) are system constants describing the contribution of the aerosol
phase to the sorption
process. The capital letters are solute
descriptors representing the complementary properties of the compounds. Specifically, L is the gas-liquid partition constant on hexadecane
at 298 K; E the excess molar refraction; S the ability of a solute to stabilize a neighboring 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 the contribution from cavity formation and dispersion interactions, l, the contribution from interactions with solute n- or Pi electrons, e, the contribution from dipole-type interactions, s, the contribution from hydrogen-bond basicity (because a basic sorbent
will interact with an acidic solute), a, and b the contribution from hydrogen-bond acidity to the transfer of the solute from air to the aerosol phase.
Physical organic chemistry
Physical organic chemistry is the study of the interrelationships between structure and reactivity in organic molecules. It can be seen as the study of organic chemistry using tools of physical chemistry such as chemical equilibrium, chemical kinetics, thermochemistry, and quantum chemistry...
, a free-energy relationship or linear Gibbs energy relation relates the logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
of a reaction rate constant or equilibrium constant for one series of reactions with the logarithm of the rate or equilibrium constant for a related series of reactions. Establishing free-energy relationships helps in the understanding of the reaction mechanism
Reaction mechanism
In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs.Although only the net chemical change is directly observable for most chemical reactions, experiments can often be designed that suggest the possible sequence of steps in...
for a chemical reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...
and allows the prediction of reaction rates and equilibrium constants.
The Brønsted catalysis equation
Brønsted catalysis equation
The Brønsted catalysis equation or law or correlation, after Johannes Nicolaus Brønsted, gives the relationship between acid strength and catalytic activity in general acid catalysis.\ \log k = \alpha*\log + C...
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
Hammett equation
The Hammett equation in organic chemistry describes a linear free-energy relationship relating reaction rates and equilibrium constants for many reactions involving benzoic acid derivatives with meta- and para-substituents to each other with just two parameters: a substituent constant and a...
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.
It has been suggested that this name should be replaced by linear Gibbs energy relation, but at present there is little sign of acceptance of this change.
The area of physical organic chemistry which deals with such relations is commonly referred to as 'Linear Free-Energy Relationships'.
For example, a typical LFER relation for predicting solubility
Solubility
Solubility is the property of a solid, liquid, or gaseous chemical substance called solute to dissolve in a solid, liquid, or gaseous solvent to form a homogeneous solution of the solute in the solvent. The solubility of a substance fundamentally depends on the used solvent as well as on...
can be defined as follows:
log SP = eE + sS +aA + bB + lL +c
where SP is some free energy
Gibbs free energy
In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure...
related property, such as an adsorption
Adsorption
Adsorption is the adhesion of atoms, ions, biomolecules or molecules of gas, liquid, or dissolved solids to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. It differs from absorption, in which a fluid permeates or is dissolved by a liquid or solid...
or absorption constant. The lower case letters (e, s, a, b, l) are system constants describing the contribution of the aerosol
Aerosol
Technically, an aerosol is a suspension of fine solid particles or liquid droplets in a gas. Examples are clouds, and air pollution such as smog and smoke. In general conversation, aerosol usually refers to an aerosol spray can or the output of such a can...
phase to the sorption
Sorption
Sorption refers to the action of absorption* Absorption is the incorporation of a substance in one state into another of a different state ....
process. The capital letters are solute
Solution
In chemistry, a solution is a homogeneous mixture composed of only one phase. In such a mixture, a solute is dissolved in another substance, known as a solvent. The solvent does the dissolving.- Types of solutions :...
descriptors representing the complementary properties of the compounds. Specifically, L is the gas-liquid partition constant on hexadecane
Hexadecane
Hexadecane is an alkane hydrocarbon with the chemical formula C16H34. Hexadecane consists of a chain of 16 carbon atoms, with three hydrogen atoms bonded to the two end carbon atoms, and two hydrogens bonded to each of the 14 other carbon atoms.Cetane is often used as a short-hand for cetane...
at 298 K; E the excess molar refraction; S the ability of a solute to stabilize a neighboring dipole
Dipole
In physics, there are several kinds of dipoles:*An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some distance. A permanent electric dipole is called an electret.*A...
by virtue of its capacity for orientation and induction interactions; A the solute’s effective hydrogen bond
Hydrogen bond
A hydrogen bond is the attractive interaction of a hydrogen atom with an electronegative atom, such as nitrogen, oxygen or fluorine, that comes from another molecule or chemical group. The hydrogen must be covalently bonded to another electronegative atom to create the bond...
acidity; and B the solute’s effective hydrogen-bond basicity. The complementary system constants are identified as the contribution from cavity formation and dispersion interactions, l, the contribution from interactions with solute n- or Pi electrons, e, the contribution from dipole-type interactions, s, the contribution from hydrogen-bond basicity (because a basic sorbent
Sorbent
A sorbent is a material used to absorb liquids or gases. Examples include:*A material similar to molecular sieve material. It has a large internal surface area and good thermal conductivity. It is typically supplied in pellets of 1 mm to 2 mm diameter and roughly 5 mm length or as...
will interact with an acidic solute), a, and b the contribution from hydrogen-bond acidity to the transfer of the solute from air to the aerosol phase.
External links
- IUPAC Compendium of Chemical Terminology (The Gold Book)
- http://goldbook.iupac.org/L03551.htmlIUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.doi:10.1351/goldbook]