In
physical organic chemistry
Physical organic chemistry, a term coined by Louis Hammett in 1940, refers to a discipline of organic chemistry that focuses on the relationship between chemical structures and reactivity, in particular, applying experimental tools of physical ch ...
, a free-energy relationship or Gibbs energy relation relates the
logarithm
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...
of a
reaction rate constant In chemical kinetics a reaction rate constant or reaction rate coefficient, ''k'', quantifies the rate and direction of a chemical reaction.
For a reaction between reactants A and B to form product C
the reaction rate is often found to have the ...
or
equilibrium constant
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
for one series of
chemical reaction
A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
s with the logarithm of the rate or equilibrium constant for a related series of reactions.
Free energy relationships establish the extent at which
bond
Bond or bonds may refer to:
Common meanings
* Bond (finance), a type of debt security
* Bail bond, a commercial third-party guarantor of surety bonds in the United States
* Chemical bond, the attraction of atoms, ions or molecules to form chemica ...
formation and
breakage happen in the
transition state
In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked wi ...
of a reaction, and in combination with
kinetic isotope experiments a
reaction mechanism
In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs.
A chemical mechanism is a theoretical conjecture that tries to describe in detail what takes place at each stage of ...
can be determined. Free energy relationships are often used to calculate equilibrium constants since they are experimentally difficult to determine.
The most common form of free-energy relationships are linear free-energy relationships (LFER). The
Brønsted catalysis equation The Brønsted catalysis equation or law of correlation, after Johannes Nicolaus Brønsted, gives the relationship between acid strength and catalytic activity in general acid catalysis.Brønsted, J. N.; Pedersen, K. J. Zeitschrift für Phys. Chemie ...
describes the relationship between the
ionization constant
In chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted ) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction
:HA ...
of a series of catalysts and the reaction rate constant for a reaction on which the
catalyst
Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
operates. The
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 ju ...
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
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
has suggested that this name should be replaced by linear
Gibbs energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work (physics), work that may be performed by a closed system, thermodynamically closed system a ...
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'.
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):
:
where is some
free-energy related property, such as an
adsorption
Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which a f ...
or absorption constant, , anesthetic potency, etc. The lowercase letters (, , , , ) are system constants describing the contribution of the
aerosol
An aerosol is a suspension (chemistry), suspension of fine solid particles or liquid Drop (liquid), droplets in air or another gas. Aerosols can be natural or Human impact on the environment, anthropogenic. Examples of natural aerosols are fog o ...
phase to the
sorption
Sorption is a physical and chemical process by which one substance becomes attached to another. Specific cases of sorption are treated in the following articles:
; Absorption: "the incorporation of a substance in one state into another of a d ...
process.
The capital letters (, , , , ) are
solute
In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent ...
descriptors representing the complementary properties of the compounds. Specifically,
* is the gas–liquid partition constant on
''n''-hexadecane at 298 K;
* = the excess
molar refraction ( for ''n''-alkanes).
* = the ability of a solute to stabilize a neighbouring
dipole
In physics, a dipole () is an electromagnetic phenomenon which occurs in two ways:
*An electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system i ...
by virtue of its capacity for orientation and induction interactions;
* = the solute's effective
hydrogen bond
In chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a ...
acidity
In computer science, ACID ( atomicity, consistency, isolation, durability) is a set of properties of database transactions intended to guarantee data validity despite errors, power failures, and other mishaps. In the context of databases, a sequ ...
; and
* = the solute's effective hydrogen-bond
basicity
In chemistry, there are three definitions in common use of the word base, known as Arrhenius bases, Brønsted bases, and Lewis bases. All definitions agree that bases are substances that react with acids, as originally proposed by G.-F. ...
.
The complementary system constants are identified as
* = the contribution from cavity formation and dispersion interactions;
* = the contribution from interactions with solute
n-electrons and
pi electron
In chemistry, pi bonds (π bonds) are covalent chemical bonds, in each of which two lobes of an orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap occurs laterally. Each of these atomic orbitals ...
s;
* = the contribution from dipole-type interactions;
* = the contribution from hydrogen-bond basicity (because a basic
sorbent
A sorbent is a material used to absorb or adsorb liquids or gases. Examples include:
*A material similar to molecular sieve material, which acts by adsorption (attracting molecules to its surface). It has a large internal surface area and good t ...
will interact with an acidic solute); and
* = 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 , is given by
:
where is
McGowan's characteristic molecular volume in cubic centimeters per mole divided by 100.
See also
*
Brønsted catalysis equation The Brønsted catalysis equation or law of correlation, after Johannes Nicolaus Brønsted, gives the relationship between acid strength and catalytic activity in general acid catalysis.Brønsted, J. N.; Pedersen, K. J. Zeitschrift für Phys. Chemie ...
*
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 ju ...
*
Taft equation
The Taft equation is a linear free energy relationship (LFER) used in physical organic chemistry in the study of reaction mechanisms and in the development of quantitative structure–activity relationships for organic compounds. It was develo ...
*
Swain–Lupton equation
In physical organic chemistry, the Swain–Lupton equation is a Free-energy relationship, linear free energy relationship (LFER) that is used in the study of reaction mechanisms and in the development of Quantitative structure-activity relationshi ...
*
Grunwald–Winstein equation
In physical organic chemistry, the Grunwald–Winstein equation is a linear free energy relationship between relative rate constants and the ionizing power of various solvent systems, describing the effect of solvent as nucleophile on different ...
*
Yukawa–Tsuno equation The Yukawa–Tsuno equation, first developed in 1959,Yukawa Y, Tsuno Y. "Resonance Effect in Hammett Relationship. II. Sigma Constants in Electrophilic Reactions and their Intercorrelation." ''Bull. Chem. Soc. Jpn.'' 32 965-71 (1959) is a linear fre ...
*
Edwards equation
*
Marcus equation
*
Bell–Evans–Polanyi principle In physical chemistry, the Evans–Polanyi principle (also referred to as the Bell–Evans–Polanyi principle, Brønsted–Evans–Polanyi principle, or Evans–Polanyi–Semenov principle) observes that the difference in activation energy between ...
*
Quantitative structure–activity relationship
Quantitative structure–activity relationship models (QSAR models) are regression or classification models used in the chemical and biological sciences and engineering. Like other regression models, QSAR regression models relate a set of "predic ...
References
External links
* {{GoldBookRef , title=linear free-energy relation , file=L03551
Solutions
Physical organic chemistry