In
chemistry and
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, activation energy is the minimum amount of energy that must be provided for compounds to result in a
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 ...
. The activation energy (''E''
a) of a reaction is measured in
joules per mole (J/mol),
kilojoules per mole (kJ/mol) or
kilocalories per mole (kcal/mol). Activation energy can be thought of as the magnitude of the
potential barrier
In quantum mechanics, the rectangular (or, at times, square) potential barrier is a standard one-dimensional problem that demonstrates the phenomena of wave-mechanical tunneling (also called "quantum tunneling") and wave-mechanical reflection. ...
(sometimes called the energy barrier) separating
minima of the
potential energy surface pertaining to the initial and final
thermodynamic state. For a chemical reaction to proceed at a reasonable rate, the temperature of the system should be high enough such that there exists an appreciable number of molecules with translational energy equal to or greater than the activation energy. The term "activation energy" was introduced in 1889 by the Swedish scientist
Svante Arrhenius
Svante August Arrhenius ( , ; 19 February 1859 – 2 October 1927) was a Swedish scientist. Originally a physicist, but often referred to as a chemist, Arrhenius was one of the founders of the science of physical chemistry. He received the Nob ...
.
Other uses
Although less commonly used, activation energy also applies to
nuclear reaction
In nuclear physics and nuclear chemistry, a nuclear reaction is a process in which two nuclei, or a nucleus and an external subatomic particle, collide to produce one or more new nuclides. Thus, a nuclear reaction must cause a transformatio ...
s and various other physical phenomena.
Temperature dependence and the relation to the Arrhenius equation
The
Arrhenius equation gives the quantitative basis of the relationship between the activation energy and the rate at which a reaction proceeds. From the equation, the activation energy can be found through the relation
where ''A'' is the
pre-exponential factor
In chemical kinetics, the pre-exponential factor or A factor is the pre-exponential constant in the Arrhenius equation (equation shown below), an empirical relationship between temperature and rate coefficient. It is usually designated by A when ...
for the reaction, ''R'' is the universal
gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
, ''T'' is the absolute temperature (usually in
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
s), and ''k'' is the
reaction rate coefficient. Even without knowing ''A'', ''E''
a can be evaluated from the variation in reaction rate coefficients as a function of temperature (within the validity of the Arrhenius equation).
At a more advanced level, the net Arrhenius activation energy term from the Arrhenius equation is best regarded as an experimentally determined parameter that indicates the sensitivity of the reaction rate to temperature. There are two objections to associating this activation energy with the threshold barrier for an elementary reaction. First, it is often unclear as to whether or not reaction does proceed in one step; threshold barriers that are averaged out over all elementary steps have little theoretical value. Second, even if the reaction being studied is elementary, a spectrum of individual collisions contributes to rate constants obtained from bulk ('bulb') experiments involving billions of molecules, with many different reactant collision geometries and angles, different translational and (possibly) vibrational energies—all of which may lead to different microscopic reaction rates.
Catalysts
A substance that modifies the transition state to lower the activation energy is termed a
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 ...
; a catalyst composed only of protein and (if applicable) small molecule cofactors is termed an
enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products ...
. A catalyst increases the rate of reaction without being consumed in the reaction. In addition, the catalyst lowers the activation energy, but it does not change the energies of the original reactants or products, and so does not change equilibrium. Rather, the reactant energy and the product energy remain the same and only the ''activation energy'' is altered (lowered).
A catalyst is able to reduce the activation energy by forming a transition state in a more favorable manner. Catalysts, by nature, create a more "comfortable" fit for the
substrate of a reaction to progress to a transition state. This is possible due to a release of energy that occurs when the substrate binds to the
active site of a catalyst. This energy is known as Binding Energy. Upon binding to a catalyst, substrates partake in numerous stabilizing forces while within the active site (e.g.
hydrogen bonding or
van der Waals force
In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and th ...
s). Specific and favorable bonding occurs within the active site until the substrate forms to become the high-energy transition state. Forming the transition state is more favorable with the catalyst because the favorable stabilizing interactions within the active site ''release'' energy. A chemical reaction is able to manufacture a high-energy transition state molecule more readily when there is a stabilizing fit within the active site of a catalyst. The binding energy of a reaction is this energy released when favorable interactions between substrate and catalyst occur. The binding energy released assists in achieving the unstable transition state. Reactions without catalysts need a higher input of energy to achieve the transition state. Non-catalyzed reactions do not have free energy available from active site stabilizing interactions, such as catalytic enzyme reactions.
Relationship with Gibbs energy of activation
In the
Arrhenius equation, the term activation energy (''E''
a) is used to describe the energy required
to reach the transition state, and the exponential relationship holds. In transition state theory, a more sophisticated model of the relationship between reaction rates and the transition state, a superficially similar mathematical relationship, the
Eyring equation
The Eyring equation (occasionally also known as Eyring–Polanyi equation) is an equation used in chemical kinetics to describe changes in the rate of a chemical reaction against temperature. It was developed almost simultaneously in 1935 by Henr ...
, is used to describe the rate constant of a reaction: . However, instead of modeling the temperature dependence of reaction rate phenomenologically, the Eyring equation models individual elementary steps of a reaction. Thus, for a multistep process, there is no straightforward relationship between the two models. Nevertheless, the functional forms of the Arrhenius and Eyring equations are similar, and for a one-step process, simple and chemically meaningful correspondences can be drawn between Arrhenius and Eyring parameters.
Instead of also using ''E''
a, the Eyring equation uses the concept of
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 that may be performed by a thermodynamically closed system at constant temperature and pre ...
and the symbol Δ''G''
‡ to denote the Gibbs energy of activation to achieve the
transition state. In the equation, ''k''
B and ''h'' are the Boltzmann and Planck constants, respectively. Although the equations look similar, it is important to note that the Gibbs energy contains an
entropic
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
term in addition to the enthalpic one. In the Arrhenius equation, this entropic term is accounted for by the pre-exponential factor ''A''. More specifically, we can write the Gibbs free energy of activation in terms of enthalpy and
entropy of activation In chemical kinetics, the entropy of activation of a reaction is one of the two parameters (along with the enthalpy of activation) which are typically obtained from the temperature dependence of a reaction rate constant, when these data are analyzed ...
: . Then, for a unimolecular, one-step reaction, the ''approximate'' relationships and hold. Note, however, that in Arrhenius theory proper, ''A'' is temperature independent, while here, there is a linear dependence on ''T''. For a one-step unimolecular process whose half-life at room temperature is about 2 hours, Δ''G''
‡ is approximately 23 kcal/mol. This is also the roughly the magnitude of ''E''
a for a reaction that proceeds over several hours at room temperature. Due to the relatively small magnitude of ''T''Δ''S''
‡ and ''RT'' at ordinary temperatures for most reactions, in sloppy discourse, ''E''
a, Δ''G''
‡, and Δ''H''
‡ are often conflated and all referred to as the "activation energy".
The enthalpy, entropy and Gibbs energy of activation are more correctly written as Δ
‡''H''
o, Δ
‡''S''
o and Δ
‡''G''
o respectively, where the o indicates a quantity evaluated between
standard states. However, some authors omit the o in order to simplify the notation.
The total free energy change of a reaction is independent of the activation energy however. Physical and chemical reactions can be either
exergonic or
endergonic, but the activation energy is not related to the
spontaneity
Spontaneous may refer to:
* Spontaneous abortion
* Spontaneous bacterial peritonitis
* Spontaneous combustion
* Spontaneous declaration
* Spontaneous emission
* Spontaneous fission
* Spontaneous generation
* Spontaneous human combustion
* Spontan ...
of a reaction. The overall reaction energy change is not altered by the activation energy.
Negative activation energy
In some cases, rates of reaction ''decrease'' with increasing temperature. When following an approximately exponential relationship so the rate constant can still be fit to an Arrhenius expression, this results in a negative value of ''E''
a.
Elementary reactions exhibiting negative activation energies are typically barrierless reactions, in which the reaction proceeding relies on the capture of the molecules in a potential well. Increasing the temperature leads to a reduced probability of the colliding molecules capturing one another (with more glancing collisions not leading to reaction as the higher momentum carries the colliding particles out of the potential well), expressed as a reaction
cross section
Cross section may refer to:
* Cross section (geometry)
** Cross-sectional views in architecture & engineering 3D
*Cross section (geology)
* Cross section (electronics)
* Radar cross section, measure of detectability
* Cross section (physics)
**Abs ...
that decreases with increasing temperature. Such a situation no longer leads itself to direct interpretations as the height of a potential barrier.
Some multistep reactions can also have apparent negative activation energies. For example, the overall rate constant k for a two-step reaction A B, B → C is given by k = k
2K
1, where k
2 is the rate constant of the rate-limiting slow second step and K
1 is the equilibrium constant of the rapid first step. In some reactions, K
1 decreases with temperature more rapidly than k
2 increases, so that k actually decreases with temperature corresponding to a negative observed activation energy.
An example is the oxidation of
nitric oxide which is a termolecular reaction
. The rate law is