In theArrhenius model of reaction rates,activation energy is the minimum amount of energy that must be available to reactants for achemical reaction to occur.[1] The activation energy (Ea) of a reaction is measured inkilojoules per mole (kJ/mol) orkilocalories per mole (kcal/mol).[2] Simplified:
Activation energy is the minimum energy barrier that reactant molecules must overcome to transform intoproducts. A reaction occurs only if enough molecules have kinetic energy equal to or greater than this barrier, which usually requires sufficiently high temperature. The term "activation energy" was introduced in 1889 by the Swedish scientistSvante Arrhenius.[3]
Although less commonly used, activation energy also applies tonuclear reactions[4] and various other physical phenomena.[5][6][7]
TheArrhenius 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
whereA is thepre-exponential factor for the reaction,R is the universalgas constant,T is the absolute temperature (usually inkelvins), andk is thereaction rate coefficient. Even without knowingA,Ea can be evaluated from the variation in reaction rate coefficients as a function of temperature (within the validity of the Arrhenius equation).[citation needed]
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.[citation needed]
A substance that modifies the transition state to lower the activation energy is termed acatalyst; a catalyst composed only of protein and (if applicable) small molecule cofactors is termed anenzyme. A catalyst increases the rate of reaction without being consumed in the reaction.[8] 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.[9] Rather, the reactant energy and the product energy remain the same and only theactivation energy is altered (lowered).[citation needed]
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 thesubstrate 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 theactive 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 orvan der Waals forces). 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 siterelease 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.[10]
In theArrhenius equation, the term activation energy (Ea) is used to describe the energy requiredto reach thetransition state, and the exponential relationshipk =A exp(−Ea/RT) holds. In transition state theory, a more sophisticated model of the relationship between reaction rates and the transition state, a superficially similar mathematical relationship, theEyring equation, is used to describe the rate constant of a reaction:k = (kBT /h) exp(−ΔG‡ /RT). 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.[citation needed]
Instead of also usingEa, the Eyring equation uses the concept ofGibbs energy and the symbol ΔG‡ to denote the Gibbs energy of activation to achieve thetransition state. In the equation,kB andh are the Boltzmann and Planck constants, respectively. Although the equations look similar, it is important to note that the Gibbs energy contains anentropic term in addition to the enthalpic one. In the Arrhenius equation, this entropic term is accounted for by the pre-exponential factorA. More specifically, we can write the Gibbs free energy of activation in terms of enthalpy andentropy of activation:ΔG‡ = ΔH‡ −T ΔS‡. Then, for a unimolecular, one-step reaction, theapproximate relationshipsEa = ΔH‡ +RT andA = (kBT/h) exp(1 + ΔS‡/R) hold. Note, however, that in Arrhenius theory proper,A is temperature independent, while here, there is a linear dependence onT. For a one-step unimolecular process whose half-life at room temperature is about 2 hours, ΔG‡ is approximately 23 kcal/mol. This is also the roughly the magnitude ofEa for a reaction that proceeds over several hours at room temperature. Due to the relatively small magnitude ofTΔS‡ andRT at ordinary temperatures for most reactions, in sloppy discourse,Ea, ΔG‡, and ΔH‡ are often conflated and all referred to as the "activation energy".[citation needed]
The enthalpy, entropy and Gibbs energy of activation are more correctly written as Δ‡Ho, Δ‡So and Δ‡Go respectively, where the o indicates a quantity evaluated betweenstandard states.[11][12] However, some authors omit the o in order to simplify the notation.[13][14]
The total free energy change of a reaction is independent of the activation energy however. Physical and chemical reactions can be eitherexergonic orendergonic, but the activation energy is not related to thespontaneity of a reaction. The overall reaction energy change is not altered by the activation energy.[citation needed]
In some cases, rates of reactiondecrease 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 ofEa.[citation needed]
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 reactioncross section that decreases with increasing temperature. Such a situation no longer leads itself to direct interpretations as the height of a potential barrier.[15]
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 = k2K1, where k2 is the rate constant of the rate-limiting slow second step and K1 is the equilibrium constant of the rapid first step. In some reactions, K1 decreases with temperature more rapidly than k2 increases, so that k actually decreases with temperature corresponding to a negative observed activation energy.[16][17][18]
An example is the oxidation ofnitric oxide which is a termolecular reaction. The rate law is with a negative activation energy.[19][20] This is explained by the two-step mechanism: and.
Certaincationic polymerization reactions have negative activation energies so that the rate decreases with temperature. Forchain-growth polymerization, the overall activation energy is, where i, p and t refer respectively to initiation, propagation and termination steps. The propagation step normally has a very small activation energy, so that the overall value is negative if the activation energy for termination is larger than that for initiation. The normal range of overall activation energies for cationic polymerization varies from40 to 60 kJ/mol.[21]
... but we shall omit the standard state sign to avoid overburdening the notation.
The overall activation energy is negative if Ea1 + Ea2 < Ea−1
