Activation energy

Last updated
The sparks created by striking steel against a piece of flint provide the activation energy to initiate combustion in this Bunsen burner. The blue flame sustains itself after the sparks stop because the continued combustion of the flame is now energetically favorable. Incandescence.jpg
The sparks created by striking steel against a piece of flint provide the activation energy to initiate combustion in this Bunsen burner. The blue flame sustains itself after the sparks stop because the continued combustion of the flame is now energetically favorable.

In the Arrhenius model of reaction rates, activation energy is the minimum amount of energy that must be available to reactants for a chemical reaction to occur. [1] The activation energy (Ea) of a reaction is measured in kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol). [2] Activation energy can be thought of as the magnitude of the potential barrier (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. [3]

Contents

Other uses

Although less commonly used, activation energy also applies to nuclear reactions [4] and various other physical phenomena. [5] [6] [7]

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 for the reaction, R is the universal gas constant, T is the absolute temperature (usually in kelvins), and k is the reaction rate coefficient. Even without knowing A, Ea 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.[ citation needed ]

Catalysts

Example of an enzyme-catalysed exothermic reaction Activation2 updated.svg
Example of an enzyme-catalysed exothermic reaction
The relationship between activation energy ( E a {\displaystyle E_{\textrm {a}}} ) and enthalpy of reaction (DH) with and without a catalyst, plotted against the reaction coordinate. The highest energy position (peak position) represents the transition state. With the catalyst, the energy required to enter transition state decreases, thereby decreasing the energy required to initiate the reaction. Activation energy.svg
The relationship between activation energy () and enthalpy of reaction (ΔH) with and without a catalyst, plotted against the reaction coordinate. The highest energy position (peak position) represents the transition state. With the catalyst, the energy required to enter transition state decreases, thereby decreasing the energy required to initiate the reaction.

A substance that modifies the transition state to lower the activation energy is termed a catalyst; a catalyst composed only of protein and (if applicable) small molecule cofactors is termed an enzyme. 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 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 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 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. [10]

Relationship with Gibbs energy of activation

In the Arrhenius equation, the term activation energy (Ea) is used to describe the energy required to reach the transition state, and the exponential relationship k = 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, the Eyring 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.

Instead of also using Ea, the Eyring equation uses the concept of Gibbs energy and the symbol ΔG‡ to denote the Gibbs energy of activation to achieve the transition state. In the equation, kB 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 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: ΔG‡ = ΔH‡ − T ΔS‡. Then, for a unimolecular, one-step reaction, the approximate relationships Ea = ΔH‡ + RT and A = (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 on T. 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 of Ea for a reaction that proceeds over several hours at room temperature. Due to the relatively small magnitude of TΔS‡ and RT at ordinary temperatures for most reactions, in sloppy discourse, Ea, ΔG‡, and ΔH‡ 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‡Ho, Δ‡So and Δ‡Go respectively, where the o indicates a quantity evaluated between standard 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 either exergonic or endergonic, but the activation energy is not related to the spontaneity 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 Ea.

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 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 of nitric 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 .

Certain cationic polymerization reactions have negative activation energies so that the rate decreases with temperature. For chain-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 from 40 to 60 kJ/mol. [21]

See also

Related Research Articles

<span class="mw-page-title-main">Chemical reaction</span> Process that results in the interconversion of chemical species

A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an energy change as new products are generated. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei, and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur.

In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that the van 't Hoff equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and reverse reactions. This equation has a vast and important application in determining the rate of chemical reactions and for calculation of energy of activation. Arrhenius provided a physical justification and interpretation for the formula. Currently, it is best seen as an empirical relationship. It can be used to model the temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally induced processes and reactions. The Eyring equation, developed in 1935, also expresses the relationship between rate and energy.

<span class="mw-page-title-main">Reaction rate</span> Speed at which a chemical reaction takes place

The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit time. Reaction rates can vary dramatically. For example, the oxidative rusting of iron under Earth's atmosphere is a slow reaction that can take many years, but the combustion of cellulose in a fire is a reaction that takes place in fractions of a second. For most reactions, the rate decreases as the reaction proceeds. A reaction's rate can be determined by measuring the changes in concentration over time.

Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction.

In chemistry, reactivity is the impulse for which a chemical substance undergoes a chemical reaction, either by itself or with other materials, with an overall release of energy.

In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical reaction occurs.

<span class="mw-page-title-main">Activated complex</span> Unstable configurations of atoms formed while a chemical reaction progresses

In chemistry, an activated complex represents a collection of intermediate structures in a chemical reaction when bonds are breaking and forming. The activated complex is an arrangement of atoms in an arbitrary region near the saddle point of a potential energy surface. The region represents not one defined state, but a range of unstable configurations that a collection of atoms pass through between the reactants and products of a reaction. Activated complexes have partial reactant and product character, which can significantly impact their behaviour in chemical reactions.

In chemical kinetics, the overall rate of a reaction is often approximately determined by the slowest step, known as the rate-determining step or rate-limiting step. For a given reaction mechanism, the prediction of the corresponding rate equation is often simplified by using this approximation of the rate-determining step.

<span class="mw-page-title-main">Collision theory</span> Chemistry principle

Collision theory is a principle of chemistry used to predict the rates of chemical reactions. It states that when suitable particles of the reactant hit each other with the correct orientation, only a certain amount of collisions result in a perceptible or notable change; these successful changes are called successful collisions. The successful collisions must have enough energy, also known as activation energy, at the moment of impact to break the pre-existing bonds and form all new bonds. This results in the products of the reaction. The activation energy is often predicted using the Transition state theory. Increasing the concentration of the reactant brings about more collisions and hence more successful collisions. Increasing the temperature increases the average kinetic energy of the molecules in a solution, increasing the number of collisions that have enough energy. Collision theory was proposed independently by Max Trautz in 1916 and William Lewis in 1918.

In chemical kinetics, a reaction rate constant or reaction rate coefficient is a proportionality constant which quantifies the rate and direction of a chemical reaction by relating it with the concentration of reactants.

In chemistry, molecularity is the number of molecules that come together to react in an elementary (single-step) reaction and is equal to the sum of stoichiometric coefficients of reactants in the elementary reaction with effective collision and correct orientation. Depending on how many molecules come together, a reaction can be unimolecular, bimolecular or even trimolecular.

In theoretical chemistry, Marcus theory is a theory originally developed by Rudolph A. Marcus, starting in 1956, to explain the rates of electron transfer reactions – the rate at which an electron can move or jump from one chemical species (called the electron donor) to another (called the electron acceptor). It was originally formulated to address outer sphere electron transfer reactions, in which the two chemical species only change in their charge with an electron jumping (e.g. the oxidation of an ion like Fe2+/Fe3+), but do not undergo large structural changes. It was extended to include inner sphere electron transfer contributions, in which a change of distances or geometry in the solvation or coordination shells of the two chemical species is taken into account (the Fe-O distances in Fe(H2O)2+ and Fe(H2O)3+ are different).

The Eyring 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 Henry Eyring, Meredith Gwynne Evans and Michael Polanyi. The equation follows from the transition state theory, also known as activated-complex theory. If one assumes a constant enthalpy of activation and constant entropy of activation, the Eyring equation is similar to the empirical Arrhenius equation, despite the Arrhenius equation being empirical and the Eyring equation based on statistical mechanical justification.

In chemical kinetics, the entropy of activation of a reaction is one of the two parameters that are typically obtained from the temperature dependence of a reaction rate constant, when these data are analyzed using the Eyring equation of the transition state theory. The standard entropy of activation is symbolized ΔS‡ and equals the change in entropy when the reactants change from their initial state to the activated complex or transition state.

<span class="mw-page-title-main">Transition state theory</span> Theory describing the reaction rates of elementary chemical reactions

In chemistry, transition state theory (TST) explains the reaction rates of elementary chemical reactions. The theory assumes a special type of chemical equilibrium (quasi-equilibrium) between reactants and activated transition state complexes.

In chemical kinetics, an Arrhenius plot displays the logarithm of a reaction rate constant, (, ordinate axis) plotted against reciprocal of the temperature (, abscissa). Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions. For a single rate-limited thermally activated process, an Arrhenius plot gives a straight line, from which the activation energy and the pre-exponential factor can both be determined.

<span class="mw-page-title-main">Energy profile (chemistry)</span> Representation of a chemical process as a single energetic pathway

In theoretical chemistry, an energy profile is a theoretical representation of a chemical reaction or process as a single energetic pathway as the reactants are transformed into products. This pathway runs along the reaction coordinate, which is a parametric curve that follows the pathway of the reaction and indicates its progress; thus, energy profiles are also called reaction coordinate diagrams. They are derived from the corresponding potential energy surface (PES), which is used in computational chemistry to model chemical reactions by relating the energy of a molecule(s) to its structure.

In chemical kinetics, the Lindemann mechanism is a schematic reaction mechanism for unimolecular reactions. Frederick Lindemann and J. A. Christiansen proposed the concept almost simultaneously in 1921, and Cyril Hinshelwood developed it to take into account the energy distributed among vibrational degrees of freedom for some reaction steps.

In thermodynamics, enthalpy–entropy compensation is a specific example of the compensation effect. The compensation effect refers to the behavior of a series of closely related chemical reactions, which exhibit a linear relationship between one of the following kinetic or thermodynamic parameters for describing the reactions:

  1. Between the logarithm of the pre-exponential factors and the activation energies where the series of closely related reactions are indicated by the index i, Ai are the preexponential factors, Ea,i are the activation energies, R is the gas constant, and α, β are constants.
  2. Between enthalpies and entropies of activation where H‡
    i     are the enthalpies of activation and S‡
    i     are the entropies of activation.
  3. Between the enthalpy and entropy changes of a series of similar reactions where Hi are the enthalpy changes and Si are the entropy changes.

In chemical kinetics, the Aquilanti–Mundim deformed Arrhenius model is a generalization of the standard Arrhenius law.

References

  1. ↑ "Activation Energy". www.chem.fsu.edu. Archived from the original on 2016-12-07. Retrieved 2017-01-13.
  2. ↑ Espenson, James (1995). Chemical Kinetics and Reaction Mechanisms. McGraw-Hill. ISBN   0070202605.
  3. ↑ "Activation Energy and the Arrhenius Equation – Introductory Chemistry- 1st Canadian Edition". opentextbc.ca. Archived from the original on 2017-07-08. Retrieved 2018-04-05.
  4. ↑ Kagan, Harris; Barrett, Tom. "Energy in a Modern Society: XIV. Nuclear energy" (Course). Ohio State University. Archived from the original on 22 March 2019. Retrieved 15 October 2021.
  5. ↑ Wang, Jenqdaw; Raj, Rishi (1990). "Estimate of the Activation Energies for Boundary Diffusion from Rate-Controlled Sintering of Pure Alumina, and Alumina Doped with Zirconia or Titania". Journal of the American Ceramic Society. 73 (5): 1172. doi:10.1111/j.1151-2916.1990.tb05175.x.
  6. ↑ Kiraci, A; Yurtseven, H (2012). "Temperature Dependence of the Raman Frequency, Damping Constant and the Activation Energy of a Soft-Optic Mode in Ferroelectric Barium Titanate". Ferroelectrics. 432: 14–21. doi:10.1080/00150193.2012.707592. S2CID   121142463.
  7. ↑ Terracciano, Anthony C; De Oliveira, Samuel; Vazquez-Molina, Demetrius; Uribe-Romo, Fernando J; Vasu, Subith S; Orlovskaya, Nina (2017). "Effect of catalytically active Ce 0.8 Gd 0.2 O 1.9 coating on the heterogeneous combustion of methane within MgO stabilized ZrO 2 porous ceramics". Combustion and Flame. 180: 32–39. doi:10.1016/j.combustflame.2017.02.019.
  8. ↑ "General Chemistry Online: FAQ: Chemical change: What are some examples of reactions that involve catalysts?". antoine.frostburg.edu. Archived from the original on 2016-11-29. Retrieved 2017-01-13.
  9. ↑ Bui, Matthew (2 October 2013). "The Arrhenius Law: Activation Energies". Chemistry LibreTexts. UC Davis. Archived from the original on February 18, 2017. Retrieved February 17, 2017.
  10. ↑ Berg, Jeremy (2019). Biochemistry - Ninth Edition. New York, NY: WH Freeman and Company. pp. 240–244. ISBN   978-1-319-11467-1.
  11. ↑ "Enthalpy of activation". IUPAC Gold Book (2nd edition, on-line version). IUPAC (International Union of Pure and Applied Chemistry). 2019. doi: 10.1351/goldbook.E02142 . Archived from the original on 21 February 2020. Retrieved 10 May 2020.
  12. ↑ Steinfeld, Jeffrey I.; Francisco, Joseph S.; Hase, William L. (1999). Chemical Kinetics and Dynamics (2nd ed.). Prentice Hall. p. 301. ISBN   0-13-737123-3.
  13. ↑ Atkins, Peter; de Paula, Julio (2006). Atkins' Physical Chemistry (8th ed.). W.H.Freeman. p.  883. ISBN   0-7167-8759-8. ... but we shall omit the standard state sign to avoid overburdening the notation.
  14. ↑ Laidler, Keith J.; Meiser, John H. (1982). Physical Chemistry. Benjamin/Cummings. p. 381. ISBN   0-8053-5682-7.
  15. ↑ Mozurkewich, Michael; Benson, Sidney (1984). "Negative activation energies and curved Arrhenius plots. 1. Theory of reactions over potential wells". J. Phys. Chem. 88 (25): 6429–6435. doi:10.1021/j150669a073.
  16. ↑ Espenson, James H. (1981). Chemical kinetics and reaction mechanisms. McGraw-Hill. p. 121. ISBN   0-07-019667-2.
  17. ↑ Atkins, Peter; de Paula, Julio (2006). Atkins' Physical Chemistry (8th ed.). W. H. Freeman. p. 822. ISBN   0-7167-8759-8.
  18. ↑ Kadir, Tamara (10 September 2020). "3.2.2: Pre-equilibrium Approximation". Chem Libre Texts. Retrieved 23 January 2022. The overall activation energy is negative if Ea1 + Ea2 < Ea−1
  19. ↑ Moore, John W.; Pearson, Ralph G. (1981). Kinetics and mechanism (3rd ed.). John Wiley and Sons. p. 316. ISBN   0-471-03558-0.
  20. ↑ Engel, Thomas; Reid, Philip (2006). Physical Chemistry. Pearson. Benjamin-Cummings. p. *34. ISBN   0-8053-3842-X.
  21. ↑ Cowie, J. M. G. (1991). Polymers: Chemistry and Physics of Modern Materials (2nd ed.). Blackie (USA: Chapman & Hall+). p. 88. ISBN   0-216-92980-6.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.