Activation energy

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 chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. ^[1] 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). ^[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]

Other uses

Although less commonly used, activation energy also applies to nuclear reactions ^[4] and various other physical phenomena. ^{[5] [ failed verification ] [6] [7] [8]}

Temperature dependence and the relation to the Arrhenius equation

Main article: 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

$${\displaystyle k=Ae^{{-E_{\textrm {a}}}/{(RT)}}}$$

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, 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.^{[ citation needed ]}

Catalysts

Main article: Catalysis

Example of an enzyme-catalysed exothermic reaction

The relationship between activation energy (${\displaystyle E_{\textrm {a}}}$) 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. ^[9] 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. ^[10] 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. ^[11]

Relationship with Gibbs energy of activation

Main article: Transition state theory

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 k = A exp(−E_a/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 = (k_BT / 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 E_a, 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, 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 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 E_a = ΔH^‡ + RT and A = (k_BT/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 E_a 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, E_a, 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^‡H^o, Δ^‡S^o and Δ^‡G^o respectively, where the o indicates a quantity evaluated between standard states. ^{[12] [13]} However, some authors omit the o in order to simplify the notation. ^{[14] [15]}

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 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 that decreases with increasing temperature. Such a situation no longer leads itself to direct interpretations as the height of a potential barrier. ^[16]

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. ^{[17] [18] [19]}

An example is the oxidation of nitric oxide which is a termolecular reaction ${\displaystyle {\ce {2 NO + O2 -> 2 NO2}}}$. The rate law is ${\displaystyle v=k\,\left[{\rm {NO}}\right]^{2}\,\left[{\rm {O_{2}}}\right]}$ with a negative activation energy. ^{[20] [21]} This is explained by the two-step mechanism: ${\displaystyle {\ce {2 NO <=> N2O2}}}$ and ${\displaystyle {\ce {N2O2 + O2 -> 2 NO2}}}$.

Certain cationic polymerization reactions have negative activation energies so that the rate decreases with temperature. For chain-growth polymerization, the overall activation energy is ${\displaystyle \textstyle E=E_{i}+E_{p}-E_{t}}$, 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. ^[22]

Activation energy in a 2D potential energy surface

These are PES profiles for the reaction of hydrogen gas and tungsten. The reaction profile in the left shows a 2 dimensional pathway of the procedure. On the right side it is shown a 1 dimension perspective of the same trajectory.

Activation energy can be represented in 2D potential energy surfaces (PES), where the relation between the geometry of the reactants and the energy involved is represented as a topographic map.

In the following graphic there is a representation of a reaction between hydrogen in the gas phase and a metal: tungsten. The potential energy is obtained with PES calculations and consistent with the position of H from the NEB method calculations. A 2-dimensional interpolation with the spline method can be used to evaluate the potential energy at these positions. ^[23] Products and reactants can be found in the blue surface, however the red surface corresponds to the steady-state approximation.

The depics^{[ definition needed ]} correspond to the trajectories. The bluer the surface, the stronger the hydrogen bonds, so blue colors represent minima energy and red colors are maxima. Tungsten’s PES is symmetric, and has a dip at the bridge site, this dip corresponds to the change of color in the center of the depic.

The bluer the surface between the energy minima, the lower the energy barriers, and therefore the more easily hydrogen travels along the surfaces.

See also

• Activation energy asymptotics
• Chemical kinetics
• Fire point
• Mean kinetic temperature
• Quantum tunnelling
• Hydrogen safety
• Dust explosion
• Spark plug

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. Retrieved 15 October 2021.
5. Pratt, Thomas H. "Electrostatic Ignitions of Fires and Explosions" Wiley-AIChE (July 15, 1997) Center for Chemical Process Safety
6. 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.
7. 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.
8. 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.
9. "General Chemistry Online: FAQ: Chemical change: What are some examples of reactions that involve catalysts?". antoine.frostburg.edu. Retrieved 2017-01-13.
10. Bui, Matthew. "The Arrhenius Law: Activation Energies". Chemistry LibreTexts. UC Davis. Retrieved February 17, 2017.
11. Berg, Jeremy (2019). Biochemistry - Ninth Edition. New York, NY: WH Freeman and Company. pp. 240–244. ISBN   978-1-319-11467-1.
12. "Enthalpy of activation". IUPAC Gold Book (2nd edition, on-line version). IUPAC (International Union of Pure and Applied Chemistry). 2019. Retrieved 10 May 2020.
13. 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.
14. 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.
15. Laidler, Keith J.; Meiser, John H. (1982). Physical Chemistry. Benjamin/Cummings. p. 381. ISBN   0-8053-5682-7.
16. 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.
17. Espenson, James H. (1981). Chemical kinetics and reaction mechanisms. McGraw-Hill. p. 121. ISBN   0-07-019667-2.
18. Atkins, Peter; de Paula, Julio (2006). Atkins' Physical Chemistry (8th ed.). W. H. Freeman. p. 822. ISBN   0-7167-8759-8.
19. 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
20. Moore, John W.; Pearson, Ralph G. (1981). Kinetics and mechanism (3rd ed.). John Wiley and Sons. p. 316. ISBN   0-471-03558-0.
21. Engel, Thomas; Reid, Philip (2006). Physical Chemistry. Pearson. Benjamin-Cummings. p. *34. ISBN   0-8053-3842-X.
22. 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.
23. Kristinsdóttir, Lilja; Skúlason, Egill (2012-09-01). "A systematic DFT study of hydrogen diffusion on transition metal surfaces". Surface Science. 606 (17): 1400–1404. doi:10.1016/j.susc.2012.04.028. ISSN   0039-6028.