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# Activation energy (Ea)

In chemistry, the minimum amount of energy needed to activate atoms or molecules to a condition in which a chemical transformation or physical transport can be generated is called activation energy , Ea . In transition state theory, activation energy is the difference in energy content between atoms or molecules in an active or transition state configuration and atoms or molecules in an initial configuration. Almost always, the state of a reaction occurs at a higher energy level than the reacting products (reactants). Therefore, the activation energy always has a positive value. This positive value occurs regardless of whether the reaction absorbs energy ( endergonic orendothermic ) or produces it ( exergonic or exothermic ).

Activation energy is shorthand for Ea. The most common units of Ea units are kilojoules per mole (kJ/mol) and kilocalories per mole (kcal/mol).

## The Arrhenius Ea Equation

Svante Arrhenius was a Swedish scientist who in 1889 demonstrated the existence of activation energy, developing the equation that bears his name. The Arrhenius equation describes the correlation between temperature and reaction rate. This relationship is essential to calculate the speed of chemical reactions and, above all, the amount of energy required for these reactions to take place.

In the Arrhenius equation, K is the reaction rate coefficient (the reaction rate), A is the factor of how often the molecules collide, and e is a constant (approximately equal to 2.718). On the other hand, Ea is the activation energy and R is the universal gas constant (energy units per temperature increase per mole). Finally, T represents the absolute temperature, measured in degrees Kelvin.

Thus, the Arrhenius equation is represented as k= Ae^(-Ea/RT). However, like many equations, it can be rearranged to calculate different values. However, it is not necessary to know the value of A to calculate the activation energy (Ea), since this can be determined from the variation of the reaction rate coefficients as a function of temperature.

### Chemical Significance of Ea

All molecules have a small amount of energy, which can be in the form of kinetic energy or potential energy. When molecules collide, their kinetic energy can disrupt and even destroy the bonds, which is what happens when chemical reactions take place.

If the molecules move slowly, that is, with little kinetic energy, either they do not collide with other molecules or the impacts do not generate any reaction because they are weak. The same happens if the molecules collide with the wrong or improper orientation. However, if the molecules are moving fast enough and in the right orientation, a successful collision will occur. Thus, the kinetic energy when colliding will be greater than the minimum energy, and after that collision a reaction will take place. Even exothermic reactions require a minimal amount of energy to get started. That minimum energy requirement, as we have explained before, is called activation energy.

Knowledge of data about the activation energy of substances implies the possibility of taking care of our environment. In other words, if we are aware that, depending on the characteristics of the molecules, a chemical reaction can be produced, we could not carry out actions that, for example, could cause a fire. For example, knowing that a book could catch fire if a candle is placed on top of it (whose flame would provide the activation energy), we will be careful that the candle flame does not spread to the paper of the book.

## Catalysts and Activation Energy

A catalyst increases the rate of reaction in a slightly different way than other methods used for the same purpose. The function of a catalyst is to lower the activation energy , so that a larger proportion of particles have enough energy to react. Catalysts can lower activation energy in two ways:

1. By orienting the reacting particles so that collisions are more likely to occur, or by changing the speed of their movements.
2. Reacting with the reactants to form an intermediate substance that requires less energy to form the product.

Some metals, such as platinum, copper, and iron, can act as catalysts in certain reactions. In our own body there are enzymes that are biological catalysts (biocatalysts) that help speed up biochemical reactions. Catalysts generally react with one or more of the reactants to form an intermediate, which then reacts to become the final product. Such an intermediate substance is often referred to as an “activated complex . “

#### Example of a reaction involving a catalyst

The following is a theoretical example of how a reaction involving a catalyst might proceed. A and B are reactants, C is the catalyst, and D is the product of the reaction between A and B.

First step (reaction 1): A+C → AC
Second step (reaction 2): B+AC → ACB
Third step (reaction 3): ACB → C+D

ACB stands for Chemical Intermediate. Although catalyst (C) is consumed in reaction 1, it is later released again in reaction 3, so the overall reaction with a catalyst is: A+B+C → D+C

From this it follows that the catalyst is released at the end of the reaction, completely unchanged. Without taking the catalyst into account, the overall reaction would be written: A+B → D

In this example, the catalyst has provided a set of reaction steps that we can call “alternative reaction pathway.” This pathway in which the catalyst intervenes requires less activation energy and is therefore faster and more efficient.

## The Arrhenius equation and the Eyring equation

Two equations can be used to describe how the rate of reactions increases with temperature. First, the Arrhenius equation describes the dependence of reaction rates on temperature. On the other hand, there is the Eyring equation, proposed by said researcher in 1935; His equation is based on transition state theory and is used to describe the relationship between reaction rate and temperature. The equation is:

k= ( kB T /h) exp(-ΔG ‡ /RT).

However, while the Arrhenius equation explains the dependence between temperature and reaction rate phenomenologically, the Eyring equation informs about the individual elementary steps of a reaction.

On the other hand, the Arrhenius equation can only be applied to the kinetic energy in the gas phase, while the Eyring equation is useful in the study of reactions both in the gas phase and in the condensed and mixed phases (phases that have no relevance in the gas phase). the collision model). Likewise, the Arrhenius equation is based on the empirical observation that the rate of reactions increases with temperature. Instead the Eyring equation is a theoretical construction based on the transition state model.

### Principles of the transition state theory:

• There is a thermodynamic equilibrium between the transition state and the state of the reactants at the top of the energy barrier.
• The chemical reaction rate is proportional to the concentration of the particles in the high energy transition state.

## Relationship between activation energy and Gibbs energy

Although the rate of reaction is also described in the Eyring equation, with this equation instead of using the activation energy, the Gibbs energy (ΔG ‡ ) of the transition state is included.

Since the kinetic energy of the colliding molecules (ie those with sufficient energy and proper orientation) is transformed into potential energy, the energetic state of the activated complex is characterized by a positive molar Gibbs energy. Gibbs energy, originally called “available energy,” was discovered in 1870 by Josiah Willard Gibbs. This energy is also called the standard free energy of activation .

The Gibbs free energy of a system at any moment is defined as the enthalpy of the system minus the product of the temperature times the entropy of the system:

G=H-TS.

H is the enthalpy, T is the temperature, and S is the entropy. This equation that defines the free energy of a system is capable of determining the relative importance of enthalpy and entropy as driving forces of a specific reaction. Now, the balance between the contributions of the enthalpy and entropy terms to the free energy of a reaction depends on the temperature at which the reaction takes place. The equation used to define free energy suggests that the entropy term will become more important as temperature increases : ΔG° = ΔH° – TΔS°.

### Sources

• Brainard, J. (2014). Activation energy. At https://www.ck12.org/
• Arrhenian law. (2020). Activation energies.
• Mitchell, N. (2018). Eyring Activation Energy Analysis of Acetic Anhydride Hydrolysis in Acetonitrile Cosolvent Systems.