# Activation energy

The activation energy , coined in 1889 by Svante Arrhenius , is an energetic barrier that the reaction partners have to overcome during a chemical reaction . In general, the lower the activation energy, the faster the reaction. A high activation energy inhibits reactions that would be expected for energetic reasons due to the firm binding of the end products, and thus prevents or delays the establishment of a (thermodynamic) chemical equilibrium . A mixture of methane and the oxygen in the air can exist almost unchanged under standard conditions (i.e. the reaction proceeds immeasurably slowly), although the combustion products carbon dioxide and water are much more stable thermodynamically. Exceptions to this are, for example, acid-base reactions .

The activation energy according to Arrhenius is an empirical quantity that can be determined by the high temperature dependence of the speed of many chemical reactions.

## Reaction kinetics

The relationship between activation energy ( E a ) and enthalpy of formationH ) with and without a catalyst using the example of an exothermic reaction . The energetically highest position represents the transition state. A catalyst reduces the energy required to reach the transition state.

In the conception of physical chemistry, a rearrangement of the atoms from the arrangement of the reactants into that of the products must take place in the course of a chemical reaction , with old bonds being broken and new bonds being made. The reactants go through an activated state for the conversion into their products, the so-called transition state (see figure on the right, curve maximum), the formation of which requires a certain energy (activation energy). The speed of a chemical reaction therefore (at constant temperature) does not depend on the energies of the reactants and products, but only on the energy difference between reactants and the transition state. The higher the temperature of the reaction system, the higher the probability that the reactants will provide the required activation energy, overcome the energy barrier and continue to react to form the product.

### Temperature dependence of the reaction rate

The relationship between the rate constant , the activation energy and the thermodynamic temperature can be described (neglecting the activation volume or at low pressures) in many cases by the Arrhenius equation with the pre-exponential frequency factor and the gas constant : ${\ displaystyle k}$${\ displaystyle E_ {A}}$ ${\ displaystyle T}$ ${\ displaystyle A}$ ${\ displaystyle R}$

${\ displaystyle k = A \ cdot \ mathrm {e} ^ {\ frac {-E _ {\ mathrm {A}}} {R \ cdot T}}}$

Taking the logarithm of the equation results in:

${\ displaystyle \ ln (k / A) = - {\ frac {E _ {\ mathrm {A}}} {R}} \ cdot {\ frac {1} {T}}}$

Since the pre-exponential factor is often sufficient regardless of the temperature, applies to the value of : ${\ displaystyle A}$${\ displaystyle \ {k \}}$${\ displaystyle k}$

${\ displaystyle \ ln \ {k \} = - {\ frac {E _ {\ mathrm {A}}} {R}} \ cdot {\ frac {1} {T}} + \ mathrm {const.}}$

If the determination of the rate constants of irreversible reactions at different temperatures is successful, it can be plotted against and determined from the slope of the straight line; see Arrhenius graph . ${\ displaystyle \ ln \ {k \}}$${\ displaystyle 1 / T}$${\ displaystyle E_ {A}}$

If two rate constants ( and ) of a reaction at two temperatures ( and ) are known, one can use ${\ displaystyle k_ {1}}$${\ displaystyle k_ {2}}$${\ displaystyle T_ {1}}$${\ displaystyle T_ {2}}$

${\ displaystyle E _ {\ mathrm {A}} = {\ frac {R \ cdot T_ {1} \ cdot T_ {2}} {T_ {1} -T_ {2}}} \ ln {\ frac {k_ { 1}} {k_ {2}}}}$

calculate the activation energy. The equation is a transformed difference between two logarithmized Arrhenius equations (one per temperature). In many reactions in solution, the activation energy is in the range of 50 kJ · mol −1 . A temperature increase from 290  K to 300 K almost doubles the rate constant (see RGT rule ). It should always be noted, however, that with increasing activation energy (i.e. with increasing slope in the Arrhenius graph ) the effect of the temperature dependence is increased. Reactions with low activation energies (approx. 10 kJ · mol −1 ) are only slightly accelerated by increasing the temperature. The rate of reactions with large activation energies (approx. 60 kJ · mol −1 ), however, increases sharply with increasing temperature. The values ​​for the molar activation energies of many common reactions are between 30 and 100 kJ mol −1 .

In some reactions the temperature dependence of the rate constant does not follow the Arrhenius equation. These are, for example, reactions without activation energy, explosive reactions, reactions with upstream equilibria and many enzymatic or heterocatalytic reactions.

### Theoretical background

In fact, Arrhenius' model does not fully describe the processes involved in a chemical reaction. The Arrhenius equation can be theoretically justified by the classical impact theory . The high effect of a temperature increase on the speed of a reaction is based on the strong increase in the proportion of particles that have enough energy to overcome the barrier. In addition, the frequency of the collisions (the number of collisions) of the reactants increases with an increase in temperature. In practice, however, the increase in the number of collisions leads to a very small increase in the reaction speed and is lost as a component in the “temperature-independent” pre-exponential factor A in the Arrhenius equation . If the activation energy is small or zero, the impact number or the diffusion rate determine the reaction rate. According to Eyring (see also the theory of the transition state ), the free enthalpy of activation is the determining factor for the reaction rate. ${\ displaystyle \ Delta ^ {\ ddagger} G}$

### catalysis

A catalyst reduces the activation energy for chemical reactions, but does not change the free enthalpy of reaction . It is assumed that in the presence of a catalyst a complex with a lower activation energy is formed and thus the probability of a reaction increases. ${\ displaystyle \ Delta _ {\ mathrm {R}} G}$

## Individual evidence

1. Entry on activation energy (Arrhenius activation energy) . In: IUPAC Compendium of Chemical Terminology (the “Gold Book”) . doi : 10.1351 / goldbook.A00102 Version: 2.3.2 ..
2. Jacobus Henricus van't Hoff, Études de dynamique chimique , Frederik Muller & Co., Amsterdam 1884, pp. 114-118.
3. ^ Svante Arrhenius, Z. Phys. Chem. 1889, 4 , pp. 226-248.
4. Hans Rudolf Christen: Fundamentals of general and inorganic chemistry , Otto Salle, Frankfurt a. M., Sauerländer, Aarau, 9th edition, 1988, p. 333.
5. ^ Hans Kuhn, Horst-Dieter Försterling: Principles of Physical Chemistry , John Wiley, Chichester, 1999, p. 683.
6. ^ Georg Job, Regina Rüffler: Physikalische Chemie , Vieweg + Teubner Verlag, Wiesbaden, 1st edition 2011, pp. 401–402.
7. Gerd Wedler: Textbook of Physical Chemistry , VCH, Weinheim, 3rd edition, 1987, p. 169.

## Web links

Wiktionary: activation energy  - explanations of meanings, word origins, synonyms, translations