# How to calculate pre-exponential factor units

## Activation energy

### The activation energy - chemistry

You are probably familiar with the chemical reaction between sodium and water. This reaction is quick and emits light and heat. Under the same conditions (same pressure, same temperature), other substances do not react with one another, such as chlorine with hydrogen. This reaction does not take place because the particles involved lack the necessary energy, or more precisely that Activation energy.

### What is activation energy?

Activation Energy - Definition
In chemistry it is Activation energy than the necessary Minimum energy defined for a chemical reaction.

The energy diagram
In order to visualize the activation energy, we draw the energy curve of a chemical reaction in an energy-time diagram. The x-axis describes the Course of reaction, the y-axis is the energy of the reactants involved. Either Educts as well Products a chemical reaction have a certain energy. The position to one another differs in exothermic and endothermic reactions. If the starting materials have a higher energy than the products, the reaction takes place exothermic. Is the reaction endothermic, the products have a higher energy than the starting materials.

• \$ E_ {Edukte}> E_ {Products} \$: exothermic, energy is released
• \$ E_ {Edukte}

Regardless of whether a reaction is endothermic or exothermic, in most cases a mountain of energy has to be overcome. The difference from the top of the mountain to the energy of the educts is called the activation energy \$ Ea \$. The summit itself is called Transitional state or Saddle point designated. The structure, which corresponds to the saddle point, lies between the structures of the educts and the products. ### Relationship between activation energy and kinetics

Under kinetics one understands in chemistry the Teaching the speed of reaction. Activation energy and reaction speed are directly related to one another: the higher the activation energy, the lower the reaction speed.

Dependency of the activation energy
But how can one increase the reaction speed or lower the activation energy? You can temperature increase or also the concentration of the particles involved in the reaction. Both factors lead to the fact that the number of particles with sufficient activation energy increases and thus the probability of a "successful" collision of the particles is increased.

Catalysts and enzymes
Another option is to add a Catalyst, an accelerator of the reaction. The catalyst reduces the activation energy of a reaction by directing the reaction onto a new reaction path. You can imagine it to be like driving a car where your navigation system (catalytic converter) shows you a shorter route to your destination. Not only will you reach your goal faster, but you will also use less energy. In the case of a chemical reaction with a catalyst, the activation energy is also reduced compared to the old reaction path and the reaction becomes faster. In biology there is Biocatalysts, so-called Enzymeswhich reduce the activation energy. Enzymes are particularly selective catalysts that only catalyze a specific reaction.

### Relationship between kinetics and thermodynamics

After looking at the relationship between activation energy and kinetics, let's take a brief look at the relationship between kinetics and thermodynamics. In the following diagram you can see the activation energies \$ \ color {red} Ea \$, which are kinetic quantities, and thermodynamic quantities - the reaction energy \$ \ color {blue} \ Delta E \$. Note: Depending on the direction in which the reaction takes place, the reaction energy is positive or negative, i.e. energy is released or it has to be supplied:

\$ {\ color {blue} \ Delta E} _ {A \ rightarrow B} = - {\ color {blue} \ Delta E} _ {A \ leftarrow B} \$

The following relationship can be established between the thermodynamic and kinetic quantities:

\$ {\ color {red} Ea} _ {A \ rightarrow B} + {\ color {blue} ΔE} _ {A \ rightarrow B} = {\ color {red} Ea} _ {A \ leftarrow B} \$

Note: It is very important to pay attention to the signs in both the kinetics and the thermodynamics.

### Calculation of the activation energy

Now we have already learned a lot about activation energy. But how can you calculate the activation energy? In 1889 Svante Arrhenius developed the one named after him Arrhenius equation:

\$ k = A \ cdot e ^ {- \ frac {Ea} {R \ cdot T}} \$ (1)

The definition of the individual variables and their units are as follows:

• k - rate constant of the reaction
• Ea - activation energy [\$ \ frac {J} {mol} \$]
• T - absolute temperature [\$ K \$]
• R - universal gas constant [\$ \ frac {J} {mol \ cdot K} \$]
• A - pre-exponential factor, it is characteristic of each reaction

If you log the Arrhenius equation and then divide by \$ A \$, you get the following formula:

\$ ln (\ frac {k} {A}) = - \ frac {Ea} {R} \ cdot \ frac {1} {T} \$ (2)

Now you can change according to the activation energy \$ Ea \$:

\$ Ea = - \ frac {R} {T} \ cdot ln \ frac {k} {A} \$ (3a)

With this form of the equation, it is easy to see that the activation energy is temperature-dependent. The activation energy \$ Ea \$ can also be determined graphically. To do this, one converts the Arrhenius equation into the following linear form:

\$ \ underbrace {ln ~ k} _y = \ underbrace {- \ frac {Ea} {R}} _ m \ cdot \ underbrace {\ frac {1} {T}} _ x + \ underbrace {ln ~ A} _n \$ ( 3b)

From experimental measurements one obtains a certain rate constant \$ k \$ for a certain reaction at every temperature \$ T \$. These values ​​can be plotted graphically as \$ ln ~ k \$ against \$ \ frac {1} {T} \$.

The constant \$ A \$ can be derived from the interface with the y-axis (\$ n = ln ~ A \$). The activation energy \$ Ea \$ can be calculated from the increase \$ m \$.

\$ m = \ frac {\ Delta ln ~ k} {\ Delta \ frac {1} {T}} = - \ frac {Ea} {R} \$

### Significance of the activation energy:

Every reaction needs its activation energy! Let's look at a couple of examples:

• Gasoline and coal don't just react with the oxygen in the air and burn. You need activation. With gasoline, a burning match is enough, while coal needs burning wood.

• Let's look at another example: diamond and graphite, the two modifications of carbon. Did you know that graphite is energetically more stable than diamond? However, in order to convert a diamond into graphite, it needs extremely high temperatures to achieve the necessary activation energy.

• The activation energy is also of great importance in biology. In order for reactions, such as those of the vital respiratory chain, to take place, the activation energy must be reduced. This is done by means of enzymes. The reactions are also regulated by these enzymes. If the enzyme is present, the reaction takes place. If the enzyme is inhibited, no reaction takes place.

### This video

What is the activation energy? To the subject Activation energy To understand chemistry well, you should have prior knowledge too Reaction speed and chemical Have balance. The video uses an example to explain the effects of activation energy on chemical reactions.

You want your knowledge of Activation energy testing? A worksheet and exercises can be found on this page.