# What is activation energy?

The **activation energy** ( **E _{a}** ) is defined as the minimum energy necessary for a chemical reaction to take place. In other words, it is the energy barrier that must be overcome so that the reactants can be converted into products.

Activation energy can be seen in action in everyday life. Indeed, we all know that, when you open the gas stopcock in the kitchen, it does not burn immediately when it comes into contact with the air.

For the combustion reaction to begin, it is necessary to provide a spark or the fire of a lit match. This spark or this fire represents the activation energy of the combustion reaction.

**Why is activation energy required?**

To understand why reactions require minimal energy to occur, it is important to understand how they occur in the first place. In order for two atoms or molecules to react, they must first collide. In addition, they must do so in the proper orientation so that new chemical bonds can form and old ones can be broken.

For this reason, it is necessary that, in addition to a correct orientation, the molecules also travel with a certain speed or with a certain minimum kinetic energy that ensures that the collision is strong enough to counteract the repulsion of the electrons.

This minimum kinetic energy required at the microscopic level is what is translated into the activation energy of the reaction.

**How does it look on an energy diagram?**

An energy diagram is a graphical representation that shows how the energy of reactants varies as they are transformed into products. In these diagrams, like the one below, it is easy to see and interpret the activation energy.

In this graph the blue line shows the energy as the reaction progresses. Here it can be seen that, to become the products, the reactants must first cross a hill to reach the transition state. Otherwise, they will be returned to their initial state.

**Activation energy units**

Activation energy is an intensive quantity that is expressed in units of energy over mass or moles. Since there are different units of energy and different units of mass, the activation energy can be expressed in several different units. However, the most frequently used in chemistry are:

Which unit is used depends on the data from which it is calculated, or how it will be used in other calculations.

**Activation energy formula**

The activation energy is related to the reaction rate. In fact, the higher the activation energy, the lower the speed. This relationship is expressed mathematically by means of the Arrhenius equation, which relates the rate constant of a reaction with temperature.

In this equation, *k* is the rate constant of the reaction, E _{a} is the activation energy, R is the ideal gas constant, T is the absolute temperature, and A is called the Arrhenius pre-exponential factor, also called the factor. collision.

This equation can be rearranged to give:

If the value of A for the reaction is known, then the activation energy can be obtained by solving the above equation. However, this is not how the activation energy of a reaction is usually determined. Normally the rate constant is determined at two or more temperatures, which makes it unnecessary to know A.

**How is activation energy calculated?**

The activation energy is determined from the values of the rate constant at different temperatures. At least two values of *k* measured at different values of T are needed to be able to calculate the activation energy without the need to know A, which is usually the case.

Depending on how many values of *k* you have, you can calculate E _{a} in two ways:

**1. When you have ***k* at two temperatures

*k*at two temperatures

In these cases, it is easier to start from the first form of the Arrhenius equation. If call *k _{1}* to the rate constant at temperature

*T*and

_{1}*k*the rate constant at temperature

_{2}*T*, then we can write the Arrhenius equation twice:

_{2}Now, we can divide either of the two equations by the other to cancel A:

Then, taking natural logarithm on both sides and solving for E _{a} , we obtain:

**2. When you have ***k* at more than two temperatures

*k*at more than two temperatures

In cases where you have several determinations of the rate constant at various temperatures, it is preferable to find the activation energy graphically or by means of linear regression. This is based on the equation in logarithmic form, which is in the form of a line:

If we make a graph of ln (k) versus (1 / T), we will obtain a straight line that intersects the *y-* axis at ln (A) and whose slope is equal to – (E _{a} / R). From there the activation energy is obtained.

**Activation energies calculation examples**

**Example 1**

The rate constant of a first order reaction was determined at two different temperatures. At 298 K it had a value of 0.058 s ^{-1} , while at 350 K the value increased to 0.425 s ^{-1} . Determine the activation energy of this reaction in J / mol.

**Solution:**Since you have the constant at two temperatures, you can directly use the activation energy formula shown above. Since the energy is requested in units of J / mol, then we must use the gas constant in these units:

**Example 2**

The rate constant for a second order chemical reaction at different temperatures is measured. The values are presented in the following table. Determine the activation energy in kcal / mol.

**Solution:**As in this case there are several temperatures, it is preferable to determine the activation energy graphically. To do this, a graph of ln (k) vs 1 / T is made, which is presented below.

From the equation of the line shown in the graph, the slope is obtained, which is -6456.2. Since the slope (m) is equal to – E _{a} / R, then:

That is, the activation energy of this reaction is 12.83 kcal / mol.