Activation Energy

Activation Energy Definition

Before we get into things, let's first look at the definition of our topic: activation energy.

The amount of energy required is dependent on whether a reaction is endothermic or exothermic

For endothermic reactions, you can think of activation energy like the electricity required to power a toaster. A toaster may require an outlet capable of 1200 Watts in the same way an endothermic reaction can require 100 Joules of energy to complete. The toaster doesn't release energy, just absorbs it.For an exothermic reaction, the reaction releases more energy than it requires (i.e. the activation energy).

Activation energy is the energy required to break bonds in reactants that prevent the reaction from taking place, some bonds are stronger than others, which is why it takes more energy to break them. This is why all reactions have an activation energy requirement! Forming bonds is what releases energy. If the bonds in the products are stronger than those in the reactants, there is a net release of heat (exothermic reaction). If these bonds are weaker, and therefore less stable, then the reaction is a net gain of heat (endothermic reaction).

Importance of Activation Energy

So, why is activation energy important in Chemistry? As discussed in the intro, activation energy is the hill that reactions have to climb to happen. It is very important to know how much energy will be needed, or else your reaction might never happen!

Take boiling water for an example again. If you put your stove at 90 °C, your water will never boil. If you were instead using a Bunsen burner to heat a flask with reactants, your reaction would similarly never happen. Knowing activation energy is critical to allow for reactions to even happen in the first place.

Activation Energy Formula

When we calculate activation energy, we use the Arrhenius equation:

There is another form of this equation that we use: $$ln(k)=\frac{-E_A}{RT}+ln(A)$$

Look familiar? Here's the equation of a line: $$y=mx+b$$

The formula is set up this way, so we can easily determine the activation energy. When the inverse temperature (1/T) is graphed as a function of ln(k), the slope (m) of the graph will be \(\frac{-E_A}{R}\), so we can easily solve for it.

Activation Energy Units

Lastly, let’s take a brief look at relevant units:

• Activation energy is generally measured in Joules per mole (J/mol)

• Temperature is measured in Kelvin (K)

• R is our gas constant, and there are several constants with different units. Because temperature is generally measured in Kelvin and activation energy is often measured in Joules/mol, typically we’ll use the gas constant of 8.314 \(\frac{J}{molK}\) which will cancel out our other units.

• k is the rate constant and its units depend on our order of the reaction. A zero-order reaction uses units of M/s, a first order-reaction uses units of 1/s, a second-order reaction uses units of 1/M*s, and so on. What units you use will depend on the reaction being looked at.

• The letter, A, in the Arrhenius equation is also a constant and will have units identical to the rate constant.

Activation Energy Graph

There are two types of graphs you'll typically see when discussing activation energy. The first is an energy diagram.

Here is an example of two below:

Energy diagrams for exothermic and endothermic reactions. StudySmarter Original

The activation energy is measured from the reactants to the graph's peak. If the activation energy is the "hill" we have to climb to get to the other side, then the energy diagram is your "energy path". The activation energy for an endothermic reaction (right) is much greater than for an exothermic reaction (left).

This is because the products are higher in energy than the reactants for an endothermic reaction, and systems always want to be at the lowest energy as possible. This is why energy/heat needs to be added to the system for endothermic reactions to occur.

The activation energy can be lowered if a catalyst is added.

A diagram for this phenomenon looks like this:

The top curve (in purple), shows the original reaction, while the bottom curve (in green), shows the reaction with a catalyst. As you can see, the catalyst greatly lowers the activation energy. It does this by giving the reaction a different pathway to follow. It is similar to taking a different route to get to your destination faster.The second type of graph is the plot of 1/T versus ln(k). Here is some example data:

Graph of the Arrhenius equation. StudySmarter Original.

As we saw before, the slope of this graph is equal to \(\frac{-E_A}{R}\), so we can easily calculate the activation energy from this data:

We can also calculate activation energy using two data points. Here's how we would do that: