# Activation Energy Calculator

Created by Gabriela Diaz
Last updated: Jul 21, 2022

The activation energy calculator allows you to determine the energy required for a given reaction to take place.

If you're wondering, does temperature affects a chemical reaction or how to find the activation energy? Then you might find the text below useful. In it, we include some key ideas for understanding activation energy. Keep reading to learn:

• What is activation energy?;
• How is temperature related to the speed of a reaction;
• How to calculate the activation energy;
• The activation energy equation; and
• The activation energy units.

## What is activation energy?

The activation energy $E_a$ is the minimal amount of energy necessary for a reaction to take place. Even in the case of reactions that release energy (those with negative Gibbs free energy change), such as combustion, a certain amount of energy is needed to initiate. This is why spontaneous combustion is not possible at room temperature (thankfully!).

But why is an initial energy required for a reaction to get going? Well, this is related to the reactants' molecular bonds. In order for the products of a reaction to appear, at least some of the bonds of the reactants must break and rearrange into the new bonds found in the products. This stage, where bonds break, is known as the transition state and is a high-demand energy state. The energy required to achieve the transition state is precisely the activation energy. The higher the activation energy is, the slower the reaction.

Temperature is highly related to the activation energy. As you might have noticed from everyday experience, at higher temperatures, it's easier to start a fire or for food to spoil, that's why food in the fridge helps it to last longer.

Typically, chemical reactions are faster at higher temperatures than at lower temperatures. — At higher temperatures, molecules move faster (kinetic energy rises), and the number of collisions between them increases, raising the probability of bonds breaking and rearranging.

## Activation energy equation — Arrhenius equation

Let's first look at the Arrhenius equation to better understand how to calculate the activation energy. This is a formula that describes how the rate of a reaction varies with temperature:

$\small k = A \cdot \text{exp}(-E_a \ / R \ T)$

By rearranging this equation from its exponential form to a logarithm form, it is possible to get an expression that allows calculating the activation energy. This is the activation energy equation:

$\small E_a = - R \ T \ \text{ln}(k/A)$

where:

• $E_a$ — Activation energy;
• $R$ — Gas constant, equal to 8.314 J/(K⋅mol)
• $T$ — Temperature of the surroundings, expressed in Kelvins;
• $k$ — Reaction rate coefficient. It is measured in 1/sec and dependent on temperature; and
• $A$ — Frequency factor (or pre-exponential factor), also expressed in 1/sec.

The most commonly used activation energy units are the joules per mol (J/mol).

As suggested above, not all the molecules that collide will result in bond breakage and reaction. The frequency factor $A$ (or pre-exponential factor) is related to this, as it describes how often two molecules collide. Although it's frequently depicted as not affected by temperature, it actually does since it is linked to molecular collisions, which are a function of temperature. This factor can be derived experimentally or numerically.

The reaction rate coefficient $k$ is a proportionality constant that relates the molar concentration of reactants to the rate of a chemical reaction. It can be obtained empirically with the molar concentrations of the reactants or calculated using the Arrhenius equation.

## How to use the activation energy calculator

Calculating the activation energy necessary for a chemical reaction is made simpler with the help of the activation energy calculator! Let's see how to find the activation energy using this tool:

1. Enter the temperature at which the reaction takes place.

2. In the row below, indicate the Rate coefficient (k).

3. Input the Frequency factor (A) (or pre-exponential factor). This coefficient does not vary with temperature and is constant for a reaction.

4. The calculator will display the Activation energy (Eₐ) associated with your reaction.

🙋 Remember, our tools can be used in any direction! This means that you could also use this calculator as the Arrhenius equation ($k = A \ \text{exp}(-E_a/R \ T)$) to find the rate constant $k$ or any other of the variables involved in the calculation.

Gabriela Diaz
Temperature (T)
°C
Rate coefficient (k)
1/
per s
Constant (A)
1/
per s
Activation energy (Eₐ)
kJ
/mol
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