# Activation Energy Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Feb 14, 2023

This activation energy calculator (also called the Arrhenius equation calculator can help you calculate the minimum energy required for a chemical reaction to happen. For example, you may want to know what is the energy needed to light a match.

This article will provide you with the most important information — how to calculate the activation energy using the Arrhenius equation, as well as what is the definition and units of activation energy.

Make sure to also take a look at the kinetic energy calculator and potential energy calculator, too!

## What is the activation energy?

Activation energy is the energy required for a chemical reaction to occur. You can picture it as a threshold energy level; if you don't supply this amount of energy, the reaction will not take place.

Activation energy is required for many types of reactions, for example, for combustion. Every time you want to light a match, you need to supply energy (in this example, in the form of rubbing the match against the matchbox). That's why your matches don't combust spontaneously. This is the same principle that was valid in the times of the Stone Age — flint and steel were used to produce friction and hence sparks.

## Activation energy equation

You can find the activation energy for any reactant using the Arrhenius equation:

$E_\mathrm{a} = -R × T × \ln\biggl(\frac{k}{A}\biggr)$

where:

• $R$ — Gas constant. It is equal to $\mathrm{8.314\ J/(K\!\cdot\!mol)}$;
• $T$ — Temperature of the surroundings, expressed in Kelvins;
• $k$ — Reaction rate coefficient. It is measured in 1/sec and dependent on temperature;
• $A$ — Pre-exponential factor (also called the frequency factor), also expressed in 1/sec. This coefficient does not vary with temperature and is constant for a reaction; and
• $E_\mathrm{a}$ — Activation energy of the reaction.

## Activation energy units

The most commonly used units of activation energy are joules per mol (J/mol). You can convert them to SI units in the following way:

$1 \frac{\mathrm{J}}{\mathrm{mol}} = 1 \frac{\mathrm{kg} × \frac{\mathrm{m}^2}{\mathrm{s}^2}}{\mathrm{mol}} = 1 \frac{\mathrm{kg} × \mathrm{m}^2}{\mathrm{s}^2 × \mathrm{mol}}$

## How to calculate the activation energy

To calculate the activation energy:

1. Begin with measuring the temperature of the surroundings. We can assume you're at room temperature (25 °C).

2. Then, choose your reaction and write down the frequency factor. For example, for reaction 2ClNO → 2Cl + 2NO, the frequency factor is equal to A = 9.4×109 1/sec.

3. Choose the reaction rate coefficient for the given reaction and temperature. Let's assume it is equal to 2.8373×10-8 1/sec.

4. Input all these values into our activation energy calculator. It will find the activation energy — in this case, equal to 100 kJ/mol.

## FAQ

### Do enzymes lower activation energy?

Yes, enzymes generally reduce the activation energy and fasten the biochemical reactions. Enzymes are a special class of proteins whose active sites can bind substrate molecules. In this way, they reduce the energy required to bind and for the reaction to take place. The activities of enzymes depend on the temperature, ionic conditions, and pH of the surroundings.

### What is the activation energy of a reaction at 326°C?

1.60×10⁵ J/mol, assuming that you have H₂ + I₂ → 2HI reaction with rate coefficient k of 5.4×10⁻⁴ s⁻¹ and frequency factor A of 4.73×10¹⁰ s⁻¹. To calculate this:

1. Convert temperature in Celsius to Kelvin: 326°C + 273.2 K = 599.2 K.

2. Put data into Arrhenius equation:

Eₐ = -R×T×ln(k/A) = -8.314 J/(K×mol) × 599.2 K × ln(5.4×10⁻⁴ s⁻¹/4.73×10¹⁰ s⁻¹) = 1.60×10⁵ J/mol.

### What will be k coefficient if Eₐ is 50 kJ/mol at 345 K?

8.07×10⁻⁶ s⁻¹, assuming that pre-exponential factor A is 30 s⁻¹ at 345 K. To calculate this:

1. Transform Arrhenius equation to the form:

k = A × e(-Ea/RT)

2. Enter the data:

k = 30 × e(-50/(8.314×345)) = 8.07×10⁻⁶ s⁻¹

### How can I find activation energy from a graph?

To calculate the activation energy from a graph:

1. Draw ln k (reaction rate) against 1/T (inverse of temperature in Kelvin).

2. Find the slope of the line m knowing that m = -Eₐ/R, where Eₐ is the activation energy, and R is the ideal gas constant.

Or:

1. Make a plot of the energy of the reaction versus the reaction progress.

2. Find the energy difference between the transition state and the reactants.

### Can we have a negative activation energy?

Yes, although it is possible in some specific cases. When the reaction rate decreases with increasing temperature, this results in negative activation energy. Generally, activation energy is almost always positive.

Bogna Szyk
Temperature (T)
°C
Rate coefficient (k)
1/
sec
Constant (A)
1/
sec
Activation energy (Eₐ)
kJ
/mol
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