# Arrhenius Equation Calculator

Created by Davide Borchia
Last updated: Jul 11, 2022

The Arrhenius equation tells us how our reaction will change with the temperature: with our Arrhenius equation calculator, you will learn how to quantify this change; leave the math to us, and keep reading to understand this fundamental concept of chemistry.

• What is the Arrhenius equation?
• How do I calculate the Arrhenius equation;
• What is the Arrhenius constant; or
• How to calculate the pre-exponential factor;

You are in the right place!

## What are reaction rates?

During a chemical reaction, the concentrations of the chemical species there involved vary: depending on the direction of the reaction, the products or reactants may get more or less concentrated.

This variation is defined by the reaction rates. Apart from depending on the concentration and the stoichiometric coefficient, these quantities vary according to other physical parameters*.

The Arrhenius equation quantifies the dependence on the temperature. Let's see what the Arrhenius equation is.

## What is the Arrhenius equation?

The Arrhenius equation, from a chemical point of view, is:

$k = A\cdot e^{\frac{-E_{\text{a}}}{R \cdot T}}$

We can identify many elements in the Arrhenius equation:

• $k$ is the rate constant, usually expressed in the units $\text{M}^{1-n}\text{s}$, where $n$ is the reaction order;
• $A$ is the pre-exponential factor or Arrhenius constant;
• $E_{\text{a}}$ is the activation energy of the reaction (with units $\text{kJ}/\text{mol}$);
• $T$ is the temperature (in $K$: if you need to convert from Celsius or Fahrenheit, use our temperature converter); and
• $R$ is the gas constant.

Let's check the argument of the exponential. The activation energy is a measure of the easiness with which a chemical reaction starts. The lower it is, the easier it is to jump-start the process. In the Arrhenius equation, we consider it to be a measure of the successful collisions between molecules, the ones resulting in a reaction. On the other hand, the temperature influences the energy of the molecules: the higher the temperature, the higher the number of collisions. The entire exponential measures the probability that a collision will result in a reaction.

The other factors affecting the outcome of a collision are modeled by the pre-exponential factor, $A$. The factor has the same units of the Arrhenius equation result, the reaction rate: $\text{M}^{1-n}\text{s}$. Notice how the higher the molarity, the faster the reaction: the chance of a collision is high!

## The Arrhenius equation: a different approach

The form of the Arrhenius equation we gave above is fitting for chemistry: in fact, the argument of the exponential is an energy per mole. Physicists often think in terms of energy per molecule: we can rearrange the Arrhenius equation to reflect this change:

$k = A\cdot e^{\frac{-E_{\text{a}}}{k_{\text{B}} \cdot T}}$

We introduced the Boltzmann's constant, $k_\text{B}$ Mind that the activation energy has now to be expressed in $\text{eV}$ per molecule. These changes don't affect the result of the Arrhenius equation, but it requires a small arrangement of the units in the Arrhenius equation.

## How to calculate the Arrhenius equation and the Arrhenius constant

To calculate the Arrhenius equation, we assumed all of the parameters appearing in the formula to be independent from the temperature. You can find their values in tables available in the literature. Once you know the values, you can plug them into our Arrhenius equation calculator. Remember to choose the correct units in the Arrhenius equation. At the top of our tool you can choose which form of the Arrhenius equation you need.

You can use our Arrhenius calculator in reverse: you can input the reaction rate to find the other parameters. How do you calculate the Arrhenius constant? It's pretty easy: divide the rate by the exponential.

## Visualizing the Arrhenius equation: plot of the reaction rates

The presence of an exponential in the Arrhenius equation makes for difficult plots: it's better to take the logarithm:

$\ln{k} = -\frac{E_{\text{a}}}{R}\cdot\frac{1}{T} +\ln{(A)}$

This equation is straightforward to plot on a graph with coordinates:

• $x \rightarrow \frac{1}{T}$: and
• $y\rightarrow \ln{(k)}$.

The result is a straight line, sloping downward as the temperature decreases (and the inverse of the temperature increases). You can visualize the plot by choosing yes in the field show Arrhenius plot.

🙋 We included the calculations of the reaction rate in logarithmic form in our Arrhenius equation calculator: in the first drop-down menu, choose either per mole (ln) or per molecule (ln).

Davide Borchia
Arrhenius equation form
per mole (exponential) Arrhenius constant, A
x10⁰
Activation energy, Eₐ
kJ
/mol
Temperature, T
°F
Rate constant, k
x10⁰
The units for the Arrhenius constant and the rate constant are the same, and depend on the rate of reaction. The units for corresponding orders are in the brackets: order zero (M * s-1), one (s-1), two (M-1 * s-1), ..., up to order n (M1-n * s-1).
Show Arrhenius plot?
No
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