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# Arrhenius Equation Calculator + Online Solver With Free Steps

The **Arrhenius Equation Calculator** is used to compute the **frequency factor** of a chemical reaction. The user must know the rate constant, activation energy, and the temperature at which the reaction is taking place.

The Arrhenius Equation comes from the **collision theory** of molecules.

It states that for a chemical reaction to take place, the **molecules **must** collide** with each other and should have the correct **molecular orientation** for the reaction to proceed.

It is an important equation used in** chemical kinetics**. The user will find the calculator helpful when dealing with problems related to chemical reactions.

## What Is an Arrhenius Equation Calculator?

**The Arrhenius Equation Calculator is an online tool that calculates the frequency factor A of a chemical reaction when the values for the rate constant k, the activation energy $E_{a}$, and the temperature T is known.**

To understand the Arrhenius Equation Calculator, the user must know about the Arrhenius Equation itself.

The **Arrhenius Equation** is expressed as follows:

\[ k = A. exp \Big\{ \frac{ – E_{a} }{ RT } \Big\} \]

In this equation, the **exponential factor** represents the fraction of molecules that have sufficient energy to keep the reaction going.

R is the **energy constant** which is equal to 8.3145 J/mol.K.

In the Arrhenius equation, the **temperature** T is measured in Kelvin (K). The **activation energy** $E_{a}$ is measured in Joules per moles (J/mol).

The **frequency factor** **A** of a chemical reaction represents the total number of collisions per second that occurs in a reaction with the right orientation. It can be expressed as follows:

**A = Z.p **

Where Z is the **collision frequency**. The rate of the reaction increases when the collision frequency increases.

p is the **steric factor** that depends upon the nature of the reactants. The value of p ranges from** 0** to** 1** and shows the probability of two molecules colliding with the right orientation.

## How To Use the Arrhenius Equation Calculator?

You can use the **Arrhenius Equation Calculator** by inputting the rate constant, activation energy, and temperature of the given chemical equation. To calculate the frequency factor of a chemical reaction follow the steps mentioned below.

### Step 1

The user must first enter the rate constant k in the block against the title, “**input the equation’s rate constant (k)**”.

The **rate constant** k represents the total number of collisions per second Z having the proper molecular orientation p as well as sufficient energy needed to overcome the activation energy for the reaction to proceed.

### Step 2

Secondly, the user must enter the **activation energy** $E_{a}$ in the input block of the calculator titled “**input the equation’s activation energy**”.

The activation energy $E_{a}$ is the energy required to start a chemical reaction. The calculator takes the activation energy in kilo-Joules per mole (kJ/mol) by default.

### Step 3

The user must now enter the **temperature** at which the chemical takes place. It should be in Kelvin K. If the temperature is in degrees Celsius, the user must first convert it into Kelvins by adding 273 K to it.

This temperature is entered into the block against the title, “**input the kelvin temperature of experiment**”.

### Step 4

The user must enter the “**Submit**” button after entering the input values in the Arrhenius Equation Calculator.

### Output

The calculator processes the inputs of the Arrhenius equation and displays the output in the following windows.

#### Input Interpretation

The calculator interprets the input and the values of k, $E_{a}$, T, and R are placed into the **Arrhenius equation** and displayed in this window.

#### Result

In the Result window, the **exponential part** of the Arrhenius equation is solved by taking the natural logarithm ln on both sides of the equation.

#### Solution

The Solution window shows the final output **A** of the Arrhenius equation. **A** is the **frequency factor** of the chemical reaction and is measured per second ($s^{-1}$).

## Solved Examples

The following examples show the calculation of the frequency factor **A** through the Arrhenius Equation Calculator.

### Example 1

Calculate the **frequency factor** **A** for a chemical reaction taking place at a temperature of 10 K with the rate constant k as 2 $s^{-1}$. The activation energy required for the experiment is 5 kJ/mol.

### Solution

The user enters the rate constant k, activation energy $E_{a}$ and the temperature T in the Arrhenius equation as follows:

\[ k = 2 \ s^{-1} \]

**$E_{a}$ = 5 kJ/mol **

**T = 10 K **

Then, the user presses “**Submit**” for the calculator to process the input and displays the output window.

The **input interpretation** shows the Arrhenius equation with the input values placed in the equation as follows:

\[ 2 = A.exp \Big\{ \frac{4}{8.3145 \ × \ 10^{-3} \ × \ 10 } \Big\} \]

Where,

**R = 8.3145 J/mol.K **

Notice that the activation energy is converted from kJ/mol to J/mol by multiplying and dividing $10^{-3}$ in the exponential part of the Arrhenius equation.

The calculator **computes the exponential part** and displays the equation in the Result window as follows:

**2 = ( 7.82265 × $10^{20}$ )A **

The calculator **computes the frequency factor** A and shows it in the Solution window as follows:

**A = 2.55668 × $10^{-21} \ s^{-1}$ **

### Example 2

The rate constant k, activation energy $E_{a}$ and temperature T of a chemical reaction is given as follows:

\[ k = 10 \ s^{-1} \]

**$E_{a}$ = 25 kJ/mol **

**T = 200 K **

Calculate the **frequency factor** A for the chemical reaction.

### Solution

The **input** values of rate constant k, activation energy $E_{a}$, and temperature T are placed in the calculator’s input window. The “**Submit**” button is pressed and the calculator shows the output in three different windows.

The **input interpretation** window shows the Arrhenius equation as follows:

\[ 10 = A.exp \Big\{ \frac{25}{8.3145 \ × \ 10^{-3} \ × \ 200 } \Big\} \]

The calculator computes the exponential part by taking the natural log on both sides of the equation. The **Result **window shows the equation as follows:

**10 = (3.382 × $10^{6}$ )A **

The calculator computes for the frequency factor A and gives the **Solution** as follows:

**A = 2.85683 × $10^{-6} \ s^{-1}$**