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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 × $10^{-6} \ s^{-1}$