Arrhenius Equation Calculator

Q: 3 How do you calculate Activation Energy Ea using Two Rate Constants (k1, k2) and Temperatures (T1, T2)?

Using two-point form of the Arrhenius equation , it can be calculated.

In reaction kinetics, the Arrhenius equation is commonly used to explain how temperature influences reaction rates. To make these calculations easier, we’ve built this Arrhenius Equation Calculator. It allows you to determine the rate constant (k), activation energy (Ea), or the pre-exponential factor (A).

Apart from this, we have posted various chemical engineering calculation tools that will help you with quick and reliable results.

Rate constant (k)

Pre-exponential factor (A)

Activation energy (Eₐ)

Temperature (T)

Result

How to use the Arrhenius Equation calculator?

Choose the mode as calculator can calculate k, Ea, or A.
Enter numerical values and select the unit. eg. 2.7 and select x10¹¹
Enter the temperature value and select °C or °F. The calculator converts the temperature to Kelvin automatically.
Make sure the units of A match the reaction order you are working with, because the final units of k depend on it.

If you need help with the units, then you can use our Unit Converter tool for chemical engineers. (Free PDF included)

What is the Arrhenius Equation

The Arrhenius equation explains how temperature affects the rate of a chemical reaction. As the temperature rises, more molecules have enough energy to cross the activation energy barrier, which increases the reaction rate.

$k = A\, e^{-E_a/(RT)}$

k = rate constant
A = pre-exponential factor
Ea = activation energy
R = 8.314 J·mol⁻¹·K⁻¹
T = temperature in Kelvin

Example

At 500 °C, a reaction has a pre-exponential factor A=2.5×10¹¹ M⁻¹s⁻¹ and activation energy of 185 kJ/mol. Calculate the rate constant k at this temperature. R = 8.314 J·mol⁻¹·K⁻¹

Temperature: 500 °C →T= 500+273.15 =773.15 K

Activation energy:
185 kJ/mol →Ea=185×1000=185000 J/mol

Arrhenius Equation

$k = A\, e^{-E_a/(RT)}$

$-\frac{E_a}{RT} = -\frac{185000}{8.314 \times 773.15}\approx -28.7805$

k = 2.5×10¹¹×e^−28.7805 ≈ 7.920×10⁻² M⁻¹s⁻¹

Example : Calculate Activation Energy Using the Two-Point Arrhenius Equation

The rate constant of a reaction is k₁=0.015 s⁻¹ at T₁=300k. At a higher temperature of T₂=330 K, the rate constant increases to k₂=0.065 s⁻. Calculate the activation energy Ea of the reaction in kJ/mol. Take the gas constant R=8.314 J mol⁻¹K⁻¹

$\ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)$

$\ln\left(\frac{0.065}{0.015}\right)=\frac{E_a}{8.314}\left(\frac{1}{300}-\frac{1}{330}\right)$

$\ln(4.333)\approx 1.466$

$\frac{1}{300}-\frac{1}{330}=0.000303$

Calculate Activation Energy

$E_a=\frac{1.466\times 8.314}{0.000303}\approx 4.02\times 10^4\ \text{J/mol}$

$E_a\approx 40.2\ \text{kJ/mol}$

FAQ

1. What is the Arrhenius constant?

The Arrhenius constant, also called the pre-exponential factor (A), indicates how often reacting molecules collide with the right orientation to form products. It represents the maximum possible rate of a reaction before considering the activation energy barrier.

2. What is the value of r in the Arrhenius constant?

The value of R (the gas constant) is 8.314 J·mol⁻¹·K⁻¹. This is the standard value used when activation energy is expressed in joules per mole and temperature is in Kelvin.

3 How do you calculate Activation Energy Ea using Two Rate Constants (k₁, k₂) and Temperatures (T₁, T₂)?

Using two-point form of the Arrhenius equation, it can be calculated.

Arrhenius Equation Calculator