Arrhenius Equation Calculator

Calculate Rate Constant, Activation Energy, Frequency Factor, or Rate Constant at a Second Temperature

Select the calculation type and enter the required values. The Arrhenius Equation describes how reaction rates depend on temperature and activation energy.

Practical Examples

Explore real-world Arrhenius equation calculations:

Calculate Rate Constant (k)

Calculate Rate Constant (k)

Given Ea = 50 kJ/mol, A = 1e12 1/s, T = 298 K, calculate k.

Calculation Type: Calculate Rate Constant (k)

Activation Energy (Ea): 50 kJ/mol

Frequency Factor (A): 1000000000000

Temperature (T): 298 K

Rate Constant (k): undefined

Second Temperature (T₂): undefined undefined

Second Rate Constant (k₂): undefined

Calculate Activation Energy (Ea)

Calculate Activation Energy (Ea)

Given k = 2.5e5 1/s, A = 1e12 1/s, T = 350 K, calculate Ea.

Calculation Type: Calculate Activation Energy (Ea)

Activation Energy (Ea): undefined undefined

Frequency Factor (A): 1000000000000

Temperature (T): 350 K

Rate Constant (k): 250000

Second Temperature (T₂): undefined undefined

Second Rate Constant (k₂): undefined

Calculate Frequency Factor (A)

Calculate Frequency Factor (A)

Given k = 1.2e6 1/s, Ea = 60 kJ/mol, T = 400 K, calculate A.

Calculation Type: Calculate Frequency Factor (A)

Activation Energy (Ea): 60 kJ/mol

Frequency Factor (A): undefined

Temperature (T): 400 K

Rate Constant (k): 1200000

Second Temperature (T₂): undefined undefined

Second Rate Constant (k₂): undefined

Calculate Rate Constant at Second Temperature (k₂)

Calculate Rate Constant at Second Temperature (k₂)

Given k₁ = 2.5e5 1/s at T₁ = 298 K, Ea = 50 kJ/mol, T₂ = 350 K, calculate k₂.

Calculation Type: Calculate Rate Constant at Second Temperature (k₂)

Activation Energy (Ea): 50 kJ/mol

Frequency Factor (A): undefined

Temperature (T): 298 K

Rate Constant (k): 250000

Second Temperature (T₂): 350 K

Second Rate Constant (k₂): undefined

Other Titles
Understanding the Arrhenius Equation Calculator: A Comprehensive Guide
Master the science of reaction rates and temperature dependence with the Arrhenius Equation Calculator.

What is the Arrhenius Equation?

  • Fundamental Principles
  • Mathematical Formulation
  • Physical Meaning
The Arrhenius Equation is a fundamental formula in chemical kinetics that describes how the rate constant (k) of a reaction depends on temperature (T) and activation energy (Ea). It is widely used to predict how reaction rates change with temperature.
Arrhenius Equation Formula
k = A exp(-Ea / (R T)), where A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the absolute temperature in Kelvin.

Arrhenius Equation in Practice

  • If Ea = 50 kJ/mol, A = 1e12 1/s, and T = 298 K, then k can be calculated using the Arrhenius equation.
  • A higher activation energy means a slower reaction at a given temperature.

Step-by-Step Guide to Using the Calculator

  • Selecting Calculation Type
  • Entering Input Values
  • Interpreting Results
Choose which parameter you want to calculate: rate constant (k), activation energy (Ea), frequency factor (A), or rate constant at a second temperature (k₂). Enter the required values in the appropriate fields.
Input Fields and Units
Ensure all values are entered in the correct units. The calculator supports both kJ/mol and J/mol for activation energy, and Kelvin or Celsius for temperature.

How to Use the Calculator

  • To find k, enter Ea, A, and T.
  • To find Ea, enter k, A, and T.

Real-World Applications of the Arrhenius Equation

  • Industrial Chemistry
  • Laboratory Research
  • Environmental Science
The Arrhenius equation is used in various fields to predict reaction rates, optimize industrial processes, and understand environmental phenomena such as ozone depletion and combustion.
Practical Examples
Engineers use the Arrhenius equation to design reactors, while researchers use it to analyze experimental data and determine activation energies.

Applications in Science and Industry

  • Predicting shelf life of pharmaceuticals.
  • Modeling atmospheric reactions.

Common Misconceptions and Correct Methods

  • Misinterpreting Units
  • Incorrect Temperature Conversion
  • Assuming Linear Relationships
A common mistake is to use Celsius instead of Kelvin for temperature, or to mix units for activation energy. Always use consistent units and convert temperatures to Kelvin before calculation.
Avoiding Calculation Errors
The relationship between rate constant and temperature is exponential, not linear. Double-check all conversions and input values.

Tips for Accurate Calculations

  • Always convert °C to K by adding 273.15.
  • Ensure activation energy is in J/mol if using the default gas constant.

Mathematical Derivation and Examples

  • Derivation of the Arrhenius Equation
  • Graphical Representation
  • Worked Examples
The Arrhenius equation can be derived from collision theory and transition state theory. Plotting ln(k) versus 1/T yields a straight line with slope -Ea/R, which is useful for experimental determination of activation energy.
Arrhenius Plot
By measuring rate constants at different temperatures, you can plot ln(k) against 1/T to find the activation energy from the slope.

Mathematical Insights

  • Given k values at two temperatures, calculate Ea graphically.
  • Use the calculator to generate ln(k) and 1/T for plotting.