Skip to main content
CalcStack

Arrhenius Equation Reaction Rate & Activation Energy Calculator

The Arrhenius equation describes the exponential temperature dependence of chemical reaction rate constants (k = A · e^(-Ea / RT)).

Minimum kinetic barrier needed for reactant molecules to react (typically 40–100 kJ/mol).

Frequency of molecular collisions with correct steric orientation (typically 10¹⁰ to 10¹³ s⁻¹).

Initial reaction operating temperature in Celsius.

Elevated temperature to determine rate acceleration factor.

Calculated Result
1.92×

Rate Acceleration Factor (k₂/k₁)

Rate Acceleration

1.92×

Rate Constant k₁

1.739e+2 s⁻¹

Rate Constant k₂

3.347e+2 s⁻¹

Activation Energy

50 kJ/mol

Temperature Shift

25°C → 35°C

Calculation Breakdown

  1. Arrhenius Reaction Rate Constant k₁k₁ = 1.739e+2 s⁻¹ @ 25°C (298.15 K)k1=Aexp⁡(−EaRT1),R=8.314×10−3 kJ/(mol⋅K)k_1 = A \exp\left(-\frac{E_a}{R T_1}\right), \quad R = 8.314 \times 10^{-3} \text{ kJ}/(\text{mol}\cdot\text{K})
  2. Arrhenius Reaction Rate Constant k₂k₂ = 3.347e+2 s⁻¹ @ 35°C (308.15 K)k2=Aexp⁡(−EaRT2)k_2 = A \exp\left(-\frac{E_a}{R T_2}\right)
  3. Rate Acceleration Factor1.92× faster (+92.4% speed increase)k2k1=exp⁡[EaR(1T1−1T2)]\frac{k_2}{k_1} = \exp\left[\frac{E_a}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)\right]

Reaction Rate Acceleration vs Temperature Rise (Ea = 50 kJ/mol from 25°C)

Interactive visualization based on your current inputs

Relative Speed
0.02.85.58.31125°C35°C45°C55°C65°CTemperature (°C)Relative Speed (Fold-Increase)

What Is the Arrhenius Equation Reaction Rate & Activation Energy Calculator?

The Arrhenius equation, formulated in 1889 by Swedish chemist Svante Arrhenius, is the fundamental equation of chemical reaction kinetics.

It links thermodynamic temperature to chemical reaction velocities across combustion, pharmaceuticals, material degradation, and shelf-life testing.

How Does the Arrhenius Equation Reaction Rate & Activation Energy Calculator Work?

Molecules must collide with sufficient energy to surpass the activation barrier.

The exponential Boltzmann factor exp(-Ea / RT) calculates the fraction of energetic collisions.

Multiplying by the frequency factor A gives the overall reaction rate constant k.

Arrhenius Equation Reaction Rate & Activation Energy Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

k=Aexp⁡(−EaRT)  ⟹  k2k1=exp⁡[EaR(1T1−1T2)]k = A \exp\left(-\frac{E_a}{R T}\right) \implies \frac{k_2}{k_1} = \exp\left[\frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)\right]

The Boltzmann exponential factor e^(-Ea / RT) gives the exact fraction of molecular collisions that possess energy exceeding the activation threshold.

How to Use the Arrhenius Equation Reaction Rate & Activation Energy Calculator

  1. Enter the activation energy barrier in kJ/mol.
  2. Supply base temperature T₁ and elevated temperature T₂ to evaluate speed acceleration.

Step-by-Step Example Calculation

10°C Reaction Temperature Jump

Input Values:

activationEnergy:50
frequencyFactor:100000000000
temp1:25
temp2:35
Worked Steps: With Ea = 50 kJ/mol, raising temperature from 25°C to 35°C accelerates the reaction rate constant by a factor of 1.92× (nearly doubling reaction velocity).

Understanding Your Result

Rate Constants (k₁ & k₂): Specific reaction rate coefficients at both temperatures.

Acceleration Factor (k₂/k₁): Fold-increase in reaction speed achieved by heating.

Factors That Affect the Result

  • Activation Energy: Higher Ea makes reaction speed dramatically more sensitive to temperature changes.
  • Temperature: Heating produces non-linear exponential acceleration.

When Should You Use This Calculator?

  • Pharmaceutical accelerated stability shelf-life testing (ASTM F1980).
  • Polymer thermal aging, combustion chemistry, and enzyme kinetics.

Assumptions & Limitations

  • Assumes activation energy and frequency factor remain constant over the temperature range.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard chemical kinetics formulation utilizing universal gas constant R = 8.314 J/(mol·K).

Related Calculators

Explore more tools and calculators in Education Calculators

Radioactive Half-Life & Decay Calculator

Calculate radioactive decay remaining quantity, decay constant (λ), mean lifetime, and percentage decayed over elapsed time.

Carnot Heat Engine Efficiency Calculator

Calculate the theoretical maximum thermodynamic Carnot efficiency, mechanical work output, and rejected waste heat for thermal engines.

Ideal Gas Law (PV = nRT) Calculator

Calculate pressure, volume, moles, or temperature of an ideal gas using the equation of state PV = nRT with unit conversions.

Chilled Water Cooling Coil Capacity & Flow Calculator

Calculates total cooling capacity (kW and Tons TR), sensible heat ratio (SHR), and required hydronic water flow rate (L/s and GPM) for AHU cooling coils.

Cooling Tower Evaporation & Blowdown Makeup Water Calculator

Calculates evaporative losses, chemical blowdown purge, drift rate, and total makeup water requirements based on cycles of concentration (CoC).

Heat Pipe Two-Phase Thermal Resistance & Conductivity Calculator

Calculates envelope radial wall conduction resistance, sintered wick resistance, total thermal impedance (°C/W), and effective thermal conductivity for copper-water heat pipes.