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Arrhenius Equation & Reaction Kinetics Calculator

Computes chemical reaction rate constants, activation energy (Ea), pre-exponential frequency factor (A), and temperature-dependent rate ratios using the Arrhenius equation with a dynamic Arrhenius plot SVG.

Arrhenius Equation & Reaction Kinetics Calculator

Compute reaction activation energy (Ea), rate constant temperature scaling, and Arrhenius plot slope

Rate Constant k₁ (s⁻¹)

Temperature T₁ (K)

Rate Constant k₂ (s⁻¹)

Temperature T₂ (K)

Activation Energy (Ea)

59.39 kJ/mol

Temperature Q₁₀ Factor: 2.16×

In Joules/mol:

59,386 J/mol

Log Ratio ln(k₂/k₁):

3.401

What is the Arrhenius Equation?

The Arrhenius equation describes the mathematical relationship between the rate constant (k) of a chemical reaction and absolute temperature (T).

It proves that reaction rates increase exponentially with temperature because a higher fraction of colliding molecules possess thermal energy exceeding the activation energy barrier (Ea).

Formula & Step-by-Step Calculation

k = A \cdot e^{-E_a / (R T)}, \quad \ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right)

Arrhenius exponential form and two-temperature linear logarithmic form with universal gas constant R = 8.314 J/(mol·K).

Worked Step-by-Step Examples

Example 1

Reaction has rate constant k1 = 0.0015 s⁻¹ at 300 K and k2 = 0.045 s⁻¹ at 350 K. Find Ea.

Solution: Ea = 59.86 kJ/mol

• ln(k2 / k1) = ln(0.045 / 0.0015) = ln(30) ≈ 3.4012

• 1/T1 - 1/T2 = (1/300) - (1/350) = 0.003333 - 0.002857 = 0.0004762 K⁻¹

• Ea = R × 3.4012 / 0.0004762 = 8.31446 × 7142.4 = 59,862 J/mol = 59.86 kJ/mol

Common Real-World & Academic Use Cases

✓ Chemical kinetics and reaction mechanism studies
✓ Pharmaceutical drug shelf-life accelerated stability testing
✓ Polymer degradation and thermal aging prediction
✓ Determining catalytic enzyme activation barriers

How to Use the Arrhenius Equation & Reaction Kinetics Calculator

Select Calculation Mode

Choose Two-Temperature Mode (solve Ea from k1, k2, T1, T2) or Single-State Mode (solve k from A, Ea, T).

Input Known Variables

Enter rate constants and temperatures in Celsius (°C) or Kelvin (K).

Inspect Results & Arrhenius Plot

View calculated activation energy, temperature coefficient, and dynamic SVG plot showing ln(k) vs 1/T slope.

Frequently Asked Questions

Q: What is the typical rule of thumb for reaction rates and temperature?

A common chemical rule of thumb states that for many reactions near room temperature, the reaction rate approximately doubles for every 10 °C increase in temperature (corresponding to an Ea around 50 kJ/mol).

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