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Formulas

Activation Energy (Arrhenius Form)

Temperature dependence of rate constant.

Chemistry
Subject
Chemical Kinetics
Sub Subject
Temperature Dependence
Chapter
Arrhenius Equation
Topic

Activation Energy (Arrhenius Form)

📊 advanced
$$k = A e^{-E_a/(RT)}$$
Temperature dependence of rate constant.
Variables & Units
$k$
Rate constant
Unit: $\text{s}^{-1}$ (first order)
$A$
Frequency factor
Unit: $\text{s}^{-1}$
$E_a$
Activation energy
Unit: $\text{J/mol}$
$R$
Gas constant
Unit: $\text{J/(mol·K)}$
$T$
Absolute temperature
Unit: $\text{K}$
Key Information
📐 Derived From
Empirical, collision theory
💡 Example
Reaction with $E_a=50\,\text{kJ/mol}$, $A=10^{10}\,\text{s}^{-1}$, $T=298\,\text{K}$: $k = 10^{10} e^{-50000/(8.314\times298)} = 10^{10} e^{-20.18} \approx 10^{10} \times 1.7\times10^{-9} \approx 17\,\text{s}^{-1}$.
🔧 Applications
Reaction engineering, shelf-life prediction, catalysis
⚠️ Constraints
Valid over limited temperature range

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