All calculatorsActivation Energy Calculator
Compute activation energy Eₐ from two rate constants and temperatures, or predict a new rate constant k₂ at temperature T₂ given Eₐ — using the Arrhenius equation k = A e^{-Eₐ/(RT)}. Toggle sig-fig rounding, see steps, and an optional Arrhenius plot.
Background
The Arrhenius equation relates reaction rate constant k to absolute temperature: ln k = ln A − Eₐ/(RT). For two conditions (k₁,T₁) and (k₂,T₂): ln(k₂/k₁) = (−Eₐ/R)(1/T₂ − 1/T₁) = (Eₐ/R)(1/T₁ − 1/T₂). If Eₐ is known, then k₂ = k₁ · exp[−Eₐ/R · (1/T₂ − 1/T₁)].
How to use this calculator
- Find Eₐ: enter k₁, k₂, T₁ (K), T₂ (K). We compute Eₐ (kJ/mol).
- Find k₂: enter k₁, Eₐ (kJ/mol), T₁ (K), T₂ (K). We compute k₂.
- Temperatures must be in Kelvin. Keep k-units consistent in a single calculation.
Formula & Equation Used
Arrhenius: k = A e−Eₐ/(RT), so ln k = ln A − Eₐ/(RT)
Two-point form: ln(k₂/k₁) = (Eₐ/R)(1/T₁ − 1/T₂)
Solve Eₐ: Eₐ = R · ln(k₂/k₁) / (1/T₁ − 1/T₂)
Solve k₂: k₂ = k₁ · exp[ −Eₐ/R · (1/T₂ − 1/T₁) ]
R: 8.314 J·mol⁻¹·K⁻¹ (we convert Eₐ between kJ/mol and J/mol as needed)
Example Problems & Step-by-Step Solutions
Example 1 — Find Eₐ
k₁=1.2×10⁻³ s⁻¹ at T₁=298 K; k₂=3.8×10⁻³ s⁻¹ at T₂=308 K.
Eₐ = R ln(k₂/k₁) / (1/T₁ − 1/T₂) ≈ 48 kJ/mol.
Example 2 — Find k₂
k₁=2.5×10⁻² s⁻¹ at T₁=300 K; Eₐ=55 kJ/mol; T₂=350 K.
k₂ = k₁ · exp[ −Eₐ/R · (1/T₂ − 1/T₁) ] ≈ 7.2×10⁻² s⁻¹.
Frequently Asked Questions
Q: Do the units of k matter?
Not when solving for Eₐ — they cancel in ln(k₂/k₁). When solving for k₂, keep units consistent across k and the rate law.
Q: Why Kelvin?
Arrhenius uses absolute temperature; Celsius would give incorrect results.
Q: What if T₁ = T₂?
Then the two-point formula is undefined. Change temperatures or switch modes.
