All calculatorsArrhenius Equation Calculator
Compute rate constant k from A, Eₐ, T, or determine activation energy Eₐ from two rate measurements, or scale k with temperature. Clear steps and a responsive Arrhenius mini plot (ln k vs 1/T) included.
Background
The Arrhenius equation relates rate constants to temperature: k = A e^{-Eₐ/(RT)}. Taking natural logs gives a linear form: ln k = ln A − (Eₐ/R)(1/T). Two-temperature forms allow solving for Eₐ or a new k₂ given k₁.
How to use this calculator
- Pick a mode: Find k, find Eₐ, or find k₂.
- Temperatures must be in Kelvin. Eₐ is entered in kJ/mol; we convert to J/mol.
- Turn on sig-fig rounding for ~3 significant figures throughout.
Formula & Equation Used
Arrhenius (exponential): k = A e^{-Eₐ/(RT)}
Arrhenius (linearized): ln k = ln A − (Eₐ/R)(1/T)
Two-temperature (Eₐ): ln(k₂/k₁) = (Eₐ/R)(1/T₁ − 1/T₂)
Temperature scaling: k₂ = k₁ · exp( −Eₐ/R · (1/T₂ − 1/T₁) )
Example Problems & Step-by-Step Solutions
Example 1 — Find k
A=1.0×10¹², Eₐ=75 kJ/mol, T=298 K → k ≈ 0.0080 (units of A)
Example 2 — Find Eₐ
k₁=0.0200 at 290 K; k₂=0.0850 at 320 K → Eₐ ≈ 60 kJ/mol
Example 3 — Find k₂
k₁=1.00×10⁻³; Eₐ=75 kJ/mol; 298→320 K → k₂ ≈ 0.0080
Frequently Asked Questions
Q: Do k’s units matter?
For Eₐ from two rates, units cancel in ln(k₂/k₁). For k or k₂ predictions, keep units consistent with A and your rate law.
Q: Why Kelvin only?
Arrhenius uses absolute temperature. Using °C would give incorrect results.
Q: What if T₁ = T₂?
The two-temperature formula becomes undefined (division by zero). Use distinct temperatures or choose “Find k”.
