Acids, equilibrium & kinetics · HL

Arrhenius Eₐ (HL)

Estimate activation energy from two rate constants.

Your values

Number formats & units

Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.

Arrhenius Activation Energy Calculator (HL) inputs

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Result & working

Example

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Formula & example

The relationship

ln⁡ ⁣(k2k1)=−EaR(1T2−1T1)\ln\!\left(\frac{k_2}{k_1}\right)=-\frac{E_{\mathrm a}}R\left(\frac1{T_2}-\frac1{T_1}\right)
k=Ae−Ea/(RT)k=Ae^{-E_{\mathrm a}/(RT)}
What the variables mean
SymbolMeaning
EAE_{A}Activation energy.
AAPre-exponential factor in the same units as k.

Worked example

Temperature T₁ / K
298.15
Rate constant k₁
0.0100
Temperature T₂ / K
318.15
Rate constant k₂
0.0300

43.32269 kJ mol⁻¹

Follow the example steps
  1. ln(k₂/k₁) = ln(0.03/0.01) = 1.098612
  2. 1/T₁ − 1/T₂ = 0.000210845
  3. Eₐ = R ln(k₂/k₁)/(1/T₁ − 1/T₂) = 43322.69 J mol⁻¹ = 43.32269 kJ mol⁻¹
  4. A = k₁e^(Eₐ/RT₁) = 388871.7

Common mistakes

Convert both temperatures to kelvin.

Incorrect approach

20 °C, 30 °C: 1/20 − 1/30

Correct approach

293.15 K, 303.15 K: 1/293.15 − 1/303.15

More checks before you submit
  • Temperature must be in K.
  • The units of A follow the units of k.
Method notes

This two-point form assumes an Arrhenius model over the temperature interval. A multi-point plot of ln k against 1/T is usually stronger evidence.