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Arrhenius Equation Calculator

Uses the two-point Arrhenius equation ln(k2/k1) = (Ea/R)(1/T1 − 1/T2) to find the rate constant at a second temperature and the rate ratio from the activation energy, or the activation energy from rate constants measured at two temperatures, plus the pre-exponential factor A.

When to use

You need how much faster a reaction runs at a different temperature, the rate constant at a new temperature, or the activation energy from two measured rate constants.

Do not use when: The rate constant is unknown at both temperatures and only Ea and A are known (compute k = A·exp(−Ea/RT) directly), or the reaction changes mechanism between the temperatures.

Formula

k = A × exp(−Ea / (R × T)); ln(k2 / k1) = (Ea / R) × (1/T1 − 1/T2) with R = 8.314462618 J/(mol·K) and T in kelvin; Ea = R × ln(k2 / k1) / (1/T1 − 1/T2); A = k1 × exp(Ea / (R × T1))

Assumes Ea and A are independent of temperature over the range considered, which holds well for intervals of a few tens of kelvin.

Inputs

ParameterTypeUnitRequiredDescription
activation_energy_kj_per_molnumberkJ/molnoActivation energy in kJ/mol. Leave empty to solve it from two rate constants. Range: > 0, ≤ 5000
temperature_1numberyesFirst temperature in temperature_unit.
temperature_2numberyesSecond temperature in temperature_unit.
temperature_unitenum: celsius | kelvindefault celsiusUnit of the temperature inputs; the calculation uses kelvin (K = °C + 273.15).
rate_constant_1numbernoRate constant at temperature_1 in any unit (s⁻¹, L/(mol·s)); k2 is returned in the same unit. Range: > 0
rate_constant_2numbernoRate constant at temperature_2 (same unit as k1); needed to solve Ea. Range: > 0

Outputs

OutputTypeUnitDescription
activation_energy_kj_per_molnumberkJ/molEa, given or solved.
activation_energy_j_per_molnumberJ/molEa in joules per mole.
rate_ratio_k2_over_k1numberexp((Ea/R)(1/T1 − 1/T2)): factor by which the rate changes from T1 to T2.
rate_constant_1numberRate constant at T1 (unit of the input).
rate_constant_2numberRate constant at T2 (unit of the input).
pre_exponential_factornumberA = k1 × exp(Ea / (R·T1)), same unit as k (only when k1 is known).
temperature_1_knumberKFirst temperature in kelvin.
temperature_2_knumberKSecond temperature in kelvin.
solved_forstringrate_constant_2, rate_constant_1, rate_ratio_k2_over_k1 or activation_energy_kj_per_mol.

Example

Ea 50 kJ/mol, k1 = 0.001 at 25 °C, k2 at 35 °C: {"activation_energy_kj_per_mol":50,"temperature_1":25,"temperature_2":35,"rate_constant_1":0.001} → {"rate_ratio_k2_over_k1":1.92426,"rate_constant_2":0.00192426,"pre_exponential_factor":574938,"temperature_1_k":298.15,"temperature_2_k":308.15,"solved_for":"rate_constant_2"}

Ea from k = 2.5e-3 at 20 °C and 1.0e-2 at 40 °C: {"temperature_1":20,"temperature_2":40,"rate_constant_1":0.0025,"rate_constant_2":0.01} → {"activation_energy_kj_per_mol":52.9056,"activation_energy_j_per_mol":52905.6,"rate_ratio_k2_over_k1":4,"solved_for":"activation_energy_kj_per_mol"}

GET https://tttkmbb.com/api/v1/calculate/arrhenius-equation?activation_energy_kj_per_mol=50&temperature_1=25&temperature_2=35&rate_constant_1=0.001

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FAQ

Does a reaction really double every 10 °C?

Only for Ea around 50 kJ/mol near room temperature (this example gives ×1.92). Reactions with larger Ea are more temperature-sensitive, smaller Ea less so.

Which unit does k need?

Any: only the ratio k2/k1 enters the equation, so the solved rate constant and A come out in the unit you used for k1.

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