EQ-ARRHENIUS · Chemical Kinetics
Arrhenius Rate Law
-A*exp(-Ea/(R*T)) + k_rate = 0
Variables
variable
A
pre-exponential factor (frequency of reactive collisions)
- Object
- reaction_mixture
- Property
- Frequency
- Context
- quasi_equilibrium
- Constraint
- pre_exponential_factor
variable
Ea
activation energy of the reaction
- Object
- reaction_mixture
- Property
- ActivationEnergy
- Context
- quasi_equilibrium
variable
R
universal gas constant, 8.31446 J/(K·mol)
- Object
- abstract_quantity
- Property
- SpecificHeatCapacity
- Context
- quasi_equilibrium
- Constraint
- universal_gas_constant
variable
T
absolute temperature
- Object
- reaction_mixture
- Property
- ThermodynamicTemperature
- Context
- quasi_equilibrium
variable
k_rate
rate constant (first-order reaction; units vary by order)
- Object
- reaction_mixture
- Property
- ReactionRateConstant
- Context
- quasi_equilibrium
Axioms
algebraic classical constant_coefficients deterministic nonlinear thermal_equilibrium
Assumptions
- A and Ea are temperature-independent over the measurement range (often fails at very high or low T)
- Thermal equilibrium: the reactant energy distribution is Boltzmann
- A single elementary reaction or a composite with an effective Ea
- Ea is real and positive (endothermic barrier)
Derivation
- Empirical; Arrhenius, Z. Phys. Chem. 4 (1889), 226
- Derivable from transition-state theory: k = (k_B T / h) exp(-ΔG‡/RT), which gives Arrhenius form with A ≈ (k_B T / h) and Ea ≈ ΔH‡
- Boltzmann-factor origin: fraction of molecules with energy above Ea is exp(-Ea/RT) in a canonical ensemble
References
- Arrhenius, Z. Phys. Chem. 4 (1889), 226
- Atkins, Physical Chemistry, 11th ed., §19.7
- Eyring, J. Chem. Phys. 3 (1935), 107 (transition-state theory)