Arrhenius Equation Calculator
Calculate the rate constant (k) for a chemical reaction using the Arrhenius equation. Calculate activation energy from rate constants at different temperatures, or find what temperature gives your desired rate. Essential for chemical kinetics and reaction engineering.
Frequency factor in same units as k
Activation energy in kJ/mol
Temperature in Kelvin
Rate constant value
What is the Arrhenius equation?
The Arrhenius equation describes how temperature affects reaction rates: k = A × e^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor (frequency factor), Ea is activation energy (J/mol), R is the gas constant (8.314 J/mol·K), and T is temperature in Kelvin. Higher temperatures and lower activation energies give faster reactions.
What does the pre-exponential factor mean?
The pre-exponential factor (A) represents the collision frequency or the rate of molecular collisions in the transition state. It's the theoretical maximum rate if every collision led to reaction (Ea = 0). Values typically range from 10⁸ to 10¹⁵ s⁻¹, varying by reaction type: unimolecular: 10¹³-10¹⁵, bimolecular: 10⁸-10¹³.
How do I find activation energy experimentally?
Plot ln(k) vs 1/T: ln(k) = ln(A) - Ea/R × 1/T. The slope = -Ea/R. Measure reaction rate at several temperatures, get k values from first-order kinetics (integrated rate law), then linear regression. Slope gives Ea = -R × slope. This is the classic Arrhenius plot method.
Why do reactions speed up with temperature?
Two effects: (1) More collisions per second (higher A from higher kinetic energy), (2) MoreFraction with energy ≥ Ea. The exponential term is critical: fraction with enough energy = e^(-Ea/RT). At 298K with Ea=50kJ, e^(-50000/8.314/298) = e^(-20.2) = 1.7×10⁻⁹. Raise to 310K: e^(-50000/8.314/310) = e^(-19.4) = 3.7×10⁻⁹ (2× increase!).
What is a typical activation energy?
Ranges: Very fast (diffusion): under 40 kJ/mol. Fast (enzyme): 40-80 kJ/mol. Moderate: 80-120 kJ/mol. Slow (hydrolysis): 100-150 kJ/mol. Very slow (atmospheric): over 150 kJ/mol. Activation energy of zero would be instant; over 200 kJ/mol makes reactions seem not to occur at room temperature.
Can the Arrhenius equation predict half-life?
Yes, for first-order reactions: t½ = ln(2)/k. Using calculated k from Arrhenius, plug in. For Ea=50kJ, A=10¹³, at 298K: k = 10¹³ × e^(-50000/2477) = 10¹³ × e^(-20.2) = 10¹³ × 1.7×10⁻⁹ = 1.7×10⁴ s⁻¹. t½ = 0.693/1.7×10⁴ = 4×10⁻⁵ s = 0.04 ms. Very fast!