Reaction Rate Arrhenius

Arrhenius equation: temperature dependence of rate constants

The Arrhenius equation k = A·e^(−Ea/RT) ties the rate constant k of a reaction to the absolute temperature T in kelvin. A is the pre-exponential factor, which folds in collision frequency and orientation; Ea is the activation energy in J/mol; and R = 8.314 J/(mol·K). Svante Arrhenius put it forward in 1889 and won the Nobel Prize in Chemistry in 1903 for the broader work. It explains the old bench rule that a 10°C rise roughly doubles the reaction rate. Work an example: with A = 1×10¹⁰, Ea = 50,000 J/mol, and T = 298.15 K, you get k ≈ 1.96×10¹⁰·e^(−20.17) ≈ 19. Take the natural log of both sides and it becomes ln k = ln A − Ea/(RT), a straight line when you plot ln k against 1/T. Read Ea off its slope.

Applications and context

It shows up in chemical kinetics, in food shelf-life prediction through the Q10 coefficient, in pharmaceutical stability testing under ICH Q1A accelerated aging, in industrial chemistry for reactor design, and in work on battery degradation and polymer cure rates. Open almost any catalysis paper and you will find an Ea pulled from an Arrhenius plot.

FAQ

Why exponential? Only the molecules carrying energy above Ea can react, and the Maxwell–Boltzmann distribution puts that fraction at e^(−Ea/RT).

Does it always hold? Not quite. At very high T, or for reactions that proceed by tunneling, the straight ln k versus 1/T line bends. In those cases reach for the Eyring equation from transition-state theory.

How do I get Ea experimentally? Measure k at a handful of temperatures, plot ln k against 1/T, then multiply the slope by −R.