Arrhenius vs Eyring Equation: Key Differences, When to Use Each
The Arrhenius Equation treats the activation energy as temperature-independent, focusing on how heat boosts the fraction of molecules that can react. The Eyring Equation, rooted in transition-state theory, treats activation as a thermodynamic step, adding an entropy term and letting the energy barrier itself change with temperature.
Pharma chemists see the mix-up all the time: the same data fit both plots, so “Arrhenius” becomes shorthand for any straight-line kinetics, even when solvent ordering (entropy) is clearly at play. Mislabeling slides at the FDA can cost months of review.
Key Differences
Arrhenius gives k = A·e^(–Ea/RT); Eyring gives k = (kBT/h)·e^(–ΔG‡/RT). The first hides mechanistic detail inside a single pre-exponential A, while the second splits it into ΔH‡ and ΔS‡, revealing if the rate is enthalpy- or entropy-driven.
Which One Should You Choose?
Use Arrhenius for quick stability assays where you just need shelf-life numbers. Switch to Eyring when catalyst design, solvent effects, or protein folding matter—any scenario where entropy changes dominate and you need physical insight, not just numbers.
Examples and Daily Life
Estimating vitamin C loss in orange juice at 40 °C? Arrhenius is fine. Predicting how an enzyme’s active-site water network speeds up a drug reaction? Eyring shows that tightening the network (lower ΔS‡) accelerates the rate even if ΔH‡ stays flat.
Can Arrhenius and Eyring parameters be converted?
Yes. Ea ≈ ΔH‡ + RT and A ≈ (kBT/h)·e^(1+ΔS‡/R), but only if the same reference temperature is used.
Do regulators prefer one equation?
FDA and ICH accept Arrhenius for stability, yet insist on Eyring when claiming mechanistic rationale or patenting catalyst improvements.