Eyring Equation

The Eyring equation relates a first-order rate constant to the Gibbs energy of activation in transition-state theory. The relation is useful for Interpret measured rate constants through activation free energy and transition-state theory.. At 298 K with ΔG‡=75.0 kJ/mol, k=(kBT/h)e^(−ΔG‡/RT)≈0.44 s⁻¹. Check: the activation exponential strongly reduces the 6.2×10¹² s⁻¹ prefactor. The final check tests a balance, direction or magnitude relevant to this formula. First map each quantity to the actual experiment, then substitute values. The result describes the modelled relationship; it does not automatically establish every mechanism in the real sample.

The symbols mean: k: first-order rate constant (s⁻¹); k_B: Boltzmann constant (J/K); T: absolute temperature (K); h: Planck constant (J·s); ΔG‡: Gibbs energy of activation (J/mol); R: universal gas constant (J·mol⁻¹·K⁻¹). Follow k in s⁻¹ · ΔG‡ in J/mol · kB in J/K · h in J·s · T in K · R in J·mol⁻¹·K⁻¹. Concentrations, activities, volumes and times must use compatible scales. A logarithm needs a dimensionless argument, and a balance must include all contributing species. State temperature and standard state whenever they are part of the definition; otherwise the result may refer to a different chemical condition. An amount is not a mass without molar mass, and activity is not an unnormalised concentration. Say whether inputs were measured or taken from a reference.

This form assumes a unimolecular first-order rate constant and transmission coefficient equal to one. A non-unit transmission coefficient scales the predicted rate. The activated-complex model and standard-state convention must fit the process. Check this assumption for the actual sample, temperature and phase. Nonideality, mass transport or side reactions can make a precise calculation systematically wrong. Compare the balanced reaction and the activity or concentration scale with the model, then state the assumption that most affects the result. Near model boundaries, check activities and phase state rather than extending a dilute-solution approximation. Different conditions require a fresh model check.

Recalculate the example: At 298 K with ΔG‡=75.0 kJ/mol, k=(kBT/h)e^(−ΔG‡/RT)≈0.44 s⁻¹. Check: the activation exponential strongly reduces the 6.2×10¹² s⁻¹ prefactor. Check k in s⁻¹ · ΔG‡ in J/mol · kB in J/K · h in J·s · T in K · R in J·mol⁻¹·K⁻¹ and substitute the value back into the relation. Also ask whether its sign, balance or magnitude is chemically plausible. If a check fails, inspect units, coefficients and reference values before blaming rounding. Substitution checks the algebra; comparing assumptions with the experiment checks whether the model is appropriate.

Eyring Equation is related to Arrhenius-Gleichung, Geschwindigkeitsgesetz (Reaktionsordnung), Gibbs-Energie (Freie Enthalpie), Steady-State Approximation for a Reaction Intermediate, but answers a distinct question: Interpret measured rate constants through activation free energy and transition-state theory.. Do not confuse it with a relation for a neighboring quantity or a different standard state. Name the target quantity and sample conditions first, then choose the equation containing that quantity. Similar-looking equations may use different stoichiometric bases or validity ranges. The linked entries may supply inputs for another step, but they do not replace this distinction. This keeps the interpretation auditable.