What is the Difference Between Arrhenius and Eyring Equation?
🆚 Go to Comparative Table 🆚The Arrhenius and Eyring equations are both used to describe the rate of chemical reactions, but they differ in their approach and assumptions. The key differences between the two equations are:
- Empirical vs. Theoretical: The Arrhenius equation is an empirical equation, while the Eyring equation is based on transition state theory.
- Temperature Dependence: The Arrhenius equation relates the rate constant of a reaction to temperature, while the Eyring equation describes the temperature dependence of reaction rates in terms of activation enthalpy, activation entropy, and energy.
- Applicability: The Arrhenius equation can be applied only to gas-phase kinetics, while the Eyring equation is useful in the study of gas, condensed, and mixed-phase reactions that have no relevance to the collision model.
- Activation Energies: The Arrhenius equation involves the activation energy (Ea), which is the energy required for a reaction to occur, while the Eyring equation involves the activation enthalpy (ΔH‡) and activation entropy (ΔS‡).
In summary, the Arrhenius equation is an empirical relationship that describes the temperature dependence of reaction rates, while the Eyring equation is based on transition state theory and provides a more detailed understanding of the factors affecting reaction rates, including activation enthalpy and activation entropy.
Comparative Table: Arrhenius vs Eyring Equation
The Arrhenius and Eyring equations are both used to describe the temperature dependence of reaction rates. However, there are key differences between the two equations:
| Arrhenius Equation | Eyring Equation |
|---|---|
| Empirical equation | Based on transition state theory |
| Can be applied only to gas-phase kinetics | Useful in the study of gas, condensed, and mixed-phase reactions |
| Describes temperature dependence of reaction rates | Also describes temperature dependence of reaction rates, but provides a more accurate calculation of rate constants and insight into the enthalpy and entropy of activation |
| Simplified form: $$k = Ae^{\frac{-E_a}{RT}}$$ | Simplified form: $$\ln{\frac{k}{T}} = \frac{-\Delta H^\ddagger}{R}\frac{1}{T} + \ln{\frac{k_B}{h}} + \frac{\Delta S^\ddagger}{R}$$ |
| Used to model temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes | Useful in the transition state theory and activated-complex theory |
The Arrhenius equation is an empirical relationship that relates reaction rate constants (k) and temperature (T), with the Arrhenius constant (A) and activation energy (Ea) as parameters. In contrast, the Eyring equation is based on transition state theory and provides a more accurate calculation of rate constants, as well as insights into the enthalpy and entropy of activation.
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