Difference Between Arrhenius and Eyring Equation

The key difference between Arrhenius and Eyring equation is that Arrhenius equation is an empirical equation whereas Eyring equation is based on the statistical mechanical justification.

Arrhenius equation and Eyring equation are two important equations in physical chemistry. When we are assuming a constant enthalpy of activation and constant entropy of activation, the Eyring equation is similar to the empirical Arrhenius equation.

1. Overview and Key Difference
2. What is Arrhenius Equation
3. What is Eyring Equation
4. Side by Side Comparison – Arrhenius vs Eyring Equation in Tabular Form
5. Summary

What is Arrhenius Equation?

Arrhenius equation is a chemical formula that involves the temperature dependence of reaction rates. This equation was proposed and developed by the scientist Svante Arrhenius in 1889. The Arrhenius equation has many applications in determining the rate of chemical reactions and in the calculation of the energy of activation. In this context, the Arrhenius equation provides a physical justification and interpretation for the formula. Therefore, we can identify it as an empirical relationship. The Arrhenius equation is expressed as follows:

K = Ae^(Ea/RT)

Where k is the rate constant for the reaction mixture, T is the absolute temperature of the system in Kelvins, A is the pre-exponential factor for the chemical reaction, Ea is the activation energy for the reaction and R is the universal gas constant. In this equation, when considering the units of the pre-exponential factor, A, it is identical to the units of the rate constant that will depend on the order of the reaction. E.g. if the reaction is first order, then the units of A is per second (s^-1). In other words, in this reaction, A is the number of collisions per second that occurs in the proper orientation. Moreover, this relationship describes that either increasing the temperature or decreasing the activation energy will result in the increasing of the rate of reaction.

Difference Between Arrhenius and Eyring Equation

Figure 01: Different Derivatives of Arrhenius Equation

What Eyring Equation?

Eyring equation is an equation that describes the changes in the rate of a chemical reaction against the temperature of the reaction mixture. This equation was developed by Henry Eyring in 1935 along with two other scientists. Eyring equation is similar to Arrhenius equation when a constant enthalpy of activation and a constant entropy of activation are considered. The general formula for the Eyring equation is as follows:

Here ΔG‡ is the Gibbs energy of activation, κ is the transmission coefficient, kB is Boltzmann’s constant, and h is Planck’s constant.

What is the Difference Between Arrhenius and Eyring Equation?

Arrhenius and Eyring equation are important equations in physical chemistry. The key difference between Arrhenius and Eyring equation is that Arrhenius equation is an empirical equation whereas Eyring equation is based on the statistical mechanical justification. Moreover, Arrhenius equation is used to model the temperature variation of diffusion coefficients, the population of crystal vacancies, creep rates, and many other thermally-induced processes, while Eyring equation is useful in the transition state theory and there, it is known as activated-complex theory.

Below infographic tabulates the differences between Arrhenius and Eyring equation for side-by-side comparison.

Summary – Arrhenius vs Eyring Equation

Arrhenius and Eyring equation are important equations in physical chemistry. The key difference between Arrhenius and Eyring equation is that Arrhenius equation is an empirical equation whereas Eyring equation is based on the statistical mechanical justification. Arrhenius equation is used to model the temperature variation of diffusion coefficients, the population of crystal vacancies, creep rates, and many other thermally-induced processes. Eyring equation, on the other hand, is useful in the transition state theory, and there, it is known as activated-complex theory.

Reference:

1. “6.2.3.1: Arrhenius Equation.” Chemistry LibreTexts, Libretexts, 11 Sept. 2020, Available here.
2. “Eyring Equation.” Wikipedia, Wikimedia Foundation, 16 Oct. 2020, Available here.