The Arrhenius equation and the Eyring equation are fundamental tools used to calculate the rates of chemical reactions.

The Arrhenius equation determines the rate constant, denoted as $k$, of a chemical reaction at a specific temperature. It is expressed as:

where:

• $A$ is the frequency factor,
• $E_a$ represents the activation energy,
• $R$ is the universal gas constant, and
• $T$ is the absolute temperature measured in Kelvin.

This equation illustrates that the rate of a reaction tends to increase with rising temperature, as the exponential term becomes larger with higher $T$.

On the other hand, the Eyring equation refines the Arrhenius equation by incorporating the influence of entropy on the reaction rate. It is formulated as:

where:

• $k_B$ is the Boltzmann constant,
• $h$ is Planck’s constant,
• $\Delta G$ signifies the activation energy in terms of Gibbs free energy, and
• $T$ again represents the temperature in Kelvin.

The Eyring equation highlights that the reaction rate is influenced not only by activation energy but also by the entropy change during the reaction.

Both equations are crucial for understanding the various factors that affect the rates of chemical reactions. They can be utilized to predict how alterations in temperature, pressure, and other conditions will impact reaction rates, as well as to design experiments that can test these theoretical predictions.