Kinetics and Thermodynamics: Relationship between activation energy, Ea, free energy change, dG and rate constant k

Definitions

What is activation energy Ea?

Activation energy is the minimum amount of energy required to start a chemical reaction.

What is free energy dG?

Free energy, also called as Gibbs free energy, is the amount of energy in a system that can be used to do work.

What is rate constant k??

A rate constant is a proportionality constant that shows the relationship between the rate of a chemical reaction and the concentration of reactants.

All above are related

Case 1

Relationship between Ea and K

The rate constant is related to temperature, activation energy, and frequency factor. Arrhenius equation, which relates rate constant (k) to temperature, activation energy (Ea), and the gas constant (R), is given by:k = A e^(-Ea/RT)

Where:

- k is the rate constant

- A is the frequency factor (or pre-exponential factor), which represents the frequency of collisions between reactant molecules

- Ea is the activation energy

- R is the gas constant

- T is the temperature in Kelvin

What does it mean?

This equation combines kinetics and thermodynamics because it incorporates the energy barrier (activation energy) that reactant molecules must overcome for a reaction to occur. As the temperature increases, the rate constant increases exponentially due to the temperature dependence of the exponential term in the Arrhenius equation. This reflects the fact that, at higher temperatures, the reactant molecules have more kinetic energy and are more likely to overcome the activation energy barrier.

Case 2

Relationship between k and dG

The rate constant (k) is related to the free energy change (ΔG) through the Arrhenius equation:

k = A e^(-ΔG/RT)

where:

- k is the rate constant,

- A is the pre-exponential factor,

- e is the base of the natural logarithm,

- ΔG is the free energy change,

- R is the gas constant,

- T is the temperature.

What does it mean?

This equation shows that the rate constant is inversely related to the free energy change. As the free energy change increases, the rate constant decreases and vice versa. In general, reactions with a lower free energy change will have a higher rate constant, indicating that they will occur more quickly.

Case 3

Relationship between Ea and dG

The activation energy (Ea) and the free energy change (ΔG) are related through the Eyring equation, which describes the rate of a chemical reaction

:k = (kB T/h) e^(-ΔG?/RT)

where:

- k is the rate constant,

- kB is the Boltzmann constant,

- T is the temperature

,- h is the Planck constant,

- ΔG? is the Gibbs free energy of activation,

- R is the gas constant.

From the Eyring equation, we can see that the activation energy (Ea) is related to the Gibbs free energy of activation (ΔG?) as Ea = ΔG? + RT

What does it mean? This relationship shows that the activation energy is directly related to the Gibbs free energy of activation.