# Gibbs free energy of activation and activation energy

• Govind
In summary: I think it's ΔG‡ as defination of Gibbs free energy states - minimum amount of work needed to supply for a non spontaneous reaction (here A -> C ) to be happened but then why arrhenius theory states that - for reactants to transform into products, they must first acquire a minimum amount of energy, called the activation energy Ea ?And also what these two energies represent physically in terms of bonds , interatomic interactions etc ?
Govind
Let's consider a reaction A (reactant) -> B(product) and activated complex is denoted by C.

This graph ( potential energy vs reaction coordinate ) tells us that reactant need some amount of activation energy (Ea) to convert in product, which has low potential energy which is shown here in terms of enthalpy ∆H. We can assume from this graph that activation represent same kind of potential energy between A (reactant) and C (activated complex ) that Enthalpy ∆H represent between A and B (product).

Now look at another graph of reaction (Gibbs free energy vs extent of reaction)

This graph represents that activation energy is difference between Gibbs free energy of reactant and activated complex or there is also possibility that the activation energy shown here is not arrhenius activation energy Ea but it is Gibbs energy of activation ΔG‡ according to transition state theory.

Q. But to perform a reaction what amount of energy we need to supply to reactants arrhenius activation energy Ea or gibbs free energy of activation ΔG‡ ? I think it's ΔG‡ as defination of Gibbs free energy states - minimum amount of work needed to supply for a non spontaneous reaction (here A -> C ) to be happened but then why arrhenius theory states that - for reactants to transform into products, they must first acquire a minimum amount of energy, called the activation energy Ea ?

And also what these two energies represent physically in terms of bonds , interatomic interactions etc ?

Mathematical equations -

ΔG‡ = ∆H‡ - T∆S‡

ΔG‡ = Ea - RT - T∆S‡ ( ∆H‡ = Ea - RT )

Arrhenius activation energy is an empirical construct from regression of reaction speed vs inverse Temperature. The point is that Delta G is itself a function of T, so that changing the temperature will not only have an explicit effect via change of 1/T but also an effect due to the temperature dependence. Also the pre-factor in the Eyring equation is temperature dependent. All this dependence on temperature makes up for the difference between Delta G in the Eyring equation and E_A in the Arrhenius equation. A similar dependence of the equilibrium constant on inverse temperature is known as van't Hoff equation.

Lord Jestocost
@Lord Jestocost I was actually asking that to perform a reaction what amount of energy we need to supply to reactants arrhenius activation energy Ea or gibbs free energy of activation ΔG‡

DrDu said:
Arrhenius activation energy is an empirical construct from regression of reaction speed vs inverse Temperature. The point is that Delta G is itself a function of T, so that changing the temperature will not only have an explicit effect via change of 1/T but also an effect due to the temperature dependence. Also the pre-factor in the Eyring equation is temperature dependent. All this dependence on temperature makes up for the difference between Delta G in the Eyring equation and E_A in the Arrhenius equation. A similar dependence of the equilibrium constant on inverse temperature is known as van't Hoff equation.
I was actually asking that to perform a reaction what amount of energy we need to supply to reactants arrhenius activation energy Ea or gibbs free energy of activation ΔG‡

Reference: https://www.physicsforums.com/threa...n-and-activation-energy.1054511/#post-6921068

Thermodynamics tells us that a reaction should go if the products are more stable (have a lower free energy) than the reactants – the reaction has a negative free energy change. Kinetics, on the other hand, tells us how fast the reaction will go, though doesn't tell us anything about the final state of things once it gets there.

Have a look at “Kinetics vs. Thermodynamics” from the University of Utah:

Lecture 1: Kinetics vs. Thermodynamics: different but related

## 1. What is the difference between Gibbs free energy of activation and activation energy?

The Gibbs free energy of activation is the energy required to initiate a chemical reaction, taking into account the changes in both enthalpy and entropy. Activation energy, on the other hand, only considers the energy barrier that must be overcome for the reaction to proceed.

## 2. How do Gibbs free energy of activation and activation energy affect reaction rates?

Both Gibbs free energy of activation and activation energy are indicators of how easily a reaction can occur. A lower value for either parameter means that the reaction is more likely to proceed at a faster rate.

## 3. Can Gibbs free energy of activation be negative?

No, Gibbs free energy of activation cannot be negative. It is always a positive value since it represents the energy required to start a reaction and overcome the energy barrier.

## 4. How is Gibbs free energy of activation related to the equilibrium constant?

The Gibbs free energy of activation is related to the equilibrium constant through the Arrhenius equation, which describes the temperature dependence of reaction rates. A lower Gibbs free energy of activation corresponds to a higher equilibrium constant, indicating a more favorable reaction.

## 5. How can Gibbs free energy of activation be calculated experimentally?

Gibbs free energy of activation can be calculated experimentally by measuring the rate of a reaction at different temperatures and using the Arrhenius equation to determine the activation energy. This value can then be used to calculate the Gibbs free energy of activation for the reaction.

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