Question

What is the effect of adding a catalyst on
(a) Activation energy ($\text{ }{{\text{E}}_{\text{a}}}\text{ }$), and
(b) Gibbs energy ($\text{ }\Delta \text{G }$ ) of a reaction?

Answer 1

Catalyst is a substance which alters the rate of reaction. The rate of reaction can be increased or decreased depending on the type of catalyst used. The rate of reaction is related to the activation energy of the reaction. It is the minimum amount of energy required by a reaction to form a product. A catalyst does not affect the equilibrium attained by the system.

Complete Solution :
A catalyst is a chemical substance when added to the reaction mixture, alters the rate of reaction. It provides an alternate pathway for the reaction to proceed. This new path has lower activation energy as compared to the reaction without catalyst (uncatalyzed reaction). Let's discuss the effect of a catalyst on:

a) Activation energy:
First, we will discuss the effect of a catalyst on the activation energy.
Let us know about the activation energy. When there is the conversion of reactant to a product, some amount of energy is required for the activation; that energy is known as activation energy.
Thus, activation energy is being affected by the catalyst. There will be two cases, i.e. one is the addition of a catalyst is positive, and the other is the addition of a catalyst is negative.
The rate of the reaction is related to the activation energy as shown below,
$\text{ k = A }{{\text{e}}^{-\dfrac{{{\text{E}}_{\text{a}}}}{\text{RT}}}}\text{ }$
Where, $\text{ }{{\text{E}}_{\text{a}}}\text{ }$ is the activation energy of a reaction, k is rate constant, A is the pre-exponential factor, etc. This is known as the Arrhenius equation. From this relation it can be said that the addition of the catalyst affects the rate of reaction and this inverse effect on the activation energy.
So, with the addition of a positive catalyst activation energy decreases, and when a negative catalyst is added, activation energy increases.

b) Gibbs free energy:
Now, we will affect the effect of a catalyst on the Gibbs energy of a reaction. Gibbs free energy is a state function and thus it is affected by the path taken by the reaction to form the product.it only depends on the state of reactant and product formed.
The Gibbs free energy is related to the equilibrium constant of the reaction. the relation is as stated below,
$\text{ }\Delta \text{G = }-\text{RT ln K}$
Where K is an equilibrium constant of reaction . During the course of the reaction the activation energy is lowered but the change in enthalpy remains unaffected. As the catalyst does not affect the equilibrium of the reaction.
Thus, the catalyst does not affect the change in free energy.
In the last, we can conclude that the catalyst shows its effect on the activation energy, but no effect on Gibbs energy.

Note: The Gibbs free energy can be also expressed as,$\text{ }\Delta \text{G = }\Delta \text{H}-\text{ T}\Delta \text{S }$, where enthalpy $\text{ }\Delta \text{H }$ , absolute temperature T, and entropy change $\text{ }\Delta S\text{ }$. During catalyzed reaction activation energy drops, thus the change in enthalpy reduces.
- It may be noted that the catalyst does affect the entropy of the reactant. It changes the entropy such that the change in enthalpy is equal to the product of $\text{T}\Delta \text{S }$ with opposite sign, thus change in enthalpy is zero. This is the alternate way to study the effect of catalyst of Gibbs free energy.