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A catalyst is a substance which can increase the rate of a reaction without being affected in the whole reaction process.

ΔG°= Free energy of activation or Gibes free energy

ΔE_a = Activation energy.

Δ³§^° = Entropy of activation

Δ±á‡ = enthalpy of the transition state - enthalpy of the reactants

ΔS‡ = entropy of the transition state - entropy of the reactants

ΔG‡ = free energy of the transition state - free energy of the reactants

k = rate constant.

K_eq = Equilibrium constant of a reaction.

Δ±á^° = Enthalpy of activation

From the arrhenius equation, we can write,

Where k= rate constant.

A = Arrhenius constant.

E_a =activation energy.

R= Gas constant.

T= temperature.

If we introduce an catalyst, the reaction rate constant(k) will increase by decreasing the activation energy. So, in presence of catalyst, E_a decreases and k increases.

There are two others relations to compare the presence of catalyst and that are,

Δ³Ò^‡ = Δ±á^‡ -TΔ S^‡ ²¹²Ô»å…â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦1

Δ·¡_a = Δ±á^‡ + RT. ………………..2

Where every terms has their own meanings.

Now, when, catalyst is applied, E_adeceases and as per equation 2, ΔH^‡also decreases as RT is a constant value.

Now, K_eq∞, Where k and k_-1 are rate constant in forward and backward direction respectively. If rate of a reaction increases which means formation of products (Forward reaction, K_eqalso increases, and from , becomes more negative or more spontaneous.

With decreasing , ΔS^‡increases to make the overall reaction negative.

The order of increase and decrease for Δ±á^°ΔG° and Δ³§^° becomes just same as for the transition state values of enthalpy, gibes free energy and entropy.