# Activation Parameters

*Activation parameters are used in chemical kinetics to describe the equilibrium between reactants of a chemical reaction and a single, unstable molecule called a transition state.*

In thermodynamics, the change in Gibbs free energy, ΔG, is defined as-

ΔG = ΔH − TΔS

where-

ΔG = change in Gibbs free energy of the reaction

ΔH = change in enthalpy

ΔS = change in entropy

ΔG

^{o}is the change in Gibbs energy in Standard State (1 atm, 298 K, pH 7).

To calculate a reaction's change in Gibbs free energy that did not happen in standard state, the Gibbs free energy equation can be written as-

ΔG = ΔG

^{o}+ RT lnK

where-

ΔG = change in Gibbs free energy of the reaction

ΔG

^{o}= standard Gibbs free energy

R = the Ideal Gas constant (8.314 J/mol K)

K = the equilibrium constant

When the reaction is at equilibrium-

ΔG = 0

The above equation becomes-

ΔG

^{o}= −RTlnK

Similarly, in transition state theory, the Gibbs energy of activation, ΔG

^{*}, is defined by-

ΔG

^{*}= −RTlnK

^{*}---Equation-1

and ΔG

^{*}= ΔH

^{*}− TΔS

^{*}---Equation-2

where,br. ΔG

^{*}= Gibbs energy of activation

ΔH

^{*}= enthalpy of activation

ΔS

^{*}= entropy of activation

Combining equations-1 and equations-2 and then solve for lnK

^{*}we have the Eyring equation-

ΔH

^{*}− TΔS

^{*}= −RTlnK

^{*}

or, lnK

^{*}= −(ΔH

^{*}/RT) + (ΔS

^{*}/R)

## Entropy of Activation

The standard free energy change is related with equilibrium constant of a reaction as-ΔF

^{o}= −RTlnK

or, K = e

^{−ΔFo/RT}

or, K = e

^{−ΔHo/RT}. e

^{ΔSo/R}

Where, ΔF

^{o}= standard free energy change

ΔS

^{o}= standard entropy change

ΔH

^{o}= standard enthalpy change

K = euqilibrium constant

For equilibrium constant K

^{*}-

or, K

^{*}= e

^{−ΔH*/RT}. e

^{ΔS*/R}

Where ΔS

^{*}and ΔH

^{*}are the difference in the value of standard entropy chnage and standard enthalpy change respectively for the activated complex and reactant-

Reactants → Activated Complex → Products

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