Activation Parameters

Activation Parameters

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
ΔGo 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 = ΔGo + RT lnK
where-
ΔG = change in Gibbs free energy of the reaction
ΔGo = 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-
ΔGo = −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-
ΔFo = −RTlnK
or, K = e−ΔFo/RT
or, K = e−ΔHo/RT. eΔSo/R
Where, ΔFo = standard free energy change
ΔSo = standard entropy change
ΔHo = standard enthalpy change
K = euqilibrium constant
For equilibrium constant K*-
or, K* = e−ΔH*/RT. eΔS*/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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