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:

• ΔG^* = Gibbs energy of activation
• ΔH^* = enthalpy of activation
• ΔS^* = entropy of activation

Combining equations 1 and 2 and then solving for lnK^*, we arrive at the Eyring equation:

ΔH^* − TΔS^* = −RTlnK^*

or,

lnK^* = −(ΔH^*/RT) + (ΔS^*/R)

Entropy of Activation

The standard free energy change is related to the 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 = equilibrium constant

For equilibrium constant K^*:

or, K^* = e^−ΔH*/RT · e^ΔS*/R

Where ΔS^* and ΔH^* are the differences in the value of standard entropy change and standard enthalpy change respectively for the activated complex and reactant:

Reactants → Activated Complex → Products