I have some enthalpies of formation for a reactant and transition state but calculated using different computational methods. I want to find the ratio of the forward rate constants determined using both methods but I'm not really sure how. I thought I could maybe use transition state theory but that equation involves Gibbs free energy not enthalpy.
To calculate the ratio of forward rate constants using the enthalpies of formation for a reactant and transition state calculated with different computational methods, you can use the concept of transition state theory. Although the equation typically involves the Gibbs free energy, you can still use enthalpy, given a few considerations.
Transition state theory relates the rate constant of a chemical reaction to the thermodynamic quantities of the reactants and transition state. The key assumption is that the rate-determining step occurs at a transition state, which lies at the highest point along the reaction coordinate.
While the Gibbs free energy is generally used in transition state theory, you can convert between Gibbs free energy (ΔG) and enthalpy (ΔH) using the equation:
ΔG = ΔH - TΔS
Here, ΔS is the entropy change, and T is the temperature.
To find the ratio of the forward rate constants using enthalpies of formation, follow these steps:
1. Calculate the ΔG of the reactant and transition state using the enthalpies of formation from each computational method.
ΔG = ΔH - TΔS
2. Calculate the difference in ΔG between the reactant and transition state for each method.
ΔΔG = ΔG_transition_state - ΔG_reactant
3. Note that the ratio of rate constants (k1/k2) is equal to the exponential of the difference in ΔG between the reactant and transition state.
k1/k2 = exp(ΔΔG / RT)
Here, R is the gas constant and T is the temperature in Kelvin.
By applying the formula above, you can find the ratio of the forward rate constants using the enthalpies of formation calculated by different computational methods. Keep in mind that the accuracy of the ratio will depend on the accuracy of the enthalpy values obtained from the respective methods.