Is equilibrium constant at a given temperature derived from Gibbs free energy of reaction valid for doing simple kinetic modelling?

Question

I intend to do a kinetic study of simple alcohol catalytic dehydrogenation reactions in the gas phase. I want to start with simple power law kinetics using $K_\mathrm{eq}$ to account for the reversibility of the reactions. Would the equation below, knowing the Gibbs free energy of reaction, be valid?

$$Δ_\mathrm{r}G^\circ = -RT\ln K_\mathrm{eq}$$

I came across a paper that used this equation to calculate $K_\mathrm{eq}$ to build a kinetic model of the ethanol-to-butadiene reaction. However, other papers I read, i.e. on the methanol-to-diethyl ether reaction, have used complex equations derived from empirical observations to calculate $K_\mathrm{eq}.$ Why use one approach over the other?

Answer 1

In general I would say 'no', thermodynamics only tells us about starting and ending points, thus you know the $\Delta G^\text{o}$ for the reaction but nothing about its actual mechanism, (since time does not come into thermodynamics). As $K_\mathrm{eq}$ is a ratio of rate constants these can take on many different values and still have the same ratio. To study the mechanism you will need to monitor species and intermediates vs time as the reaction proceeds.

Before doing any experiments you can only make informed guesses as to what the mechanism might be, even apparently simple reactions, such as between hydrogen and oxygen, is not simple but by experiment found to be a chain reaction.

Answer 2

At equilibrium, the forward and reverse rates have to be equal. For mass action kinetics, this tells you that the reverse rate constant must be equal to the forward rate constant divided by the equilibrium constant.