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?