Metal-organic molecular-beam epitaxy with trimethylgallium and ammonia is used to grow GaN on Si(111). Our analysis of the growth data shows an increase in the apparent formation energy Eapp of epitaxial GaN, from 0.168 to 0.56 eV, with an increasing flux of ammonia. A rate-equation-based growth model is proposed and used to fit the growth data. Regarding the interaction potential, the model assumes the presence of an activated state, intermediate between physisorption and chemisorption, and includes second-order recombination-desorption processes important in the modeling of high-temperature growth. It is shown that the formation energy of epitaxial GaN, Ef, depends on the growth conditions as the activation energy and surface diffusion energy barriers increase or decrease with the change in the impinging fluxes and surface density of precursors. For such a particular set of growth conditions, the model allows us to determine the formation energy of epitaxial GaN as Ef =0.11 eV, ∼35% smaller than the apparent activation energy obtained directly from the growth data. Eapp =0.168 eV.