Understanding the nucleation and growth kinetics of thin films is a prerequisite for their large-scale utilization in devices. For self-assembled molecular phases near thermodynamic equilibrium the nucleation-growth kinetic models are still not developed. Here, we employ real-time low-energy electron microscopy (LEEM) to visualize a phase transformation induced by the carboxylation of 4,4'-biphenyl dicarboxylic acid on Ag(001) under ultra-high-vacuum conditions. The initial (α) and transformed (β) molecular phases are characterized in detail by X-ray photoemission spectroscopy, single-domain low-energy electron diffraction, room-temperature scanning tunneling microscopy, noncontact atomic force microscopy, and density functional theory calculations. The phase transformation is shown to exhibit a rich variety of phenomena, including Ostwald ripening of the α domains, burst nucleation of the β domains outside the α phase, remote dissolution of the α domains by nearby β domains, and a structural change from disorder to order. We show that all phenomena are well described by a general growth-conversion-growth (GCG) model. Here, the two-dimensional gas of admolecules has a dual role: it mediates mass transport between the molecular islands and hosts a slow deprotonation reaction. Further, we conclude that burst nucleation is consistent with a combination of rather weak intermolecular bonding and the onset of an additional weak many-body attractive interaction when a molecule is surrounded by its nearest neighbors. In addition, we conclude that Ostwald ripening and remote dissolution are essentially the same phenomenon, where a more stable structure grows at the expense of a kinetically formed, less stable entity via transport through the 2D gas. The proposed GCG model is validated through kinetic Monte Carlo (kMC) simulations.