In this work, we present a DFT description of the PMF for dissociation of N 2 on Ru(0001) using a neural network-based enhanced sampling method called CFF with AIMD (i.e., CFF-AIMD). We show that neural networks accelerate enhanced sampling simulations to predict the long-timescale surface reaction phenomenon using AIMD. We find that the entropies of the intermediate states affect the topology of the FES, which consequently deviates from the PES. We use several variants of HA to show that the computed PMF using CFF-AIMD captures temperature-dependent contributions to the free energies that are not included in conventional HA methods, such as the effects of multiple dissociated states, configurational degeneracies, and vibrational entropy of surface atoms. We demonstrate that these entropic effects can be critical for predicting the free energies and barriers for reactions on metal surfaces.