A composition for hardening concrete that has a pH of less than 10, and may have a pH of 8 or less. Thus, the hardening composition may be free of or substantially free of alkaline materials. The hardening composition is water-based and includes silica particles and an aluminum-based (e.g., alumina, etc.) stabilizer, which may be present on portions of the surfaces of the silica particles. In use, the hardening composition is applied to the surface of concrete, either alone, with curing compounds, or as part of a polishing process. Any residue that remains on the treated surface may simply be swept, blown, or sprayed away.