The adsorption of H2O on Na-, K- or Cs-covered Ru(001) is studied at 120-370 K by photoemission spectroscopy and measurements of work-function changes, DELTA-phi. Molecular adsorption at 120 K is prevalent for alkali metal coverages, theta-AM, below a critical coverage which is 0.05, 0.05 and 0.08 for Na, K and Cs, respectively. Changes in DELTA-phi versus H2O adsorption in this alkali metal coverage range are smaller than on the clean surface and become positive for coverages approaching the critical theta-AM. Average dipole moments of H2O, coadsorbed with Na, K and Cs near the critical theta-AM, are approximately 0.2, 0.4 and 0.9 D, respectively. These differences represent a quantitative illustration of the alkali metal specificity of H2O coadsorption. For theta-AM above the critical coverage H2O dissociates into OH and atomic oxygen, with OH being the primary product. The ratio of OH to O is coverage and temperature dependent. H2O dissociation is connected to the finding of tightly adsorbed H2O at 220 K. This species is probably water of hydration of the ionic surface species.