ZnO nanoparticles of about 30-60 Angstrom size in ethanolic solution were etched by addition of anhydrous acetic acid. Upon dissolution, the volume-weighted particle size decreased by about 10%. The polydispersity increased slightly. The dissolution rate was strongly dependent on particle size, and size selective etching of a mixture of ZnO particles was demonstrated. The change of the particle size during etching can be modeled adequately by a Monte Carlo simulation, in which the known degree of polydispersity and the size dependence of the etch rate are taken into account. On the basis of a comparison with work on the dissolution of silica nanoparticles and oxidic thin films, and on the etching of single-crystal ZnO, it is proposed that the size dependence is caused by variations of the chemical reactivity of the nanoparticles related to, for example, the concentration of defects and kink sites. Thus, dissolution provides a convenient method to investigate size-dependent chemical properties.