The one-dimensional expansion of a plasma off a planar wall into a vacuum is studied using particle-in-cell computer simulation. Particular emphasis is put on the acceleration of ions in the plasma. Energy transfer from the electronic to the ionic subsystem, the energy spectra of the ions, and the center-of-mass motion of the ion cloud are monitored. Various parameters that influence the acceleration process are studied: the presence of several ion charge states, of neutrals, the effects of a binary mixture of ions, and of a thermal nonequilibrium between ions and electrons.