The properties of an Ar/C2H2 dusty plasma (ion, electron and neutral particle densities, effective electron temperature and dust charge) in glow and afterglow regimes are studied using a volume-averaged model and the results for the glow plasma are compared with mass spectrometry measurements. It is shown that dust particles affect essentially the properties of glow and afterglow plasmas. Due to collection of electrons and ions by dust particles, the effective electron temperature, the densities of argon ions and metastable atoms are larger in the dusty glow plasma comparing with the dust-free case, while the densities of most hydrocarbon ions and acetylene molecules are smaller. Because of a larger density of metastable argon atoms and, as a result, of the enhancement of electron generation in their collisions with acetylene molecules, the electron density in the afterglow dusty plasma can have a peak in its time-dependence. The results of numerical calculations are in a good qualitative agreement with experimental results.