Using high-resolution numerical simulations we investigate the plasma heating driven by periodic two-fluid acoustic waves that originate at the bottom of the photosphere and propagate into the gravitationally stratified and partially ionized solar atmosphere. We consider ions+electrons and neutrals as separate fluids that interact between themselves via collision forces. The latter play an important role in the chromosphere, leading to significant damping of short-period waves. Long-period waves do not essentially alter the photospheric temperatures, but they exhibit the capability of depositing a part of their energy in the chromosphere. This results in up about a five times increase of ion temperature that takes place there on a timescale of a few minutes. The most effective heating corresponds to waveperiods within the range of about 30-200 s with a peak value located at 80 s. However, we conclude that for the amplitude of the driver chosen to be equal to 0.1 km s−1, this heating is too low to balance the radiative losses in the chromosphere.