Any process that results in a change in state or activity of a cell (in terms of movement, secretion, enzyme production, gene expression, etc.) as a result of a disturbance in cellular homeostasis caused by the chemical structure of the anion portion of a dissociated acid (rather than the acid acting as a proton donor). The acid chemical may be in gaseous, liquid or solid form. [ http://www.ncbi.nlm.nih.gov/pubmed/10615049 http://www.ncbi.nlm.nih.gov/pubmed/19170886 http://en.wikipedia.org/wiki/Acid ]