Chemical processes involving sulfur and nitrogen species in clouds and precipitation have been incorporated into a diagnostic, two-dimensional numerical model for narrow cold-frontal rainbands (NCFR). The chemical species include sulfur dioxide, sulfate, ammonium, nitric acid, hydrogen peroxide and peroxyacetyl nitrate. The model is initialized through specification of the airflow field, a temperature-humidity sounding, and initial profiles of the various chemical species. Outputs of the model (discussed in detail in Part 2) (Hegg et al., this issue) are the steady state, two-dimensional fields of the mass mixing ratio of various chemical species (e.g., cloud water sulfate or nitrate, precipitation sulfate, or nitrate). In view of similarities between NCFR and moderately strong convective systems, this model should also be useful in diagnostic studies of the sulfur and nitrogen chemistry of a variety of convective clouds and storms.