Sulfur and nitrogen oxides (SOx and NOx) are harmful pollutants emitted into the atmosphere by industry and transport sectors. In addition to being hazardous gases, SOx and NOx form sulfuric and nitric acids which contribute to the formation of airborne particulate matter through nucleation and condensation, hence magnifying the environmental impact of these species. In this work, we build a modeling framework for utilizing this phenomenon for low-temperature exhaust gas cleaning. It has been reported that ammonia gas can be used to facilitate particle formation from the aforementioned acids, and thus remove these gaseous pollutants by converting them into ammonium sulfate and nitrate particles. Here we provide comprehensive modeling tools for applying this idea to exhaust gas cleaning by combining detailed models for nucleation, gas-particle mass exchange and particle population dynamics. We demonstrate how these models can be used to find advantageous operating conditions for a cleaning unit. In particular, the full model is computationally cheap and enables optimization of the particle formation efficiency and particle growth, hence ensuring sufficient conversion of gaseous pollutants into collectable particulate matter. This constitutes a ground for future engineering tools for designing next-generation sustainable exhaust gas cleaners.