Desert dust undergoes complex heterogeneous chemical reactions during atmospheric transport, forming nitrate coatings that impact hygroscopicity, gas species partitioning, optical properties, and aerosol radiative forcing. Contemporary atmospheric chemistry models show significant disparities in aerosol nitrogen species due to varied parameterizations and inaccuracies in representing heterogeneous chemistry and dust alkalinity. This study investigates key processes in nitrate formation over dust and evaluates their representation in models. We incorporate varying levels of dust heterogeneous chemistry complexity into the MONARCH model, assessing sensitivity to key processes. Our analyses focus on the condensation pathways of gas species onto dust (irreversible and reversible), the influence of nitrate representation on species' burdens and lifetimes, size distribution, and the alkalinity role. Using annual global simulations, we compare particulate and gas species surface concentrations against observations and evaluate global budgets and spatial distributions. Findings show significant outcome dependence on methodology, particularly on the reversible or irreversible condensation of gas species on particles, with a wide range of burdens for particulate nitrate (0.66 to 1.93 Tg) and correlations with observations (0.66 to 0.91). Particulate ammonium burdens display less variability (0.19 to 0.31 Tg). Incorporating dust and sea-salt alkalinity yields results more consistent with observations, and assuming reversible gas condensation over dust, along with alkalinity representation, aligns best with observations, while providing consistent gas and particle partitioning. In contrast, irreversible uptake reactions overestimate coarse particulate nitrate formation. Our analysis provides guidelines for integrating nitrate heterogeneous formation on dust in models, paving the road for improved estimates of aerosol radiative effects.