Representing secondary organic aerosol (SOA) in a numerical model is very important because SOA constitutes a sizeable fraction of fine particulate mater (PM2.5), which has impacts on human health, visibility degradation, and climate change. The formation of SOA depends on atmospheric abundance of anthropogenic and biogenic volatile organic compounds (VOCs), their chemical reactivity, solubility, and the condensable products from their photochemical oxidation, as well as gas/particle partitioning of the condensable products. The mechanism of formation of SOA is one of the least understood research areas due to the complexities of chemical and thermodynamic properties of hundreds of organic compounds; therefore, modeling SOA presents a major challenge. A number of modules have been developed for simulating SOA formation in air quality models. Two aerosol modules: Model of Aerosol Dynamics, Reaction, Ionization, and Dissolution 1 and 2 (MADRID 1 and MADRID 2) have been incorporated into EPA's Three-Dimensional (3-D) Community Multiscale Air Quality (CMAQ) modeling system to simulate SOA. MADRID 2 represents a detailed treatment for SOA formation, but it is more computationally expensive than MADRID 1. In this study, a fully-coupled gas and aerosol box model (i.e., zero-dimensional (0-D) version of CMAQ-MADRID 2) is set up to investigate the formation of SOA and to improve the module's computational efficiencies while maintaining a desirable numerical accuracy. Possible speed-up methods include activating organic-inorganic interactions only when the concentrations of hydrophilic SOA are significant, and parameterizing the calculation of activity and partition coefficients. The two coefficients will be calculated under various temperature and vapor pressure for mixtures with different mole fractions, and the results will be analyzed using statistical analysis tools (e.g., regression analysis) to obtain the parameterized expressions. This study will improve the SOA module for 3-D PM modeling.