A computationally efficient and rigorous thermodynamic model (ISORROPIA) that predicts the physical state and composition of inorganic atmospheric aerosol is presented. The advantages of this particular model render it suitable for incorporation into urban and regional air quality models. The model is embodied into the UAM-AERO air quality model, and the performance is compared with two other thermodynamic modules currently in use, SEQUILIB 1.5 and SEQUILIB 2.1. The new model yields predictions that agree with experimental measurements and the results of the other models, but at the same time proves to be much faster and computationally efficient. Using ISORROPIA accelerates the thermodynamic calculations by more than a factor of six, while the overall speed-up of UAM-AERO is at least twofold. This speedup is possible by the optimal solution of the thermodynamic equations, and the usage of precalculated tables, whenever possible.