This paper describes and evaluates a new Model for Simulating Aerosol Interactions and Chemistry (MOSAIC), with a special focus on addressing the long‐standing issues in solving the dynamic partitioning of semivolatile inorganic gases (HNO3, HCl, and NH3) to size‐distributed atmospheric aerosol particles. The coupled ordinary differential equations (ODE) for dynamic gas‐particle mass transfer are extremely stiff, and the available numerical techniques are either very expensive or produce oscillatory solutions. These limitations are overcome in MOSAIC with a new dynamic gas‐particle partitioning module, which is coupled to an efficient and accurate thermodynamics module. The algorithm includes a new concept of “dynamic pH,” a novel formulation for mass transfer to mixed‐phase and solid particles, and an adaptive time stepping scheme, which together hold the key to smooth, accurate, and efficient solutions of gas‐particle partitioning over the entire relative humidity range. MOSAIC is found to be in excellent agreement with a benchmark version of the model that uses a rigorous solver for integrating the stiff ODEs. The steady‐state MOSAIC results for monodisperse aerosol test cases are also in excellent agreement with those obtained with the benchmark equilibrium model AIM. Moreover, the CPU times required for fully dynamic solutions by MOSAIC per size bin per 5 min intervals (typical 3‐D model time steps) are similar to those for bulk equilibrium solutions by the computationally efficient but relatively less accurate model ISORROPIA. These results show that MOSAIC is extremely efficient without compromising accuracy, and is therefore highly attractive for use in air quality and regional/global aerosol models.