The paper presents a mathematical model of the condensation processes occurring in a smoke plume from a combustion process. In such a plume, the opacity may increase where the hot stack gas mixes with cooler atmosphere. The increased opacity is due to aerosol formation which may result from the condensation of vapors, such as sulfuric acid, in the stack gases. These plumes are persistent and do not disappear as rapidly as condensed water plumes. After release from the stack, the plume is cooled and diluted by mixing with ambient air. The rate of mixing depends on the local plume and ambient properties such as velocity and temperature. A dew point may eventually be reached in the plume, leading to an onset of condensation of vapors. Both heterogeneous condensation and homogeneous nucleation of vapors are considered in the model. The condensation process and plume dilution change the size distribution/concentration of aerosols in the plume and thus change plume opacity. The model is dynamic, following the plume as it travels downwind. Continuous and gradual dilution of the plume is considered, and plume properties are determined as a function of time. Initially, binary condensation of sulfuric acid and water is considered because of the interest in air pollution. Good agreement of the model has been obtained with rather sparse data available in the literature.