This thesis presents a general kinetic model and its application to feldspar dissolution. In the framework of Monte Carlo methods, the model simulates the stochastic processes of feldspar dissolution by incorporating bond breakage, bond formation, surface diffusion, and the detachment and attachment of various mineral-forming ions. Quantum mechanical calculations are implemented to quantify the energies required to break and form Si-O-Si and Si-O-Al bonds. Empirical interatomic potential modeling is used to examine the relaxation of the feldspar's surface structure from the ideal bulk structure. The kinetic model incorporates the proper crystallographic surface structures, emphasizing the essential role of dynamics of neighboring sites on the crystal surface. The application of the general kinetic model to feldspar dissolution elucidates the kinetic patterns observed in experimental observations and improves our fundamental understanding of feldspar dissolution. In addition, we use the model with the appropriate change in parameterization to investigate the morphological evolution of a (001) surface of barite etched in pure water. The generation of two sets of oppositely-oriented triangular etch pits in consecutive atomic layers validates the model's efficiency. It is the first stochastic treatment out of numerous studies concerning barite dissolution to address this unique pit morphology. We further extend the model from abiotic water-mineral interactions and apply it to microbe-water-rock interactions in order to explore this subject as a complementary approach.