Ubiquinol:cytochrome c oxidoreductase, bc1 complex, is the enzyme in the respiratory chain of mitochondria responsible for the transfer reducing potential from ubiquinol to cytochrome c coupled to the movement of charge against the electrostatic potential across the mitochondrial inner membrane. The complex is also implicated in the generation of reactive oxygen species under certain conditions and is thus a contributor to cellular oxidative stress. Here, a biophysically detailed, thermodynamically consistent model of the bc1 complex for mammalian mitochondria is developed. The model incorporates the major redox centers near the Qo- and Qi-site of the enzyme, includes the pH-dependent redox reactions, accounts for the effect of the proton-motive force of the reaction rate, and simulates superoxide production at the Qo-site. The model consists of six distinct states characterized by the mobile electron distribution in the enzyme. Within each state, substates that correspond to various electron localizations exist in a rapid equilibrium distribution. The steady-state equation for the six-state system is parameterized using five independent data sets and validated in comparison to additional experimental data. Model analysis suggests that the pH-dependence on turnover is primarily due to the pKa values of cytochrome bH and Rieske iron sulfur protein. A previously proposed kinetic scheme at the Qi-site where ubiquinone binds to only the reduced enzyme and ubiquinol binds to only the oxidized enzyme is shown to be thermodynamically infeasible. Moreover, the model is able to reproduce the bistability phenomenon where at a given overall flux through the enzyme, different rates of superoxide production are attained when the enzyme is differentially reduced.