Pulmonary capillary perfusion and gas exchange are physiological processes that take place at the alveolar level and that are fundamental to sustaining life. Present-day computational simulations of these phenomena are based on low-dimensional mathematical models solved in idealized alveolar geometries, where the chemical reactions between O-2-CO2 and hemoglobin are simplified. While providing general insights, current modeling efforts fail to capture the complex chemical reactions that take place in pulmonary capillary blood flow on arbitrary geometries and ignore the crucial impact of microstructural morphology on pulmonary function. Here, we propose a coupled continuum perfusion and gas exchange model that captures complex gas and hemoglobin dynamics in realistic geometries of alveolar tissue. To this end, we derive appropriate governing equations incorporating a two-way Hill-like relationship between gas partial pressures and hemoglobin saturations. We numerically solve the resulting boundary-value problem using a non-linear finite-element approach to simulate and validate velocity, partial pressure, and hemoglobin saturation fields in simple geometries. We further perform sensitivity studies to understand the impact of blood speed and acidity variability on key physiological fields. Notably, we simulate perfusion and gas exchange on anatomical alveolar domains constructed from 3D mu-computed-tomography images of murine lungs. Based on these models, we show that morphological variations decrease O-2 and CO2 diffusing capacity, predicting trends and values that are consistent with current medical knowledge. We envision that our model will provide an effective in silico framework to study how exercise and pathological conditions affect perfusion dynamics and the overall gas exchange function of the respiratory system.