Theory is developed that relates the reactivity of nanoparticles to the structure of aggregates they may form in suspensions. This theory is applied to consider the case of reactive oxygen species (ROS) generation by photosensitization of C-60 fullerenes. Variations in aggregate structure and size appear to account for an apparent paradox in ROS generation as calculated using values for the photochemical kinetics of fullerene (C-60) and its hydroxylated derivative, fullerol (C-60(OH)(22-24)) and assuming that structure varies between compact and fractal objects. A region of aggregation-suppressed ROS production is identified where interactions between the particles in compact aggregates dominate the singlet oxygen production. Intrinsic kinetic properties dominate when aggregates are small and/or are characterized by low fractal dimensions. Pseudoglobal sensitivity analysis of model input variables verifies that fractal dimension, and by extension aggregation state, is the most sensitive model parameter when kinetics are well-known. This theoretical framework qualitatively predicts ROS production by fullerol suspensions 2 orders of magnitude higher compared with aggregates of largely undifferentiated C-60 despite nearly an order of magnitude higher quantum yield for the undifferentiated C-60 based on measurements for single molecules. Similar to C-60, other primary nanoparticles will exist as aggregates in many environmental and laboratory suspensions. This work provides a theoretical basis for understanding how the structure of nanoparticle aggregates may affect their reactivity.