A developed model predicts local gas fraction and bubble-size distributions for turbulent gas dispersion in a stirred vessel, based on the population balance equations (PBE), with relations taken from literature for bubble coalescence and break-tip derived from isotropic turbulence theory. The transport of bubbles throughout the vessel is simulated by a scaled single-phase flow field obtained by CFD simulations. Model predictions for the gas fractions in pseudoplastic Xanthan solutions are compared with local measurements and agree well qualitatively,. This formulation overcomes the necessity of choosing a constant bubble size throughout the domain, as is done in two-fluid models and is, therefore, more reliable in mass-transfer calculations.