Gravitational waves (GWs) from binary black hole (BBH) mergers provide a new probe of massive-star evolution and the formation channels of binary compact objects. By coupling the growing sample of BBH systems with population synthesis models, we can begin to constrain the parameters of such models and glean unprecedented knowledge about the inherent physical processes that underpin binary stellar evolution. In this study, we apply a hierarchical Bayesian model to mass measurements from a synthetic GW sample to constrain the physical prescriptions in population models and the relative fraction of systems generated from various channels. We employ population models of two canonical formation scenarios in our analysis --- isolated binary evolution involving a common-envelope phase and dynamical formation within globular clusters --- with model variations for different black hole natal kick prescriptions. We show that solely with chirp mass measurements, it is possible to constrain natal kick prescriptions and the relative fraction of systems originating from each formation channel with $mathcal{O}(100)$ of confident detections. This framework can be extended to include additional formation scenarios, model parameters, and measured properties of the compact binary.
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