The concepts of Newtonian mechanics, fluids, and ideal gas law physics are often treated as separate and isolated topics in the typical introductory college-level physics course, especially in the laboratory setting. To bridge these subjects, a simple experiment was developed that utilizes computer-based data acquisition sensors and a digital gram scale to estimate the molar mass of the gas in an inflated balloon. In this experiment, the comparable density of an inflated balloon to that of atmospheric air introduces a significant role for buoyancy that must be accounted for. The ideal gas law approximation is assumed for both the isolated gas mixture within the balloon and the surrounding air, which defines the relationship between the gas pressure, volume, temperature, and molar quantity. Analysis of the forces associated with the inflated balloon with the incorporation of Archimedes' principle and the ideal gas law into Newton's second law results in an experimental method for the measurement of the molar mass and mole fraction of a gas that is easy to implement yet academically challenging for students. The following narrative describes the basic setup of this experiment, along with a sample set of data as acquired and analyzed by a typical physics student from one of my classes.