Consider an oxygen gas in a container having a molar mass of 0.0320 kg/mol at room temperature. Determine the ratio of the number of molecules with a speed of around 400 m/s to the number of molecules with a speed of around 200 m/s, the root-mean-square speed, and the most probable speed of oxygen molecules at room temperature. To solve the problem, identify the known and unknown quantities. In differential form, the number of molecules close to a speed is the product of the probability distribution function of the speed times a small interval of the speed. The ratio can be calculated by dividing the number of molecules close to the individual speeds. Substitute the terms in the Maxwell-Boltzmann distribution function for gas molecules. The ratio of the number of molecules with individual speeds can be determined. Recall the root-mean-square speed equation and the most probable speed equation for gas molecules. By substituting the known values, the root-mean-square speed and the most probable speed of the gas can be determined.