Final answer:
In a Maxwell-Boltzmann distribution of molecular speeds at the same temperature, the gas with the broader and higher speed distribution has the smaller molar mass because at a given temperature, molecules of lower mass move faster on average.
Step-by-step explanation:
Regarding the question about which gas has the smallest molar mass based on the Maxwell-Boltzmann distribution of molecular speeds at the same temperature, it's important to understand the relationship between molecular speed distribution and molar mass. According to kinetic theory and the Maxwell-Boltzmann distribution, at a given temperature, a gas with a smaller molar mass will generally have molecules with higher average speeds compared to a gas with a larger molar mass. Thus, if two different gases are at the same temperature, the gas with the broader and shifted to higher speeds distribution has the smaller molar mass. This is because the kinetic energy of the system is equal to ½ m where m is the molar mass and is the mean square speed. With equal kinetic energies at the same temperature, a smaller molar mass implies a greater speed.