Final answer:
The Maxwell-Boltzmann distribution allows us to determine the proportions of gas molecules having more than or less than the root mean square speed and the mean speed.
Step-by-step explanation:
The proportions of gas molecules with speeds more than and less than the root mean square (rms) speed can be determined using the Maxwell-Boltzmann distribution. The distribution describes the relative numbers of gas molecules at different speeds in a bulk sample. The proportion of molecules with speeds greater than the rms speed is given by the area under the tail of the distribution curve, while the proportion with speeds less than the rms speed is given by the area under the curve up to the rms speed.
The proportions of gas molecules with speeds greater and smaller than the mean speed can be determined in a similar way. The mean speed is the average of all the molecular speeds in the distribution. We can find the proportion of molecules with speeds greater than the mean speed by calculating the area under the tail of the distribution curve beyond the mean speed. Conversely, the proportion of molecules with speeds smaller than the mean speed can be found by calculating the area under the curve up to the mean speed.