Final answer:
At the same temperature and pressure, helium and argon gases have the same average kinetic energy and number of molecules per unit volume, but differ in their root mean square speed and density. The incorrect statement is that they have the same root mean square speed.
Step-by-step explanation:
The question is asking about the properties of helium gas and argon gas samples at the same temperature and pressure, specifically which statement is not true. Firstly, gases at the same temperature have the same average kinetic energy (KEavg) due to the kinetic theory of gases which states that KEavg is solely a function of temperature, regardless of the chemical identity of the gas.
However, root mean square speed (Urms) depends on the molecular mass. Gases with lighter molecules, like helium, will have higher Urms compared to heavier gases like argon at the same temperature and pressure. This means that argon molecules move more slowly on average than helium molecules.
Density and the number of molecules per unit volume also differ between gases if their molar masses are different, which is the case with helium and argon. At the same temperature and pressure, an ideal gas obeys Avogadro's law, which states that equal volumes of gases will have the same number of molecules. Thus, the densities of the two gases are different due to their different molar masses, but the number of molecules in a given volume will be the same.
In conclusion, the statement that is not true about helium and argon gas at the same temperature and pressure is that 'They have the same root mean square speed'.