Question
Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Do the vessels contain equal number of respective molecules? Is the root mean square speed of molecules the same in the three cases? If not, in which case is vrms the largest?
Solution
Using the ideal gas equation, we can say the number of moles of gas is given by
i.e. number of moles in a gas is independent of the nature of gas but depends upon P, V and T. Since P, V and T for all gases are same, therefore all the three vessels contain equal number of moles and hence molecules.
At a given temperature, the r.m.s speed is inversely proportional to mass of atom or molecules, therefore vrms is largest for lightest gas i.e. neon.
i.e. number of moles in a gas is independent of the nature of gas but depends upon P, V and T. Since P, V and T for all gases are same, therefore all the three vessels contain equal number of moles and hence molecules.
At a given temperature, the r.m.s speed is inversely proportional to mass of atom or molecules, therefore vrms is largest for lightest gas i.e. neon.
