Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), 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 v_rms the largest ?

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Solution

Avogadro’s law states that at a given temperature and pressure, equal volume of gas contains equal number of molecules. As the given gases have same conditions of pressure, volume as well as temperature, therefore they all will have same number of molecules.

Let v rms be the root mean square velocity of gas, then

v rms = 3kT m

Here, k is the Boltzmann constant, T is the temperature in Kelvin and m is the mass of gas.

The above expression shows that root mean square velocity of a gas is inversely proportional to the square root of its mass.

Hence, in the given problem, mass of neon is the lightest, therefore neon will have the largest value of v rms .

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Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), 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 v_rms the largest?

Q. 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