Question

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 Vrms the largest?

Answer 1

All the three vessels have the same capacity, which implies they have the same volume. Thus, each gas has the same pressure, volume, and temperature.

According to Avogadro’s law, the three vessels will contain an equal number of the respective molecules.


we know, $V_{rms}=\sqrt{\frac{3RT}{M}}$
where , $V_{rms}$ is the root mean square velocity, T is temperature of gas and M is molecular mass of gas.

here, T is constant for all gases but molecular masses are different.
so, root mean square speed of molecules are different.

root mean square speed is inversely proportional to square root of molecular mass. therefore, lower the value of molecular mass , higher will be rms speed.

here lower molecular mass in case of Neon.Hence, neon has the largest root mean square speed among the given gases.

Answer 2

Answer:

Given:

• 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).

Find:

• 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?

According to Avogadro's law:

• $\bold{v_{rms}=\sqrt{\frac{3RT}{M}}}$

• Avogadros law = Amount of gases = Equal number of molecules.

That's:

• The no. of molecules = Equal temperature, equal pressure.

• Vrms ∞ 1/√M

• Before proving our answer, we have to check the law:

• As per the law, it's proportion is inverse to mass of gas (Up side down) .

• Molecular mass > lesser than RMS.So, higher is the velocity.

• Therefore as per the question the number of molecules are not same.

• Therefore, Neon has the largest velocity RMS.

HENCE PROVED!!!