Root-Mean-Square (RMS) Velocity of Gas Molecules

The volume of a gas at the pressure $1.2\times {10}^7 N{m}^{-2}$ and the temperature $127°C$ is $2.0 litres$. Find the number of molecules in the gas.

Calculate the value of Boltzmann constant $k$. Given: $R=8.3\times {10}^3 J(kmol{)}^{-1}{K}^{-1}$ and Avogadro number $N=6.023\times {10}^{26} (kmol{)}^{-1}$.

Calculate the number of molecules, volume occupied by one molecule and the average distance between two molecules in the $1.00 c{m}^3$ volume of gas at $N.T.P.$

There are $4\times {10}^{24}$ gas molecules in a vessel at $50 K$ temperature. The pressure of the gas in the vessel is $0.03$ atmospheric. Calculate the volume of the vessel.

The volume of a balloon filled partially with helium is $30 m^3$ at the earth’s surface where the pressure is $76 cm$ (mercury) and the temperature is $27°C$. If this balloon rises up to a height where the pressure is $7.6 cm$ (mercury) and the temperature is $-54°C$, then what will be the volume of the gas there?

Air is filled in a bottle at atmospheric pressure and it is corked at $35°C$. If the cork can come out at $3$ atmospheric pressure then up to what temperature should the bottle be heated in order to remove the cork?

The pressure of an ideal gas filled in the bulb of a constant-volume gas thermometer at $7°C$ is $60 cm$ of mercury. What will be the pressure of the same volume of gas at $147°C$?

Write the formula for the pressure of an ideal gas in terms of molecular mass, number of molecules and their velocity on the basis of kinetic theory and with the help of it, establish the relation between kinetic energy of the molecules and temperature of the gas.

State the postulates of kinetic theory of gases. Derive an expression for the pressure of the gas on its basis.