NCERT Solutions

Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be $3 \AA$.

Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP : 1 atmospheric pressure, $0 {}^{\circ} \mathrm{C}$). Show that it is 22.4 litres.

An oxygen cylinder of volume 30 litre has an initial gauge pressure of 15 atm and a temperature of $27^{\circ} \mathrm{C}$. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to $17^{\circ} \mathrm{C}$. Estimate the mass of oxygen taken out of the cylinder ($R=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$, molecular mass of $\mathrm{O}_2=32 \mathrm{u}$).

An air bubble of volume $1.0 \mathrm{~cm}^3$ rises from the bottom of a lake 40 m deep at a temperature of $12^{\circ} \mathrm{C}$. To what volume does it grow when it reaches the surface, which is at a temperature of $35^{\circ} \mathrm{C}$ ?

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity $25.0 \mathrm{~m}^3$ at a temperature of $27^{\circ} \mathrm{C}$ and 1 atm pressure.

Estimate the average thermal energy of a helium atom at (i) room temperature ($27^{\circ} \mathrm{C}$), (ii) the temperature on the surface of the Sun (6000 K), (iii) the temperature of 10 million kelvin (the typical core temperature in the case of a star).

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 $V_{\text{rms}}$ the largest ?

At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at $-20^{\circ} \mathrm{C}$ ? (atomic mass of Ar $=39.9 \mathrm{u}$, of He $=4.0 \mathrm{u}$).

Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature $17^{\circ} \mathrm{C}$. Take the radius of a nitrogen molecule to be roughly $1.0 \AA$. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of $\mathrm{N}_2=28.0 \mathrm{u}$).