The fraction of molecular volume to the actual volume occupied by oxygen gas at STP is: (Take the diameter of an oxygen molecule to be 3 Å).
1. 4 × 10⁻⁴
2. 5 × 10⁻⁴
3. 3 × 10⁻⁴
4. 1 × 10⁻⁴

The figure shows a plot of \(\dfrac{PV}{T}\) versus \(P\) for \(1.00\times10^{-3} \) kg of oxygen gas at two different temperatures.

Then relation between \(T_1\) and \(T_2\) is: 
1. \(T_1=T_2\)
2. \(T_1<T_2\)
3. \(T_1>T_2\)
4. \(T_1 \geq T_2\)$\mathrm{}$

The value of \(\frac{PV}{T}\) where the curves meet on the \(y\)-axis is:
1. \(0.06~\text{JK}^{-1}\)
2. \(0.36~\text{JK}^{-1}\)
3. \(0.16~\text{JK}^{-1}\)
4. \(0.26~\text{JK}^{-1}\)

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cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm, and its temperature drops to 17 °C. The mass of oxygen taken out of the cylinder is: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

1. 0.14 kg
2. 0.16 kg
3. 0.18 kg
4. 0.21 kg

An air bubble of volume 1.0 $c{m}^3$ rises from the bottom of a lake 40 m deep at a temperature of 12 °C. To what volume does it grow when it reaches the surface, which is at a temperature of 35 °C?
1. 5.3 cm³
2. 4.0 cm³
3. 3.7 cm³
4. 4.9 cm³

What is the total number of air molecules (inclusive of oxygen, nitrogen, water vapor, and other constituents) in a room of capacity \(25.0\) m³ at a temperature of \(27^\circ \text C\) and \(1\) atm pressure?
1. \(6.1\times10^{23}\) molecules
2. \(6.1\times10^{26}\) molecules
3. \(7.1\times10^{23}\) molecules
4. \(7.1\times10^{26}\) molecules

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 \(-20^\circ \text{C}?\)
(Given the atomic mass of \(\mathrm{Ar}=39.9~\text{u}\) and of \(\mathrm{He}=4.0~\text{u}\))
1. \(1.01 \times 10^3 ~\text{K} \)
2. \(3.15 \times 10^3 ~\text{K} \)
3. \(1.91 \times 10^3~ \text{K} \)
4. \(2.52 \times 10^3 ~\text{K}\)

From a certain apparatus, the diffusion rate of hydrogen has an average value of 28.7 $c{m}^3 s^{-1}$. The diffusion of another gas under the same conditions is measured to have an average rate of 7.2 $c{m}^3 s^{-1}$. The unknown gas is:
1. Oxygen
2. Nitrogen
3. Helium
4. None of these