Van der Waals equation at low pressure is -

1. PV = RT - Pb

2. PV = RT - $\frac{\mathrm{a}}{\mathrm{V}}$

3. PV = RT + $\frac{\mathrm{a}}{\mathrm{v}}$

4. PV = RT + Pb

At room temperature, the average speed of Helium is higher than that of Oxygen by a factor of -

1. $2\sqrt{2}$

2. $6/\sqrt{2}$

3. 8

4. 6

The unit of van der Waals' constant 'b' is -

1. cm³ mol^-1

2. litre mol^-1

3. m³ mol^-1

4. All of the above

In which case is the rate of diffusion highest if all are present in the same container at the same temperature:

1. 4 g H₂

2. 32 g O₂

3. 22 g CO₂

4. 56 g N₂

At high pressure, the compressibility factor 'Z' is equal to -

1.  Unity

$2.$ $1-\frac{\mathrm{Pb}}{\mathrm{RT}}$
$3.$ $1+\frac{\mathrm{Pb}}{\mathrm{RT}}$

4.  Zero

20 L of SO₂ diffuses through a porous partition in 60s. The volume of O₂ that will diffuse under similar condition in 30s will be:-

1. 12.14 L

2. 14.14 L

3. 18.14 L

4. 28.14 L

The compressibility factor for 1 mol of a van der Waals gas at $0°\mathrm{C}$ and 100 atmospheric pressure is found to be 0.5. The volume of gas is-

1. 2.0224 L

2. 1.4666 L

3. 0.8542 L

4. 0.1119 L

A helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is-

1. Same as that of a hydrogen molecule

2. Half that of a hydrogen molecule

3. Two times that of a hydrogen molecule 

4. Four times that of a hydrogen molecule 

A 2.24 L cylinder of oxygen at STP is found to develop a leakage. When the leakage was plugged, the pressure dropped to 570 mm of Hg. The number of moles of gas that escaped will be:

1. 0.050

2. 0.025

3. 0.075

4. 0.01

Two flasks of equal volume are connected by a narrow tube (of negligible volume) at 27ºC and contain 0.70 mole of ${\mathrm{H}}_2$ at 0.5 atm. One of the flasks is then immersed in a hot bath, kept at 127 ºC, while the other remains at 27 ºC. The final pressure is -

1. 5.714 atm                   

2. 0.5714 atm

3. 2.5214 atm                 

4. 5.5114 atm