The equation of state corresponding to 8 g of ${\mathrm{O}}_2$ is :

1.  PV = 8RT                           

2.  PV = RT/4

3.  PV = RT                             

4.  PV = RT/2

The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be

1. $\mathrm{PV}=\left(5/32\right)\mathrm{RT}$                               

2. $\mathrm{PV}=5\mathrm{RT}$

3. $\mathrm{PV}=\left(5/2\right)\mathrm{RT}$                                 

4. $\mathrm{PV}=\left(5/16\right)\mathrm{RT}$

(where R is the gas constant)

Three containers of the same volume contain three different gases. The masses of the molecules are ${\mathrm{m}}_1, {\mathrm{m}}_2$ and ${\mathrm{m}}_3$ and the number of molecules in their respective containers are ${\mathrm{N}}_1, {\mathrm{N}}_2$ and ${\mathrm{N}}_3$ . The gas pressure in the containers are ${\mathrm{P}}_1, {\mathrm{P}}_2$ and ${\mathrm{P}}_3$ respectively. All the gases are now mixed and put in one of the containers. The pressure P of the mixture will be :

1. $\mathrm{P}<\left({\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3\right)$                               

2. $\mathrm{P}=\frac{{\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3}{3}$

3. $\mathrm{P}={\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3$                                 

4. $\mathrm{P}>\left({\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3\right)$

At a given volume and temperature, the pressure of a gas :

1. Varies inversely as its mass

2. Varies inversely as the square of its mass

3. Varies linearly as its mass

4. Is independent of its mass

The rate of diffusion is :

1. Faster in solids than in liquids and gases

2. Faster in liquids than in solids and gases

3. Equal to solids, liquids, and gases

4. Faster in gases than in liquids and solids

Two thermally insulated vessels 1 and 2 are filled with air at temperatures $\left({\mathrm{T}}_1, {\mathrm{T}}_2\right),$ volume $\left({\mathrm{V}}_1, {\mathrm{V}}_2\right)$ and pressure $\left({\mathrm{P}}_1, {\mathrm{P}}_2\right)$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

1. ${\mathrm{T}}_1+{\mathrm{T}}_2$                               

2. $\left({\mathrm{T}}_1+{\mathrm{T}}_2\right)/2$

3. $\frac{{\mathrm{T}}_1{\mathrm{T}}_2\left({\mathrm{P}}_1{\mathrm{V}}_1+{\mathrm{P}}_2{\mathrm{V}}_2\right)}{{\mathrm{P}}_1{\mathrm{V}}_1{\mathrm{T}}_2+{\mathrm{P}}_2{\mathrm{V}}_2{\mathrm{T}}_1}$                 

4. $\frac{{\mathrm{T}}_1{\mathrm{T}}_2\left({\mathrm{P}}_1{\mathrm{V}}_1+{\mathrm{P}}_2{\mathrm{V}}_2\right)}{{\mathrm{P}}_1{\mathrm{V}}_1{\mathrm{T}}_2+{\mathrm{P}}_2{\mathrm{V}}_2{\mathrm{T}}_2}$

For matter to exist simultaneously in gas and liquid phases :

1. The temperature must be 0 K.

2. The temperature must be less than $0°\mathrm{C}$.

3. The temperature must be less than the critical temperature.

4. The temperature must be less than the reduced temperature.

The value of critical temperature in terms of Vander Waal’s constant a and b is

1. ${\mathrm{T}}_{\mathrm{c}}=\frac{8 \mathrm{a}}{27 \mathrm{Rb}}$                           

2. ${\mathrm{T}}_{\mathrm{c}}=\frac{\mathrm{a}}{2 \mathrm{Rb}}$

3. ${\mathrm{T}}_{\mathrm{c}}=\frac{8}{27 \mathrm{Rb}}$                             

4. ${\mathrm{T}}_{\mathrm{c}}=\frac{27 \mathrm{a}}{8 \mathrm{Rb}}$

In Vander Waal’s equation, a and b represent $\left(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)\left(\mathrm{v}-\mathrm{b}\right)=\mathrm{RT}$

1. Both a and b represent correction in volume

2. Both a and b represent adhesive force between molecules

3. a represents adhesive force between molecules and b correction in volume

4. a represents correction in volume and b represents adhesive force between molecules

At 0°C the density of a fixed mass of a gas divided by pressure is x. At 100°C, the ratio will be:

1. $\mathrm{x}$                                   

2. $\frac{273}{373}\mathrm{x}$

3. $\frac{373}{273}\mathrm{x}$                           

4. $\frac{100}{273}\mathrm{x}$