Gaseous State

(A) When gas molecules collide with each other, high energy molecule transfers some of its energy to less energetic molecule, but the total energy remains conserved. This type of collision between gas molecules is called elastic collision. According to kinetic theory of gas, no loss of energy is observed on collisions and kinetic energy is proportional to absolute temperature of gas.

Option (A) is correct.

(B) Momentum of any particle for example, gas molecules depends upon the mass as well as the velocity of the gas. But when there is huge increase in the mass of the gas, its velocity decreases considerably. Hence, heavier gas molecules collides the walls of container with less impact. The transfer of momentum to the walls is very less.

Option (B) is incorrect.

(C) Maximum number (no.) of gas molecules have speed distributed around the most probable speed ( $v_{\mathrm{mps}}$ ). This speed corresponds to the maximum peak of Maxwell-Boltzmann distribution curve.

There are few molecules which have very high speed (the shaded area under the curve).

Option $(\mathrm{C})$ is correct.

Van der Waals equation is $\left( {P + {{a{n^2}} \over {{V^2}}}} \right)(V - nb) = nRT$, where a is a constant whose value depends on the attraction between the gas molecules and b is the volume that is occupied by one mole of gas.

In option (A), it behaves similar to an ideal gas in the limit of large molar volumes. When the volume is very large then the attraction between the gas molecules can be neglected, so a $\approx$ 0 and the volume occupied by one mole of gas compared to large volume of container will also be neglected. So, b $\approx$ 0. Now, we can neglect a and b and the gas behaves ideally. Thus, option A is correct.

In option (B), it behaves similar to an ideal gas in limit of low pressure and high temperatures. Now, the pressure is very low. So, the attraction between the particles is negligible.

Van der Waals coefficients that are dependent on the identity of the gas but are independent of the temperature. Van der Waals coefficient depends on the attraction between the gas molecules (each of which is characteristic of a gas) and b is the volume that is occupied by one mole of the molecules. So, this option is correct. Since, molecules of Van der Waals gas exert force of attraction on each other; hence, the force which they exert on the walls of the container is less than the force exerted by it if the gas would have been ideal.

Thus, option (D) is correct.