Analysis of Statement 1

1. Recall the formula for kinetic energy of an ideal gas. According to the kinetic theory of gases, the average translational kinetic energy of a single molecule of an ideal gas is given by: $E_{molecule} = \frac{3}{2} k_B T$ where $k_B$ is the Boltzmann constant and $T$ is the absolute temperature.

2. Calculate the total translational kinetic energy. For a gas containing $N$ molecules, the total translational kinetic energy ($E_{total}$) is the sum of the kinetic energies of all molecules: $E_{total} = N \times E_{molecule} = N \times \frac{3}{2} k_B T$

3. Relate the number of molecules to the number of moles. The total number of molecules $N$ can be expressed in terms of the number of moles $n$ and Avogadro's number $N_A$ as $N = n N_A$. Substituting this into the energy equation: $E_{total} = (n N_A) \times \frac{3}{2} k_B T = \frac{3}{2} n (N_A k_B) T$

4. Use the relationship between gas constants. The universal gas constant $R$ is related to Boltzmann's constant $k_B$ and Avogadro's number $N_A$ by $R = N_A k_B$. Substituting this gives: $E_{total} = \frac{3}{2} n R T$

5. Apply the Ideal Gas Law. The ideal gas law states that for $n$ moles of a gas at pressure $P$ and volume $V$: $PV = nRT$

6. Combine the equations. By substituting $nRT$ with $PV$ in the expression for total energy, we get: $E_{total} = \frac{3}{2} PV = 1.5 PV$

7. Conclusion for Statement 1: The statement that the total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume is True.

Analysis of Statement 2

1. Examine the postulates of the Kinetic Theory of Gases. One of the fundamental postulates of the kinetic theory is that gas molecules are in continuous, rapid, and random motion.

2. Consider molecular collisions. As they move, these molecules constantly collide with each other and with the walls of the container. These collisions are assumed to be perfectly elastic in the ideal gas model.

3. Effect of collisions on velocity. A collision between two molecules results in a change in their individual velocities (both magnitude and direction). While the total momentum and kinetic energy of the colliding system are conserved, the velocities of the individual particles are redistributed.

4. Conclusion for Statement 2: The statement that the molecules of a gas collide with each other and the velocities of the molecules change due to the collision is True.

Analysis of the relationship between the statements

1. Evaluate if Statement 2 explains Statement 1. Statement 1, $E_{total} = \frac{3}{2} PV$, is a direct consequence of the relationship between the macroscopic properties (Pressure, Volume) and the microscopic properties (average kinetic energy of molecules). The pressure itself arises from the collisions of gas molecules with the walls of the container, not from collisions with each other.

2. The role of intermolecular collisions. While intermolecular collisions (described in Statement 2) are crucial for the gas to reach and maintain thermal equilibrium and a stable velocity distribution (like the Maxwell-Boltzmann distribution), they are not the direct cause or explanation for the specific mathematical relationship in Statement 1. The derivation of $E = (3/2)PV$ relies on relating the pressure exerted on the walls to the average kinetic energy of the molecules hitting the walls.

3. Conclusion on the relationship: Both statements are independently true facts based on the kinetic theory of gases. However, Statement 2 does not serve as the primary explanation for Statement 1. The correct explanation for Statement 1 is the link between pressure (caused by wall collisions) and molecular kinetic energy.

Final Decision

• Statement-1 is True.
• Statement-2 is True.
• Statement-2 is NOT a correct explanation for Statement-1.

This corresponds to option B.