Statement 1: H2 and O2 have the same rms velocity at the same temperature

The statement is false. According to the kinetic theory of gases, the rms (root mean square) velocity of gas molecules is directly proportional to the square root of their temperature. It is given by the equation:

vrms = √(3kT/m)

where vrms is the rms velocity, k is the Boltzmann constant, T is the temperature in Kelvin, and m is the molar mass of the gas molecule.

Since the molar mass of H2 is 2 g/mol and the molar mass of O2 is 32 g/mol, their rms velocities will be different at the same temperature. This is because the molar mass is inversely proportional to the rms velocity. The lighter the gas molecule, the higher its rms velocity at the same temperature.

Therefore, H2 and O2 will not have the same rms velocity at the same temperature.

Statement 2: Velocity of a gas molecule is constant

The statement is false. The velocity of a gas molecule is not constant but constantly changing due to collisions with other gas molecules. Gas molecules in a sample move in random directions and collide with each other and the walls of the container. These collisions cause the gas molecules to change their velocities and directions.

However, on average, the velocity of gas molecules remains constant over time. This is because the random motion of gas molecules causes them to distribute their kinetic energy evenly, resulting in a constant average velocity. The distribution of velocities follows a Maxwell-Boltzmann distribution, which describes the probability of finding a gas molecule with a particular velocity at a given temperature.

Statement 3: Rms velocity of gas molecules is proportional to the square root of 30

The statement is incorrect. The rms velocity of gas molecules is not directly proportional to the square root of 30. As mentioned earlier, the rms velocity is directly proportional to the square root of the temperature. The square root of 30 is approximately 5.48, which does not have any direct relation to the rms velocity of gas molecules.

The rms velocity depends on the temperature and the molar mass of the gas molecules, as explained by the equation vrms = √(3kT/m). The square root of the temperature determines the average kinetic energy of the gas molecules, while the molar mass determines how fast the gas molecules move at that temperature.

Therefore, the rms velocity of gas molecules cannot be determined solely based on the square root of 30.