Final answer:
The rms speed of a molecule in an ideal gas increases with the square root of the temperature and decreases with the square root of the molecular mass. Therefore, if the temperature is doubled and diatomic gas molecules dissociate, the rms speed will increase more than by temperature alone due to the reduced mass of the resulting atoms.
Step-by-step explanation:
The root-mean-square (rms) speed of a molecule in an ideal gas is crucial for understanding gas behavior. The rms speed is the square root of the average of the square of the speed (u²). It is also known that the rms speed depends on the temperature and the mass of the gas molecules. For a gas at constant temperature, the rms speed is directly proportional to the square root of the absolute temperature and inversely proportional to the square root of the molecular mass. Therefore, when the temperature is doubled, the rms speed usually increases. However, if the diatomic gas dissociates into two atoms when the temperature is doubled, then the mass of each particle is effectively halved, and consequently, the rms speed will increase more than it would by temperature alone since it is inversely proportional to the square root of the mass.
Referring to a Maxwell-Boltzmann distribution graph comparing the molecular speeds at two different temperatures, if statement b states that 'The rms speed at T₁ is higher than that at T₂,' it is false given that T₂ represents a higher temperature. This is because rms speed should be higher at a higher temperature if no molecular dissociation occurred. The average kinetic energy of the molecules, represented by ½mv², would also increase with temperature, having a direct impact on both the average kinetic energy and the rms speed of the gas molecules.