Among the given gases d: H₂S would have the highest root mean square velocity at 400 K due to its lowest molar mass.
The root mean square velocity of a gas is directly proportional to the square root of its temperature and inversely proportional to the square root of its molar mass.
To determine which gas has the highest root mean square velocity at 400 K, we need to consider the molar masses of the gases and compare them.
a) N₂O₄: Molar mass = 92.02 g/mol
b) CO₂: Molar mass = 44.01 g/mol
c) SF₆: Molar mass = 146.05 g/mol
d) H₂S: Molar mass = 34.08 g/mol
Since the temperature is constant (400 K), the gas with the lowest molar mass will have the highest root mean square velocity.
Comparing the molar masses, we can see that H₂S has the lowest molar mass (34.08 g/mol) among the given gases. Therefore, H₂S would have the highest root mean square velocity at 400 K.
Therefore, among the given gases d: H₂S would have the highest root mean square velocity at 400 K due to its lowest molar mass.