Final answer:
The rms speed of an oxygen molecule in air at 0 degrees Celsius, using the rms speed formula and converting the molar mass to kg/mol, is calculated to be 464 m/s which corresponds to option (a).
Step-by-step explanation:
To calculate the rms speed (root mean square speed) of an oxygen molecule in air at 0 degrees Celsius, we use the formula for rms speed given by:
Urms = √(3kT/M)
where k is the Boltzmann constant (1.38 × 10-23 J/K), T is the temperature in Kelvin, and M is the molar mass of the gas in kilograms per mole (kg/mol). To match the units, the molar mass of oxygen (32.0 g/mol) must be converted to kg/mol by dividing by 1000, thus 0.032 kg/mol.
At 0 degrees Celsius (273 K), the calculation is as follows:
Urms = √(3 × 1.38 × 10-23 J/K × 273 K / 0.032 kg/mol)
After performing the calculation, the value is thus option (a) 464 m/s.