What is the root mean square speed of oxygen molecules at -23 degrees C? Molar mass is 0.032 kg/mol and R is 8.314 J/mol K.

1. Apply the root mean square speed as the square root of 3RT divided by M. 2. Convert the temperature to kelvin: -23 + 273 = 250 K. 3. Build the numerator: 3 x 8.314 J/mol K x 250 K = 6235.5 J/mol. 4. Divide by the molar mass in kilograms per mole: 6235.5 / 0.032 = 1.949 x 10^5 m squared per second squared. 5. Take the square root: 441 m/s. 6. Oxygen is heavier than nitrogen and this sample is colder, so the answer must sit below the 519 m/s found for nitrogen at 30 degrees C. 7. Forgetting the Celsius to kelvin step would put a negative number under the square root, which has no meaning. _Source: OpenStax Chemistry (CC BY 4.0), Ch 9 "Gases", section 9.5 The Kinetic-Molecular Theory_