Calculate the root mean square speed of a nitrogen molecule at 30 degrees C. Molar mass is 0.028 kg/mol and R is 8.314 J/mol K.

1. Use the root mean square speed as the square root of 3RT divided by M. 2. Convert the temperature to kelvin: 30 + 273 = 303 K. 3. Use molar mass in kilograms per mole, since R here carries joules: 28.0 g/mol becomes 0.028 kg/mol. 4. Build the numerator: 3 x 8.314 J/mol K x 303 K = 7557 J/mol. 5. Divide by the molar mass: 7557 / 0.028 = 2.70 x 10^5 m squared per second squared. 6. Take the square root: 519.5, which is reported as 519 m/s. 7. Leaving the molar mass in grams per mole would give a value about 32 times too small, which is the unit trap in this calculation. _Source: OpenStax Chemistry (CC BY 4.0), Ch 9 "Gases", section 9.5 The Kinetic-Molecular Theory_