Calculating Root-Mean-Square Speed

Calculating a gas's root-mean-square speed means substituting its molar mass in kilograms and the kelvin temperature into urms = the square root of (3RT divided by molar mass).

For nitrogen gas (N2, molar mass 28.02 g/mol) at 30 °C, first list the known quantities in the units the equation needs: R = 8.314 J/mol·K, T = 303 K, and M converted from 28.02 g/mol to 0.02802 kg/mol. Substituting gives urms = √(3 × 8.314 J/mol·K × 303 K ÷ 0.02802 kg/mol). Since a joule equals one kilogram-meter-squared per second-squared, the units under the square root reduce to meters squared per second squared, leaving units of meters per second after taking the root. Carrying the arithmetic through yields urms ≈ 517 m/s, a result in the few-hundred-meters-per-second range expected for a light gas near room temperature, with a positive value and speed units, confirming the answer is physically sensible.