Air is approximately 21% #O_2# and 78% #N_2# by mass. What is the root-mean-square speed of each gas at 273 K?
The relation between molecular kinetic energy and temperature is given by the equation
Solving this for
where the final relation is given in terms of the gas constant
Inserting values gives
and using 0.028 kg for nitrogen
Note that the molar mass had to be changed to kg per mole in order to be consistent with the other units in the equation.