If the rms speed of nitrogen molecules is 490 ms−1 at 273K, find the rms speed of hydrogen molecules at the same temperature -
1830 m/s
The molecular weight of nitrogen (N2) is 28 g mol−1 and that of hydrogen (H2) is 2 g mol−1. Let m1 and m2 be the masses, v1 and v2 be the rms speeds of a nitrogen molecule and a hydrogen molecule respectively. Then m1=14m2. Since the kinetic energies of the hydrogen and nitrogen molecules will be the same at the same temperature -
12m1v21=12m2v22
or, v2=v1√m1m2=490 m s−1×√14=1830 m s−1.