Question

Given molecular weight of hydrogen molecule is `M = 2.016 xx 10^(-3) kg//mol`. Calculate the root-mean-square speed of hydrogen molecules `(H_(2))` at `373.15 K (100^(@) C)`.

Answer 1

The mass of an `H_(2)` molecule may be calculated from the molecule weight as
`m = (M)/(N_(0)) = (2.016 xx 10^(-3) kg//mol)/(6.02 xx 10^(23) mol^(-1)) = 3.35 xx 10^(-27) kg`
Then `(1)/(2) mv_(rms)^(2) = (3)/(2) kT`
`v_(rms) = sqrt((3 kT)/(m)) = sqrt((3(1.38 xx 10^(-23))(373.15))/(3.35 xx 10^(-27))) = 2.15 km//s`