Calculate the root mean square, average, and most proable speeds of `H_(2)` molecules. The density of the gas at `101.325 kPa` is `0.09 g dm^(-3) (0.09 kg m^(-3))`. Assume ideal behaviour.

Explanation

`u_(rms)=sqrt((3RT)/(M))=sqrt((3PV)/(M))=sqrt((3P)/(d))={(3(101.325xx10^(3)Pa))/((0.09kg m^(-3)))}^(1//2)`
`=1838 m s^(-1)`
`u_(av)=sqrt((8RT)/(piM))=sqrt((8PV)/(piM))=sqrt((8P)/(pid))={(8(101.325xx10^(3)Pa))/(3.14(0.09kg m^(-3)))}^(1//2)`
`=1694 m s^(-1)`
`u_(MP)=sqrt((2RT)/(M))=sqrt((2PV)/(M))=sqrt((2P)/(d))={(2(101.325xx10^(3)Pa))/((0.09kg m^(-3)))}^(1//2)`
`=1501 m s^(-1)`