The density of the vapour of a substance at `1 atm` pressure and `500 K` is `0.36 kg m^(-3)`. The vapour effuses through a small hole at a rate of `1.33` times faster than oxygen under the same condition.
(`a`) Determine (`i`) molecular weight, (`ii`) molar volume (`iii`) compression factor(`Z`) of the vapour, and (`iv`) which forces among the gas molecules are dominating, the attractive or the repulsive?
(`b`) If the vapour behaves ideally at `1000 K`, determine the average translational kinetic energy of a molecule.

Explanation

(a) (i) `(r_("vapour"))/(r_(O_(2))) = sqrt((M_(O_(2)))/(M_("vapour")))`
`1.33 = sqrt((32)/(M_("vapour")))`
`M_("vapour") = 18.1`
(ii) Molar volume `= ("Molar mass")/("Density")`
`= (18.1)/(0.36) = 50.25 xx 10^(-3) m^(-3)`
(iii) Compressibility factor, `Z = (PV)/(RT) = (101325 xx 50.25 xx 10^(-3))/(8.314 xx 500)`
`= 1.225`
(iv) `Z gt 1` shows that repulsive forces are dominant
(b) Translational KE per molecule
`= (3)/(2) xx (R)/(N) xx T`
`= (3)/(2) xx (8.314)/(6.023 xx 10^(23)) xx 1000`
`= 2.07 xx 10^(-20) J`