The density of phosphorus vapour at `310^(@)C` and 775 torr is `2.64 g dm^(-3)`. What is the molecular formula of phosphorus ?

Explanation

We know that, `P = (d)/(M)RT " or " M = (d)/(P) RT`
given, `d = 2.64 g dm^(-3), P = (775)/(760) atm`,
`R = 0.0821 dm^(3) atm K^(-1) mol^(-1)`
and `T = 310 + 273 = 583 K`
So, `M = (2.64 xx 0.0821 xx 583 xx 760)/(775) = 123.9 mol^(-1)`
Atomic mass of `P = 31 g mol^(-1)`
No. of P atoms in a molecule `= (123.9)/(31) = 3.997 ~~ 4`
Hence, molecular formula of phosphorus `= P_(4)`