Question

The density of phosphorus vapour at ${310}^{\circ }C$ and $775torr$ is $2.64gd{m}^{-3}$.. What is the molecular formula of phosphorus?

Answer 1

We know that, $P=\frac{d}{M}RT$ or $M=\frac{d}{P}RT$
Given, $d=2.64gd{m}^{-3}$

$P=\frac{775}{760}atm$

$R=0.0821d{m}^{3}atm{K}^{-1}mo{l}^{-1}$
and $T=310+273=583K$

So, $M=\frac{2.64\times 0.0821\times 583\times 760}{775}=123.9gmo{l}^{-1}$
Atomic mass of $P=31gmo{l}^{-1}$
No. of $P$ atoms in a molecule $=\frac{123.9}{31}=3.997\approx 4$
Hence, molecular formula of phosphorus $=P_4$