Question

The density of phosphorus vapours at ${310}^{\circ }\text{C}$ and 775 torr is $2.64{\text{g dm}}^{-3}$. What is the molecular formula of phosphorus?

• A. $P_2$
• B. $P_4$
• C. $P_6$
• D. $P_8$
  

Answer 1

The correct option is B $P_4$

We know that, $P=\frac{d}{M}RT$ or $M=\frac{d}{P}RT$
Given: $d=2.64{\text{g dm}}^{-3};P=\frac{775}{760}\text{atm}$
$R=0.0821{\text{dm}}^3{\text{atm K}}^{-1}{\text{mol}}^{-1}$
and $T=310+273=583\text{K}$
So, $M=\frac{2.64\times 0.0821\times 583\times 760}{775}=123.9{\text{g mol}}^{-1}$
Atomic mass of $P=31{\text{g mol}}^{-1}$
No. of $P$ atoms in a molecule $=\frac{123.9}{31}=3.997\approx 4$
Hence, the molecular formula of phosphorus $=P_4$