How many atoms do mercury vapour molecules consist of if the density of mercury vapour relative to air is 6.92? (Hg=200). The average Mass of air is 29g/mole.

Question

aaronq · Answer

We need the definition of density:  $\sf \rho=\dfrac{m}{V}$

We know:  $\sf\rho_{Hg}=6.92 \rho_{air}$, and we know the volumes are the same. 

$\sf \dfrac{m_{air}}{\rho_{air}}=\dfrac{m_{Hg}}{6.92\rho_{air}}\rightarrow m_{Hg}=\dfrac{m_{air}*6.92\rho_{air}}{\rho_{air}}=6.92m_{air}=6.92*29g=200.68 ~g$

So by comparison, we know that the average mass of Hg is 200 g, the molar mass is also 200 g/mol, so the "molecules" in the vapour are monoatomic - they are composed of one atom.