During the weekly inspection of one of the chemical labs in a reputed research facility in Canada, the safety officials discovered a crack on the floor with mercury trapped in it $($molecular weight $=200\mathrm{.}6$ g$/$mol$).$ It is known that the mercury vapours are harmful upon exposure to anyone working in the lab.

a$)$ How much mercury would a typical employee breathe in if they work for $8$ hours a day? The average adult inhales $15$ kg$/$day of air. Assume that the mercury content in the room is exactly at the TLV of $25\backslash$mu g$/$m$3.$

b$)$ For the assumed TLV$,$ what is the corresponding mol fraction of mercury in air?

c$)$ What is the vapour pressure of mercury at $20$oC$?$ Compare the two results by using Clausius$-$Clapeyron equation $($A $=6\mathrm{.}11993,$ B $=5617\mathrm{.}6$ oR$)$ and Antoine equation?

d$)$ What mol fraction of mercury in air corresponds to equilibrium with liquid mercury? Use the number calculated above with Antoine equation.