Does Spilled Mercury Exceed EPA Air Quality Limits in the Lab?

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The Answer is "Yes", but I need to show HOW. Plz Help.

Homework Statement


A researcher breaks a thermometer & spills most of the mercury in it on the floor of a laboratory that measures 15.2 m Long, 6.6 m Wide, & 2.4 m High. Does the concetration of mercury exceed the EPA air quality regulation of .050 mg Hg/m3 of air? (Temp of the rm is 20 degrees celsius; the vapor pressure of mercury at this temp is 1.7 x 10 to -6th atm.)


Homework Equations


PV=nRT & LxWxH


The Attempt at a Solution


LxWxH=240.77 m3 x 100 to the 3rd power=2.4x10 to the 8th cm3 x 1mL/1cm3=2.4x10 to the 8th/1000 L = 2.4 x 10 to the 5th L
Hg = 200.59g/mol
n=PV/RT (1.7 x10 to -6th)(2.4 x 10 to the 5th)/ (.0821 Latm/mol K) (293K) = 1.4 x 10 to the 3rd mol

I just don't know where to go from here. I know the answer is 14.1 mg/m3, but I can't figure out how the teacher got there. HELP PLEase. Thank you in advance.
 

Discussion

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You have not said how much mercury is spilled.
 


My professor did not offer up that information in the question. A couple other students in my class were able to solve it with the information given, but I am at a loss. I appreciate you trying :)
 


Think about it backwards. You need to wind up with a density of mercury vapor. What quantities do you need in order to calculate that density?
 


Check your calculation for n. I think your answer shown is much too large.