A full 1.5 gallon glass container of benzene (specific gravity of 0.88) shatters

Question

A full 1.5 gallon glass container of benzene (specific gravity of 0.88) shatters on the floor and quickly evaporates* in a room that has dimensions of 50.0 ft. x 100.0 ft. x 10.0 ft. and extremely poor ventilation (i.e. non-existent).

What would the approximate benzene concentration be in this room after the solvent has completely evaporated and equilibrated (in mg/m3)?

Also, what approximate mass of benzene (in micrograms) might a person inhale if trapped inside this room for 4.5 hours, assuming their breathing rate was 8.0 liters per minute?

A full 1.5 gallon glass container of benzene (specific gravity of 0.88) shatters on the floor and quickly evaporates* in a room that has dimensions of 50.0 ft. x 100.0 ft. x 10.0 ft. and extremely poor ventilation (i.e. non-existent).

What would the approximate benzene concentration be in this room after the solvent has completely evaporated and equilibrated (in mg/m3)?

Also, what approximate mass of benzene (in micrograms) might a person inhale if trapped inside this room for 4.5 hours, assuming their breathing rate was 8.0 liters per minute?

Explanation / Answer

1ft = 0.3048 m

So the volume of the room = 15.24 X 30.48 X 3.048 m3 = 1415.84 m3

1.5 gallon = 5678.12 mL

density = specific gravity = 0.88 mg/mL

So mass og benzene = 4996.74 mg

So  approximate benzene concentration be in this room =  4996.74 mg / 1415.84 m3 =3.53 mg/m3.

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In 4.5h total breath = 8.0 liters X 270 = 2160 liter

1m3 = 1000 liter

So, total breath = 2.16 m3 volume.

In 1m3 bezene present = 3.53 mg

So approximate mass of benzene (in micrograms) might a person inhale = 3.53 X 2.16 X 103 = 7.62 X 103 microgram.

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