Question

4. A student obtains a 1 Liter bottle of toluene (a liquid at room temperature) from a storage room that has dimensions of 8m x 8m x 5m. Unfortunately, the student drops the bottle of toluene on the floor and it shatters, leaving liquid toluene on the ground. The density of toluene is 0.866 g/mL and its chemical formula is C7H8.

a. If the temperature in the room is 75o F and there is a complete vaporization of the toluene into the entire volume of the room, what is the concentration of toluene vapor in units of mg/m3 ? b. What is the concentration of toluene in units of ppmv?

c. If the temperature in the room is equal to 85o F instead of 75o F, how would the responses to parts (a) and (b) change?

Answer 1

Part a

Volume of room = 8 x 8 x 5 = 320 m3

Mass of toluene = volume x density

= 1L x 0.866 g/mL x 1000 mL/L

= 866 g x 1000mg/g

= 866000 mg

Concentration of toluene vapor = 866000 mg / 320 m3

= 2706.25 mg/m3

Part b

Temperature T = 75°F

T(K) = (T(F) + 459.67) x 5/9

= (75 + 459.67) x 5/9

= 297 K

V = RT/P

= 0.0821 x 297 / 1

= 24.3837

Concentration in ppmv

= concentration in mg/m3 x 24.3837 / molecular weight

= 2706.25 x 24.3837 / 92.14

= 716.18 ppmv

Part c

If T = 85 F

T(K) = = (85 + 459.67) x 5/9

= 302.6 K

V = RT/P

= 0.0821 x 302.6 / 1

= 24.84346

Concentration in ppmv

= concentration in mg/m3 x 24.84346 / molecular weight

= 2706.25 x 24.84346 / 92.14

= 729.7 ppmv