The running engine of an automobile produces carbon monoxide (CO), a toxic gas, at the rate of 174 g CO per hour. A car is left idling in a poorly ventilated garage that is 6.0 m long, 4.0 m wide, and 2.2 m high at 20.0°C. How long would it take to build up a lethal concentration of CO of 1.000 × 103 ppmv (parts per million by volume)? Assume atmospheric pressure to be 1 atm.
First, we find out the volume of garage = 6.0 m * 4.0 m * 2.2
m
=
52.8 m3
=52800
L
CO is released at 174 g / hour.
Also in one hour, the mass of CO = 174 g
Moles of CO = Mass / molar mass
=
174 g/ 28.01 g/mol
=
6.21 moles
Assume pressure, P =1 atm
Temperature = 20 C = 293 K
R = 0.0821 L-atm-
volume
occupied = nRT / P
=6.21
* 0.0821 * 293 / 1
=149.38
L
ppm of CO by volume = ( volume of CO / Volume of garage)
*10^6
=(149.38
/ 52800 ) * 10 ^6
=
2829.16 ppm
Here we require a ppm by volume of 1000.
So 1000 ppm concentration is reached approximately in
(1000/2829.16) * 60 minutes
=21.20
minutes
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