The Occupational Safety and Health Administration has set the limit on the maxim

Question

The Occupational Safety and Health Administration has set the limit on the maximum percentage of carbon dioxide (CO2) in air a worker can breathe at 0.500% by mole. If dry ice (solid CO2) is sublimating (becoming a gas) in a room at a rate of 0.750 mol/min, what is the minimum rate that fresh air has to be supplied to the room so that the concentration of CO2 in the room doesn't exceed 0.500% by mole? Assume the room is well mixed, and the volume of the solid dry ice does not change.

Please show detailed step-by-step and show how things are related or what makes them related and where certain numbers came from.

thank you!

Explanation / Answer

Basis : 100 mole of mixture of Air and CO2. Moles of CO2= 0.5 and moles of Air =100-0.5 = 99.5 moles

let flow rate of air = x . Given flow rate of CO2= 0.75 moles/min

flow rate after mixing = (x+0.75)

required CO2 % is 0.5%

hence %CO2= 100*0.75/(x+0.75)= 0.5

0.75/(x+0.75)= 0.5/100

0.75= 0.05*(x+0.75)

0.75*(1-0.05)= 0.05x

x=14.25 moles/min

Miniumum flow rate of air =14.25 moles/min ( any thing in excess of this air will reduced the CO2 levelse further, hence this is the minimum air flow)

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