A sales person comes to the door selling a service designed to check chimney rot

Question

A sales person comes to the door selling a service designed to check chimney rot. He explains that if the CO2 content of the gases leaving the chimney rises above 15 mole %, it is dangerous to your health, is against the city code, and causes your chimney to rot. On checking the flue gas from the furnace, he finds it is 30 mole % CO2. Suppose that you are burning natural gas which is about 100% CH4, and that the air supply is adjusted to provide 130% excess air, is his analysis of your flue gas correct?

Based on 1 mol/hr methane feed, calculate the actual percentage of CO2 in the outlet gas from the furnace assuming that complete combustion takes place & process is steady state. 130% excess air means that 130% of the air required for complete combustion of CH4. The chemical reaction is CH4 + 2 O2 -> CO2 + 2 H2O

Explanation / Answer

CH4 + 2 O2 -> CO2 + 2 H2O

1 mol methane needs 2 mol oxygen for complete combustion

assume that you begin with 100 moles of methane

then you will get

100 moles of carbon dioxide and 200 moles of water vapor as product

given air supplied 130% of what is needed for complete combustion

oxygen needed for complete combustion = 200 moles

oxygen supplied = 1.3*200 = 260 moles

out of 260 moles 200 moles are consumed and 60 moles go to product side

and along with 260 moles of oxygen (79/21)*260 = 978 moles of nitrogen is also supplied which remain un-reacted

hence the product side has

100 moles of carbon dioxide

200 moles of water vapor

60 moles of oxygen

978 moles of nitrogen

total moles of gases in product side = 1338

mole% of CO2 = (100/1338)*100 = 7.474%

definitely that sales person is lying

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