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Calculate the volume of air needed for the combustion of 1 kg of carbon.

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Combustion of carbon would give carbon dioxide:  C + O2 → CO2
 
The general plan would be to start with the mass of carbon, then calculate the moles of carbon, then use the mole ratio in the balanced equation to find the moles of carbon dioxide.
 
kg C → g C → mol C → mol CO2
 
At this point it is necessary to know the pressure and temperature of the container that would hold the CO2, which is a gas.  If we assume that CO2 is an ideal gas under "STP conditions" (standard temperature and pressure; P = 1 atm and T = 273 K), then we can use the fact that one mole of an ideal gas at STP has a volume of 22. 4 liters, and the final conversion is 
 
mol CO2 → Liters CO2
 
Given the above plan, the calculation goes like this:
 
1 kg C x (1000 g C/1 kg C) x (1 mol C/12.01 g C) x (1 mol CO2/1 mol C) x (22.4 L/1 mol CO2)
 
   = 2000 Liters