How much air could an activated charcoal bag or baking soda box actually purify / deodorize? Someone I know recently bought a set of small stylish and expensive cloth bags (roughly paperback book sized) filled with activated bamboo charcoal, that you place in a room and it purportedly purifies the air of the room and eliminates odors. Similar claims have been made for open boxes of baking soda in a refrigerator.
My initial reaction is skepticism, mostly from a possibly-wrong intuition that the physics don't make sense; I also don't see any studies of the effectiveness of either product, and web searches just reveal a lot of SEO affiliate pages, blog marketing and the like. And this seems the type of situation that would be rife with confirmation bias ("I definitely think I smell a difference"). 
So down to the physics of it - in, say, a 4 x 4 x 3 meter (48 m^3) room, with a small bag of charcoal (say 12 x 12 x 6 cm, or 864 cm^3), how long would it take for say 95% of the air to pass through the bag due to gas diffusion, typical air convection, etc.? Or looked at another way, how much air volume would the bag "process" per hour? The interior is little charcoal pieces with an apparently high surface area. If a stinky carpet covering the floor of the room were off-gassing a given volume of gas per minute, could the bag keep up?
 A: This answer as far my knowledge goes , is from surface chemistry . This depends on the gases present in the room and the surface covered . The surface phenomena suggests that gases which can easily be liquefied can easily be adsorbed on its surface . Now try applying the equation ,
ΔG=H-TΔS
This suggests that adsorption of gas on black charcoal bag ( which in your case is a dirty smelling gas from the carpet) is an exothermic process . Applying Le-Chatelier's principle for an exothermic process you would require quite a constant cool temperature . Also ΔH of adsorption is negative and when a gas is adsorbed on adsorbent's surface it would cause to reduce its entropy ( ΔS) and take a negative sign .Adsorption is thus accompanied by decrease in enthalpy as well as decrease in entropy .This would give the (TΔS) a positive sign which would reduce the negative(ΔH) . The gas would continue to adsorb on bag until all of its charcoal surface is occupied and until (ΔG) is zero . The process would stay spontaneous until (ΔG) is negative . 
If you want to know how much mass of gas can be adsorbed on charcoal , it can be calculated from Freundlich's Adsorption Isotherm ( constant temperature ) .
This is all if you experiment it in a lab on a small sample . For a large room this may or may not be true . I would say this might work a 50-50.You need a very large amount of charcoal and more bags with all thermodynamic conditions satisfying the phenomenon .
