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?