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I have a daughter that has bad allergies. To help keep her allergies in check I use an electrical air purifier to keep the air in my house clean and filtered. I heard that houseplants could in effect do the same thing.
If that is true are certain plants better for cleaning the air than others? Also, are there any guidelines for how many plants would be needed for a certain square footage?
Almost any plant will pick up particulates on its leaves (as permaculturists will tell you this is actually one of the functions of a leaf) so some things to think about would be:
Can you spray the plant down periodically? Most of the time, leaves function in part to trap particulates that can then be channeled down to be food for the plant (this comes up with regard to hedge rows and manure control from time to time). Being able to spray down a plant in simulated rainfall is likely to be helpful for a plant to maintain this role. so if you can water it in a way in which the leaves get washed that would be ideal.
This answer is tailored on the assumption that you are looking specifically at pulling particulate allergens from the air. Other areas may prove different.
As a side note to the accepted answer (I don't have enough reputation to comment), most, if not all, of the plants on the NASA list are poisonous to cats and dogs. So if you have animals to worry about as well, choose wisely. Aside from that it is a great list.
I have found a page saying that a spider plant is good for cleaning the air and is non-toxic to cats.