Charcoal is carbon. Activated charcoal is charcoal that has been treated with oxygen to open up millions of tiny pores between the carbon atoms.
The use of special manufacturing techniques results in highly porous charcoals that have surface areas of 300-2,000 square metres per gram. These so-called active, or activated, charcoals are widely used to adsorb odorous or coloured substances from gases or liquids.
The word adsorb is important here. When a material adsorbs something, it attaches to it by chemical attraction. The huge surface area of activated charcoal gives it countless bonding sites. When certain chemicals pass next to the carbon surface, they attach to the surface and are trapped.
Activated charcoal is good at trapping other carbon-based impurities ("organic" chemicals), as well as things like chlorine. Many other chemicals are not attracted to carbon at all -- sodium, nitrates, etc. -- so they pass right through. This means that activated charcoal will remove certain impurities while ignoring others. It also means that, once all of the bonding sites are filled, activated charcoal stops working.
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PS you can buy activated charcoal from pet shops as it is used to fish tanks
Activated charcoal when dirty can be encouraged to release the dirt (recharged) by removing it from the water and placing it in a strong salt water solution for a couple of hours