Carbon removes a class of material called dissolved organic compounds (DOC). These compounds are produced by many different processes in the aquarium. The two major categories of organic substances that carbon removes are tannins and phenols. Tannins give the water a yellow-brown color. They are produced mainly by the breakdown of plant material, but there are other sources too.
Phenols give a fish tank that characteristic "fishy" smell.
Furthermore, some types of DOC can be degraded by bacteria in the water via a process called mineralization. Heterotrophic bacteria convert DOC into substances such as ammonia and carbon dioxide and consume vital oxygen in the process. Furthermore, some DOC is released by algae and other organisms as part of their normal bodily function. In many cases activated carbon can be used to adsorb some of these compounds but carbon does not get everything.
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