This by no means is conclusive as it will depend on the type of carbon filter you use and I am not going to give detail on every different type and simply generalise on the subject. I suggest that you check with the manufacturer of your filter first and then treat your water appropriately.
Activated carbon filters remove some and reduce many volatile organic chemicals (VOC), pesticides and herbicides, as well as chlorine, benzene, trihalomethane (THM) compounds, radon, solvents and hundreds of other man-made chemicals found in your tap water.
Some activated carbon filters are moderately effective at removing some, but not all, heavy metals. In addition, densely compacted carbon block filters mechanically remove particles down to 0.5 micron, including Giardia and Cryptosporidium, turbidity and particulates.
Although some iron, manganese, and hydrogen sulfide will be removed by these higher quality activated carbon filters, a manganese greensand iron reduction filter is generally preferred to remove these contaminants as the effectiveness of carbon filter against iron and manganese is generally short-lived if the contaminant concentration is high.
Carbon filters are NOT generally successful at removing dissolved inorganic contaminants or metals such as minerals/salts (hardness or scale-causing contaminants), antimony, arsenic, asbestos, barium, beryllium, cadmium, chromium, copper, fluoride, mercury, nickel, nitrates/nitrites, selenium, sulfate, thallium, and certain radio nuclides. Removing these contaminants requires either a reverse osmosis water filter system or a distiller, which is not recomended for an aquarium situation.
Many will claim all sorts of wonderfull things they can remove and one of the major misunderstandings is the removal of Chlorine (Cl) or I should say the reduction of Chlorine as it really can not be removed totally as Cloramine is still left behind. The make up of Chlorine is basically Ammonia and Cloramine.
Chloramine (monochloramine) a toxic substance (NH2Cl) created by the chemical reaction of ammonia in your tank and sodium hypochlorite (chlorine bleach) left over in your tap water, even if filtered through carbon filters. This reaction is more potent when in an alkaline situation such as high pH tanks.
You can buy catalytic carbon filters specifically designed for Chloramine removal which would prove better than charcoal (carbon) based filters. You could always use one of these to directly supply water from your tap to your tank, but you will have serious nitrate and nitrite issues. The Chlorine from the tap water would react to the ammonia in your water and produce Chloramine and then the filter would remove the Chloramine. Definately NOT recommended.
Not to mention the elusive Nitrate and Nitrite, as it is very present in tap water filtered or not. So effectively, if you are adding any tap water to your aquarium it must be treated before you put it in. To remove Chlorine you can boil the water. You can remove Chloramine (NH2Cl) with Sodium metabisulfite (Na2S2O5) a sterilizer. However the use of Sodium metabisulfite is NOT recommended as it produces sulfur dioxide (SO2) when put in water. Great for sterilizing bottles for home brews though.
What choices have you got?
Leave it sit:
Chlorine will disapate in 2 to 3 days sitting at room temp. To speed this "aging" process up you can add an aeration to the bucket or drum to agitate the water and help gass off some of the Nitrate at the same time.
Splash some chemical in it:
Chemical De-Chlorinators work well though if you go the basic one Sodium thiosulfate (Na2S2O3) then you are still going to be left with a bunch of Ammonia. eg:
EPA Guidelines set a maximum allowed level of Chlorine of 4ppm. Most water supplies target 2-4 ppm Chlorine. Note that 4ppm of Chlorine is actually 5.8ppm Chloramine. (The Chlorine is 69% of the chloramine molecule, ammonia is the other 31%) So, with a possible 5.8ppm Chloramine, you have 4ppm Chlorine, and 1.8ppm ammonia.
There are De-Chlorinators (chemical) that will also convert Ammonia to Ammonium (NH4+ non toxic) this is conjugate acid of the base ammonia and simply has an extra Hydrogen ion. Ammonium in an aqueous solution (your tank) will disolve to create Ammonium hydroxide (NH4OH) which is yet another compound of Ammonia and is still a weak acid. Because Ammonium is considered a weak acid it will then lower your pH. The results of adding a product called "Seachem Prime" that will achieve the above, will differ at different pH levels so be sure to check that first before application.
Side Note - As far as dealing with the Ammonia, if you are experienced enough, you can always add some sulfuric acid to calcium phosphate rock to create some Phosphoric Acid to mix with your Ammonia thereby converting it to Ammonium Phosphate which will feed your bacteria used in the bio-oxidation process to create carbon dioxide and water. But that is an entirely different conversation.
My apologies. I am getting side tracked. Yes it is good to use a carbon filter (preferably GAC granulated activated carbon) though it is not recommended to rely apon it totally as the Chlorine levels in your tap water will change quite often. Not to mention that some treatment plants are starting to use Chloramine instead of Chlorine, as it is more stable in comparison. So if that happens and you dont know about it your crayfish and fish for that matter will die.
By all means use the carbon filter on your tap water. However I will recommend that you also let it sit for at least 24 hours at room temp with an air stone in it. Just to be sure. I would even go so far as to filter the water then add something like "Seachem Prime" and then let it sit aerated for 24 hours. But I am pedantic when it comes to chemical reactions in water and the fewer I have to deal with the better.
