The easiest way to remove ammonia, nitrite or nitrate from an aquarum is by doing a 75% water change and gravel cleaning the substrate each day until the levels are on 0ppm.
Make sure any new water is free of chlorine/ chloramine before it's added to the tank.
Check your tap water for ammonia, nitrite and nitrate too. If you have x amount of nitrate in the tap water, then that will be the lowest level of nitrate in the tank.
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Ammogon and other white granules that remove ammonia do actually remove ammonia from water. However, they also prevent the beneficial filter bacteria from growing and this prevents the aquarium filter from cycling. Filter cycling is simply where the filter develops good bacteria that eat ammonia and convert it in nitrite, and more good bacteria eat the nitrite and convert it into nitrate. You get rid of nitrates with water changes.
The Ammonia removing granules can become full very quickly and even if you replace them once a month or whenever, you can end up with an ammonia reading in the tank because the granules can no longer adsorb any ammonia, and the filter isn't cycled.
A lot of companies put a bag of Ammogon and Carbon in with their filters so it looks like you have more filter media, and as a sales ploy. They recommend changing the carbon and ammonia removing granules on a regular basis. This is good for their pocket but not yours, and it doesn't help the aquarium.
Yes carbon can help remove chemicals and heavy metals from water, but most tap water is reasonably safe and free from chemicals so carbon isn't normally needed.
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The best filter media/ materials for a power filter are sponges. You can buy all sorts of filter sponges from pet shops or online, and these hold good bacteria, as well as trapping gunk.
Power filters should be cleaned at least once a month and every 2 weeks is even better. However, new filters should not be cleaned for at least 6- weeks so the good bacteria can settle in. The only time you clean a new filter is if/ when the flow rate drops, then clean it.
Filter media should be washed out in a bucket of tank water and re-used. The bucket of dirty water can be tipped onto the garden/ lawn.
The filter case can be washed out under tap water.
The impellor assembly (magnet with plastic blades in the motor) can also be washed under tap water. When cleaning the impellor assembly be careful not to lose the rubber grommets or plastic washers on each end of the steel shaft that runs through the middle of the magnet.
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I would remove the carbon and ammonia granules, pads and replace them with sponges. Monitor the ammonia and nitrite levels over the next month or two and do a 75% water change and gravel clean the substrate any day you have an ammonia or nitrite reading above 0ppm, or a nitrate reading above 20ppm.
In about 4-6 weeks the filter will have cycled and you can do a water change and gravel clean once a week and you shouldn't have any more ammonia problems.