There are two different common types of decomposition- aerobic (with oxygen) and anaerobic (without oxygen). If something is in contact with the air, it will most likely decompose aerobically, with the bacteria releasing CO2 (mostly) as waste. However, in landfills, trash is pilled up and compacted, and oxygen can’t reach the bottom of the trash pile. Different types of bacteria work on decomposing this stuff, and they digest anaerobically (no oxygen) so they instead usually expel their waste as methane, CH4.
Trash in landfills contains quite a bit of organic waste (food scraps, paper, etc.). Bacteria and fungi eat that and release methane as they break it down.
A landfill is nothing but buried trash. That still gets broken down and methane builds up inside. It’s not uncommon to shove a pipe down to capture the methane, or at least bring it up and burn it.
Most organics are made up of Carbon, Oxygen, and Hydrogen. For an example sugar is 6 Carbon, 12 Hydrogen, and 6 Oxygen. In a person this would be combined with 6 more Oxygen to produce 6 water (2 hydrogen and 1 oxygen) and 6 carbon dioxide (1 carbon and 2 oxygen).
Since landfills are sealed there isn’t oxygen available for bacteria, so they break down that sugar in 3 carbon dioxide and 3 methane (3 carbon and 4 hydrogen).
Because there are millions of tons of trash and lots of food bacteria can produce A LOT of methane.
I prefer how yeast deal with sugar though without oxygen.
Another thing to keep in mind is there are two main ways to decompose things. Either with oxygen or without. When microbes use oxygen in decomposition they produce CO2 as a byproduct. When there is no oxygen microbes produce methane. Because landfills are generally densely packed there is no room for air to penetrate the piles of trash and that means we get methane as our byproduct.
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