I am wondering what kinds of materials that are released by Earth into space due to natural processes.
If possible, what are their approximate rates in kg per day or year?
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Hydrogen and Helium, mainly, at rates of 3000g and 50g per second, respectively. The process is called "Jeans Escape", and is due to the atoms being light enough to gain a significant velocity from radiation. The effect is really small - 3Kg of Hydrogen and 50g of Helium per second is tiny compared to the mass of the atmosphere. Also notice how big a disparity between H and He - He is just 4 times more massive, but is lost at a rate 60 times slower. Most other molecules are too massive to be lost this way.
If you are asking about the future, though, things get interesting. The escape of mass of the atmosphere is due to the sun. When the sun gets significantly brighter, then you will lose many more things. Like water and other massive particles. You can read more about Jeans escape here.
There is one other process that may also happen, but we have no hard evidence for it at this time. A large impact can throw material off of Earth and send it into space. This is how we think the moon formed, so in terms of how much mass - a lot! However, this requires a huge impact, which we haven't had for a while, so there is no "mass per year" number that makes sense. It is thought that maybe Apollo astronauts found one such meteorite.