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In a more physical sense, when one spills a corrosive substance onto one's skin, causing pain and usually a nasty scar. Some things that will burn you chemically: various acids, chlorine should probably do some damage and lye has recently been popularized by Fight Club. Basically anything on the extremes of the pH scale.

I recently experienced a mild burn on the tips of my fingers from Hydrochloric Acid and it was nothing to screw with, even on a small scale.