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when you shoot black powder it produces water as a byproduct of combustion of the charcoal and saltpeter, which is absorbed by the sulphur to form sulphuric acid.
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You have the acid formation correct but are slightly off on where the water comes from. There is no H in the Charcoal (C) or the Saltpeter (Potassium nitrate KNO3) The Hydrogen (H) needed to form water (h2O) is pulled from the water vapor in the air, and there is always air in the barrel and in the cartridge too, for that matter. (or the water vapor is bonded direct, I'd have to look up the exact formula bonding) either way the result is H2SO4 sulfuric acid.
Black powder residue absorbs water from the air and HOLDS it against the steel. This is where your corrosion begins.
Priming compounds also play a part, with old "corrosive priming" being the result of chemical salts left in the bore attracting water from the air and holding it on the steel.