Can you reverse the polarity of a lead-acid battery

A co-worker tells me that he (inadvertantly) reversed the polarity of one of his tractor batteries. Apparently, it drained flat over the winter, and when he hooked up his charger, he conected it to the wrong terminals. The battery now seems to have a full charge, but the wrong polarity. So he simply reversed the leads.
FWIW, this is one battery of a pair in series for his 24V system. They were charged separately, and the other battery was charged correctly. They are now reconnected, with the normal battery normally connected, and the other reversed.
Now, from what I’ve read, the plates are of different material, e.g. lead and lead peroxide. Did he just form a thin layer of lead over the lead peroxide, or what? My knowledge of electrochemistry is limited, but ready to be expanded…

Yes, it’s possible, but it’s not terribly good for the battery, and won’t provide the same capacity that it’s rated for. However, the polarity can be reset to the proper way by fully discharging the battery, then charging it with the proper polarity. I’ll leave it to someone more conversant with the chemistry involved to discuss it.

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OK, does anyone have the electro-chemical answer? How does this happen?
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Sure, no problem. Just patch the tachyon emitters into the impulse manifold and run the whole thing through the deflector array. Piece of cake. Note, however, that it may cause your Klingon crewmembers to begin aging in reverse prior to being transported back in time to Victorian England.

Chemistry isn’t one of my strengths, but this is how I understand it to work:

A lead acid battery consists of one plate which is made of lead and another plate which is made of lead dioxide, with sulfuric acid in the middle. Lead (Pb) combines with sulfuric acid (SO4) to make lead sulfate (PbSO4). On the other plate, lead dioxide combines with sulfuric acid and hydrogen ions to also make PbSO4, plus water. When you charge the battery, you are reversing the reaction to basically seperate lead on one plate and lead dioxide on the other. You must have had the battery fairly well discharged so that both plates were basically lead sulfate, at which point the battery usually won’t charge, but you must have had enough lead on one plate and lead dioxide on the other to be able to reverse charge it. Once you got the reverse reaction going, the plates just inevitably seperated into lead and lead dioxide via the normal charging process.