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say i used electrolysis to extract hydrogen from water, then froze the hydrogen into a liquid and then again used electrolysis. What would happen ?

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... then (condense) the hydrogen into a liquid and then again used electrolysis. What would happen ?

Nothing. You already separated the hydrogen and gave it's electron back to it. Hydrogen will not accept another electron (it's not stable).

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Just to clarify - you mean $H_2^-$ is not stable, right? $H_2$ is very stable! – levitopher Jul 19 '14 at 5:46
@levitopher Actually, I was thinking of $H^-$. – LDC3 Jul 19 '14 at 5:47
Ah I see. Well either way stability is a problem, but my impression is that hydrogen from electrolysis was molecular in nature. – levitopher Jul 19 '14 at 5:51
@levitopher Electrolysis converts $H^+$ to $H^.$, a reactive entity and the most likely entity to react with on the electrode is either another $H^.$ or the electrode. The reaction on the electrode will only last as long as there is not another $H^.$ to react with. Of course $H^.$ + $H^.$ gives $H_2$. – LDC3 Jul 19 '14 at 5:58

Assuming you could get down to liquid hydrogen and figure out how to do electrolysis at 33 seems like the conductivity of molecular hydrogen would be quite low, and nothing would happen. Similar to the case of very pure water.

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