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I know electrolyzing water separates it into hydrogen and oxygen. However, I am curious, if ice is electrolyzed, could it explode? My thought process is that oxygen and hydrogen bubbles would build up in the ice, and continued electrolysis would ignite the gasses (forming water again). However, since it is contained within the ice, it could ignite explosively. Is this what would indeed happen? One way to try this might be using a tazer or bug zapper on ice. I believe this could be dangerous, and appropriate precautions would need to be taken.

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Bulk electrolysis of ice would likely not get very far. Electrolysis works in liquids because the liquid is able to transport an ion to complete the circuit. In the case of water electrolysis, water is needed to transport protons (or hydroxide, but we'll stick to just one thing).

The half reactions for electrolysis of water are

Oxidation at anode:

$$\ce{2 H2O (l) -> O2(g) + 2H+(aq) + 2e-}$$

The electrons travel through the wires and the protons through solution to the cathode where the following happens:

Reduction at cathode:

$$\ce{2H+(aq) + 2e- -> H2(g)}$$

Electrolysis requires ion mobility. In solid water this mobility is severely decreased. All water molecules are locked in a rigid hydrogen bond network. A proton can propagate slowly through this network by proton exchange, but it will be slow. Thus electrolysis will be slowed.

Also, electrolysis only occurs at the surface of the electrodes, which must provide a means for the gas to escape (whether they are on the surface of the ice or driven into the ice, gaps will exist for gas to escape).

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    $\begingroup$ You're also forgetting the very low autoionisation of water 10^-7 meaning pure water electrolyses slowly and since freezing eliminates impurities from the lattice ice tends to be very pure indeed $\endgroup$ – MY2K Jul 14 '14 at 4:08

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