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I tried putting two extremities of a 6 volts battery into water. With salty water, bubbles appear close to the positive end.

With unsalted water, what looks like a thin white foam starts to squirt from the positive and and moves through the bottom of the glass.

What am I seeing there?

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You are seeing the Electrolysis. Namely, separation of water into hydrogen and oxygen. Salty water is conducting better than a non-salty one, so you see a stronger reaction in it. But the non-salty one is still impure (it still has some minerals dissolved), so some conductivity exist in it too, but the reaction is weaker.

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    \$\begingroup\$ The exact physics/chemistry of the process is out of my competence. Please take a look at the Wiki link I provided, it might give some insights. \$\endgroup\$ – Eugene Sh. Aug 20 at 21:08
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    \$\begingroup\$ Thank you. Maybe this was a question better suited for the "physics" stack exchange rather than this. \$\endgroup\$ – Dakatine Aug 20 at 21:10
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    \$\begingroup\$ You can find more questions about Electrolysis on chemistry.stackexchange.com \$\endgroup\$ – TEMLIB Aug 20 at 21:10
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    \$\begingroup\$ BTW, it's hydrogen on the positive terminal and oxygen on the negative. You will see more hydrogen than oxygen generated (by volume) because of their proportions in the water. Also the oxygen electrode is going to get oxidized quickly, so if you use something like iron nails you will quickly see a green goo appearing.. \$\endgroup\$ – Eugene Sh. Aug 20 at 21:12
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    \$\begingroup\$ @EugeneSh. The Wikipedia page on the subject says the opposite. I am inclined to believe the Wiki page because I know that hydrogen ions (a.k.a., "protons") in water are positively charged, and so they would naturally migrate toward the negative terminal. \$\endgroup\$ – Solomon Slow Aug 20 at 21:33

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