You should use an inert metal or you'll drive side reactions that involve the metal. Platinum wire is a favorite electrode material for this reason. You might try nichrome wire; it's a lot cheaper than platinum. As you found out, copper won't do. You were seeing the hydrogen come off on the negative electrode (4 H2O(l) + 4e- = 2 H2(g) + 4 OH-(aq)) but instead of oxygen at the positive electrode (2 H2O(l) = O2(g) + 4 H+(aq) + 4e-), you were getting Cu(s) = Cu2+(aq) + 2e- at the other electrode. The latter reaction is easier, and when the positive electrode is made of copper, it occurs preferentially.
You should set up five six-volt lantern batteries in series to supply the current. Use anything less, and the reaction occurs very slowly.
You might try doing sulfuric acid with water in one setup, and sulfuric acid with household hydrogen peroxide in the other; that way you can show how the composition of water and H2O2 differ.
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