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First of all, what is electrolysis? Electrolysis is where you pass electricity through an electrolyte, in this case salt water. When this is done, the water appears to be boiling, even though it's not very hot. Well, what's happening is much cooler and a lot different than boiling water. Let me explain...
This reaction is actually a decomposition reaction. However, the result depends on the type of material you use for the electrodes. For instance, using paper clips, which are mostly iron and copper, you get hydrogen gas and a compound of iron known as iron hydroxide. You get this result because of the process of decomposition. What actually happens is that the electricity breaks the water into hydride and hydroxide ions. A hydride ion is practically a hydrogen atom without its electrons. Hydrogen does not want to stay an ion for long when it's free, so it joins up with another hydrogen atom to form hydrogen gas. The hydroxide ion combines with the iron (or copper) in your paper clips to form iron hydroxide. That's the green stuff that you see in your lid.
If you were to do this with carbon electrodes (such as the graphite in a pencil: graphite is dense carbon.), you get hydrogen gas and chlorine gas. You get the chlorine out of the salt water (because salt water is actually a solution of sodium and chlorine ions in water). The reaction produces hydroxide as well, but it displaces the chlorine in the solution. You can tell this is happening because the water becomes basic because sodium and hydroxide ions in water is a strong base. The chlorine, because it's an ion, doesn't want to stay that way for long when it's alone, so it forms chlorine gas (You would recognize the smell of chlorine). The reason you get this result is because carbon, in its graphite form, is not reactive, like metals are.
Now you know!
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