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The electrodes have different charges. One is positive ( the cathode ) while one is negative (anode). They will attract the particles in the solution which are charged. Hydrogen to the cathode while oxygen will go to the anode.

I have been taught that water is a covalent bond. Also I have been taught that covalent bonds do no have a charge so how is it possible that this compound is charged if it's covalent?

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    $\begingroup$ Did you consider $\ce{2 H2O <=> H3O+ + OH-}$? $\endgroup$ – Klaus-Dieter Warzecha May 1 '14 at 22:01
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Pure water contains only small amounts of $\ce{H3O+}$ and $\ce{OH-}$ which are generated by autoprotolysis (the reaction given by Klaus Warzecha in his comment to your question). Reduction of $\ce{H3O+}$ at the cathode produces molecular hydrogen. At the anode, water is in turn oxidized, yielding molecular oxygen and $\ce{H3O+}$ (reference).

$$\mathrm{Cathode:}\ \ce{2H3O+ + 2e- \rightarrow H2 +2H2O}$$

$$\mathrm{Anode:}\ \ce{6H2O \rightarrow O2 + 4H3O+ + 4e-}$$

$$\mathrm{Overall\ reaction:}\ \ce{2H2O \rightarrow 2H2 + O2}$$

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  • $\begingroup$ So water contains some ions? $\endgroup$ – Bula May 2 '14 at 16:45
  • $\begingroup$ Yes, but at low concentration. At 25°C, the product of the concentrations (ionic product of water) is $[\ce{H3O+}][\ce{OH-}]=1 \times 10^{-14}$ $\endgroup$ – Jannis Andreska May 2 '14 at 16:50
  • $\begingroup$ Hm. It might seem like an easy question but do any other compounds contain ionic bonds at low concentrations? $\endgroup$ – Bula May 2 '14 at 19:51
  • $\begingroup$ Pure liquid ammonia can also undergo autoprotolysis: $\ce{2NH3 \rightleftharpoons NH2- + NH4+}$ $\endgroup$ – Jannis Andreska May 2 '14 at 20:01
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If you use NaCl as the aqueous electrolyte, you get sodium metal and chlorine. Sodium reacts with water to give hydrogen and hydroxide. Chlorine eats the anode, dissolves in water, and disproportionates with hydroxide to give HOCl and chloride. NaOH aqueous electrolyte gives hydrogen and oxygen. Sodium carbonate aqueous electrolyte can be interesting at the cathode versus voltage.

Chemistry tops off around 3 eV bonds. A mere transistor battery gives you nine volts. Products depend on electrolyte, concentration, voltage, current density, and electrode material (e.g., overvoltage).

http://nopr.niscair.res.in/bitstream/123456789/21833/1/IJCB%2041B(2)%20423-426.pdf
Electrochemistry can push things hard.

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    $\begingroup$ This is all correct, but I fail to see how it relates to the question. $\endgroup$ – Martin - マーチン May 2 '14 at 1:19
  • $\begingroup$ Water electrolysis does not fundamentally electrolyze water. It creates other species than can net obtain oxygen and hydrogen from reaction with water. Understanding the process accesses a broad range of answers, not merely one answer. $\endgroup$ – Uncle Al May 2 '14 at 14:12
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    $\begingroup$ You have never even hinted that something like water electrolysis might happen at all (and given pure theory this has a probability far away from zero). I very much understand that other ions in solution will catalyse the whole process, but the fundamental hypothesys is that water can be hydrosysed. $\endgroup$ – Martin - マーチン May 2 '14 at 14:49
  • $\begingroup$ So he does water get electrolysed inspire of being a covalent compound? $\endgroup$ – Ubaid Hassan Apr 23 '19 at 19:39

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