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I am writing up a lab report investigating titanium anodisation and producing oxide layers. After some searching, all I can find is the reaction $\ce{Ti + O2 \to TiO2}$, which I am having no trouble understanding.

However, I seem to be confused/mislead by the simplicity of this. The whole unit is about electrochemistry and redox reactions but I cannot find any examples (or seem to produce any either - I have tried generalizing from the rusting of iron in water) of half reactions or anything similar.

I have come about as far as including the redox reactions for the hydrolysis of water and then jumping to the above reaction but am unsure where to go from here.

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I was able to locate what appears to be a useful summary of reactions and reduction potentials that are all titanium-specific here.

The reaction $\ce{ Ti + O2 -> TiO2}$ is illustrative of $\ce{Ti}$ being oxidized while oxygen is reduced. I agree with you that it is simplistic-looking and might not appear as traditional an example of redox chemistry as you require.

You might investigate the high-temperature reaction of titanium metal and water (steam), which produces $\ce {TiO2}$ and $\ce{H2}$ gas (titanium is oxidized, hydrogen is reduced), which might be a little clearer. This reaction (and several others) are given on the page I've linked above.

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