Using a hydrometer is great for most people, but the geek in me would like to know the exact alcohol content of my brew.
What would be the process, titration? And what chemicals would I need?
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Obligatory Disclaimer: Though I do have some formal education, I am by no means a professional chemist, so please take my answer for what it is - semi-educated speculation.
As you hinted, back titration is a popular method of determining alcohol content in alcoholic beverages, especially wine. It would make sense that a similar approach could be used for calculating the alcohol content in your beer.
Ethyl alcohol has a boiling point of 78.4C. With this knowledge, you could try something like the following:
If you're aiming for high accuracy, keep in mind that you'll need to adjust the normal boiling point temperature for altitude.
Also of note is that you'll need to correct your final volume measurement to account for expansion due to the change in liquid temperature from room temperature to ~79C.
Finally, you could also just save yourself the trouble and buy a nice refractometer - many of them actually provide an alcohol content measurement.