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I had dissolved a bunch of aluminium foil in an aqeous solution of sodium hydroxide. The resulting solution consists mainly of sodium aluminate with very little excess sodium hydroxide.
What I want to do is convert this back to sodium hydroxide. I am thinking electrolysis should do the trick. But, I am not completely sure if this is right. If it is, what kind of electrodes should I use? If not, why not? (What will be the product?)
Thank you for your time.

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I don't think you will have much luck recovering the hydroxide. To do so you would need to reverse the reaction that happened when the aluminum dissolved, which was

$$\ce{2 Al + 2 NaOH + 2 H2O -> 2 NaAlO2 + 3 H2}$$

Your idea is essentially to substitute reduction at an electrode for reduction with hydrogen gas. Unfortunately electrochemical reduction of $\ce{Al(III)}$ is very difficult. If your idea was feasible, it would revolutionize aluminum manufacture! Instead of doing electrolysis of molten cryolite at ~1000 degress with sacraficial carbon electrodes, aluminum manufacturers could use your process. So if you could get it to work, you'd be rich...but I am not hopeful.

Note however that you don't necessarily need to do electrolysis to recover sodium hydroxide. There is hope! You could just boil down your solution so that it is supersatured with respect to aluminum hydroxide, and then wait for the aluminum hydroxide to precipitate, which would happen faster if you add seed crystals of aluminum hydroxide $\ce{Al(OH)3}$) to initiate precipitation.

$$\ce{2H2O + NaAlO2_{(aq)} -> Al(OH)3_{(s)} + NaOH_{(aq)}}$$

This step is part of the Bayer process for commercial refining of aluminum ore.

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Electrolysis is good, and it is also helpful if you want aluminum powder too, the electrolysis of Sodium Aluminate will yield Sodium Hydroxide in solution and aluminum metal as sponge which crumbles into a powder when dry, this is not efficient though because the Hydroxide will react with a little bit of the aluminum that had formed, so you will have a solution of Sodium Hydroxide with a little bit of Sodium Aluminate in it, this method also works with sodium zincate as well, NurdRage has a video on that topic, the Sodium Aluminate process is very similar to the Sodium zincate process he uses in his video. Link to his video: https://youtu.be/3X9c6epL7HQ

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