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Usually tetraethyl orthosilicate/tetraethoxy silane (TEOS) is mixed with both ethanol and water to produce silica in a sol-gel process. I am curious what happens if one adds TEOS to water at a high pH, without any alcohol. Would TEOS simply not mix and not react with water? Or it would hydrolyze too rapidly and not condense at all?

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It depends. if your pH is really high, silicate $\ce{SiO3^2-}$ or $\ce{SiO4^4-}$ ions will form and will become a stable dissolved solute in the solution. if it is moderately high the rate of hydrolysis will increase greatly and the silicon will crash out in the form of orthosilicate hydrates [$\ce{Si(OH)4}$], which may agglomerate to form silica particles. These results are a bit of a spectrum and there is no pH limit where the reaction gives a binary change in result, as it is also sensitive to extrinsic properties of the solution such as the amount of base.

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