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I searched much about alcoholic KOH and aqueous KOH, but I was unable to understand it.

I mean, I want to know how ionisation of KOH in alcohol is different from that in water.

I also don't know what actually happens during its ionisation. Why is alcoholic KOH used in dehydrohalogenation of alkyl halides?

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Why is alcoholic KOH used in dehydrohalogenation of alkyl halides?

One possible explanation is lack of solubility of the alkyl halides in water. Thus, one switches to a less polar, presumably alkyl side chains containing alcohol. (H2O is formed in minute amounts from OH and the proton from the hydroxyl group of the alcohol and can thus be neglected.) Boiling points vs. reaction conditions can also be relevant.

KOH forms homogenous mixtures with H2 at any ratio, this may not be true for some alcohols (For the amounts needed for the reaction this should not be relevant). In terms of ionisation, one can suspect that K+ is not as well solvated in alcohols as in water because the alcohol molecules will have a harder time arranging optimally around the ion. Also, the solvent shell structure may be a lot less pronounced. For OH-, one basically expects the same. In alcohol, one might also see some ion pair formation (or rather retention?) for KOH.

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Basically, alcohols can't stabilize the hydroxide ions as well, do potassium hydroxide is more basic. In addition, alcohol is a much better solvent for organic reactions. Those are the two prime factors for using alcoholic potassium hydroxide.

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