Why is methanol more acidic than water?
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The pKa's that you cite are in water, where solvation and H-bonds can make a large difference so it's hard to gather any information that is of predictive value from analyzing this alone.
If you take a look at DMSO acidities instead (of course there is still solvation in DMSO, so this relies on the assumption that it's much less determining a factor, which is true), it's apparent that methanol is actually quite a bit more acidic (2.5 pKa units roughly). What's suggested is that the conjugate base of methanol is stabilized by a hyperconjugative donation of p-type lone pairs on oxygen into the C-H antibonding orbitals on the methyl. This hyperconjugation is stronger on methoxide than methanol.
Returning to the problem of solvation, note that changing the solvent to water increases the acidity of both species by a huge factor. The acidities are closer to each other because water solvates hydroxide (relative to water) better than it solvates methoxide (relative to methanol). .
If you take a look at DMSO acidities instead (of course there is still solvation in DMSO, so this relies on the assumption that it's much less determining a factor, which is true), it's apparent that methanol is actually quite a bit more acidic (2.5 pKa units roughly). What's suggested is that the conjugate base of methanol is stabilized by a hyperconjugative donation of p-type lone pairs on oxygen into the C-H antibonding orbitals on the methyl. This hyperconjugation is stronger on methoxide than methanol.
Returning to the problem of solvation, note that changing the solvent to water increases the acidity of both species by a huge factor. The acidities are closer to each other because water solvates hydroxide (relative to water) better than it solvates methoxide (relative to methanol). .
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