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I was comparing the acidity of H-CH3 and H-OH, and a lot of things weren't making sense. Generally, the process of turning H-X into $H^{+}$ and $X^{-}$ can be broken into 2 hypothetical steps: 1.) Homolytic cleavage of the H-X bond, followed by 2.) Electron donation from H to X. The energy required for step 1 is correlated with bond length, while the energy released by step 2 is correlated with electronegativity of X.

The way I see it, electronegativity comes as a DIRECT consequence of atomic size. Adding an electron to smaller element means the electron is added to an orbital that's relatively close to the nucleus, which is more stable. Thus, smaller elements are generally more electronegative, particularly across a row in the periodic table.

Now we consider H-CH3 and H-OH. Oxygen, being smaller than carbon, will be more electronegative; thus, $OH^{-}$ is more stable than $CH3^{-}$ and step 2 will be more favorable for H-OH. But oxygen being smaller than carbon also means the O-H bond length is smaller than the C-H bond length, and thus harder to homolytically break. Overall, I'd expect these two steps to roughly cancel, and their acidities to be at least in the same ballpark. Yet the pKa for H-OH is 15.7, while the pKa for H-CH3 is approximately 55!

How can I make sense of this? What are other factors that impact electronegativity and homolysis that I am not considering? Or are there other aspects to this problem that I am not considering entirely?

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    $\begingroup$ "Overall, I'd expect these two steps to roughly cancel, and their acidities to be at least in the same ballpark." In light of your very correct observations about the pKa's, you may have to revise this expectation... $\endgroup$ – orthocresol Mar 30 '20 at 7:36
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    $\begingroup$ Your assumption that the process can be broken into two steps might be theoretically helpful, but it isn't what happens in the real world for hydrogen-based acids. And your assumptions about the drivers of bond length and electronegativity are also wrong. You should start with actual observations not crude theory. $\endgroup$ – matt_black Aug 28 '20 at 13:55
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As far as the acidity of water goes, It is a very special case that observes the process of homoassociation. This is when an acid forms stabilizing hydrogen-bonds with it's conjugate base This allows water to be the more stable acid, because hydrogen bonds are observed between $\ce{OH-}$ and $\ce{H2O}$, while none are observed between $\ce{CH3-}$ and $\ce{CH4}$

This factor might not be significant enough to provide explanation for all of the difference that you are seeing, so there is still another culprit out there.

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  • $\begingroup$ I mean, if we're talking about aqueous pKa's, then yes, OH- is stabilised by hydrogen bonding; but the difference in pKa is still very large even in aprotic solvents, so there's still an additional factor. I also don't get how CH4 has anything to do with stability of CH3-. Your CH3- is going to be either in the gas phase (where it's surrounded by effectively nothing) or dissolved in something (where it's surrounded by solvent molecules), and that solvent isn't gonna be methane. $\endgroup$ – orthocresol Mar 30 '20 at 14:49
  • $\begingroup$ I am not referring to hydrogen bonding with the solvent, because in this case water is not necessarily the solvent, just the acid. So, assuming you have more than one molecule of water, this would still apply, even if it is in an aprotic solvent. Also, the fact that CH4 has nothing to do with stability of CH3- actually is part of what my argument is based on. $\endgroup$ – mpprogram6771 Mar 30 '20 at 14:53
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    $\begingroup$ Uhm - let me get this right. You're saying that if we were to dissolve two molecules of water in DMSO and one dissociated, then the OH- would stick to the remaining undissociated H2O? What evidence do you have for this? $\endgroup$ – orthocresol Mar 30 '20 at 14:55
  • $\begingroup$ It probably wouldn't work like that if you had too much DMSO because the H2O and the OH- would never come into contact, but yeah, that's the basic principle. Also, like I said, it's called "homoassociation." look it up. $\endgroup$ – mpprogram6771 Mar 30 '20 at 14:59
  • $\begingroup$ The examples provided on Wikipedia, such as HF, involve concentrated solutions, where you have lots of undissociated molecules – I definitely agree with you that these can influence observed acidities. But I'm really not sure they are relevant to the pKa values we're talking about. These are usually measured at rather dilute concentrations – for a discussion of water in DMSO see e.g. pubs.acs.org/doi/pdf/10.1021/ed086p864. No mention of association is made. But, I will let other people judge. $\endgroup$ – orthocresol Mar 30 '20 at 15:08

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