Ammonium ion pKa values and gas phase acidities

There was a question posted asking why the pKa of trimethylamine did not follow the pattern of increased basicity as alkyl groups replaced hydrogen atoms.

Let’s go back over some examples[1] and the theoretical implications.

Cmpd pKa Cmpd pKa t-BuNH3(+) 10.55
NH4(+) 9.21 NH4(+) 9.21 CH2=CHCH2NH3(+) 9.49
MeNH3(+) 10.62 EtNH3(+) 10.63 (n-Bu)2NH2(+) 11.25
Me2NH2(+) 10.64 Et2NH2(+) 10.98 (n-Bu)3NH(+) 10.89
Me3NH(+) 9.76 Et3NH(+) 10.65 Me2EtNH(+) 9.99

This data is consistent with carbon being an electron donor and thus replacing a hydrogen with a carbon decreases the acidity. However, the acidity of tertiary ammonium salts increases again. Why the reversal in the trend?

Anslyn and Dougherty discuss this issue under the subheading, Solvation[2]. Anslyn and Dougherty state in the gas phase, the “intrinsic” acidity of the methylamines decrease in the order:

        NH4+ > MeNH3+ > Me2NH2+ > Me3NH+ {gas phase}

“because more alkyl groups can spread out the positive charge better (see Table). However, solvation effects favor Me3NH(+) as the most acidic, because its large size makes it the least well solvated. The solvation effect on the acidities leads to the following trend:”

        Me3NH+ > Me2NH2+ > MeNH3+ > NH4+ {solvation order}

“Apparently, a combination of these two effects leads to the observed trend …” being noted in the table above.

This argument is linked in another post in the chemicalforums. However, I do not find these arguments persuasive. They could be true, but I am troubled for several reasons. If trimethylammonium ion is increased in acidity due to solvation, then triethyl- and tributylammonium ions should be further increased. Quite to the contrary, although they are less acidic than trimethylammonium ion, though more acidic than their dialkylammonium ions. Dimethylethylammonium ion is intermediate in acidity. It appears that methyl substituents create a greater increase in acidity than other alkyl groups. This seems unexplained by the solvation argument.

Anslyn and Dougherty discuss solvation effects upon acidity and suggest acids whose anions can be written with many resonance structures do not change their pKa values if the solvent is changed. However, if you examine pKa tables in different solvents, you can find there is considerable variation in the pKa values with compounds and solvents. For example, triethylammonium ion (9.0) is more acidic in DMSO than ammonium ion (10.5). This seems like an unexpected result.

Anslyn and Dougherty also discuss gas phase acidity (p. 273). Although this would appear to be an ideal measure of acidity, I am troubled by the measurement. If gas phase acidity measured the unimolecular ionization of an acid, this would be an ideal measurement. However, Anslyn and Dougherty point out the heterolytic bond cleavage of methane requires 417 kcal/mol while homolytic cleavage requires 105 kcal/mol. Therefore, the bond to a proton/hydrogen atom is broken homolytically to give two radicals. The radical must be changed to an anion by adjusting for the ionization and electron affinity of the radicals. Therefore, gas phase acidities are calculated values.

Herein lies the problem with gas phase acidities. I argue the “best” measure of heterolytic bond strength is acidity. I am unaware of any standard for heterolytic bond strength. This is a long standing problem in physical organic chemistry. Many measurements of nucleophilicity in different solvents have been made. These require breaking and forming new bond heterolytically. I presume the lack of a standard for heterolytic bond strength results from the difference in bond energy of homolytic and heterolytic bond cleavages. It is far easier to break a bond heterolytically if one or more additional molecules participate. HCl is difficult to form ions in the gas phase but very facile in water. HCl cannot break homolytically at room temperature because it the electron-electron cohesion force is strong, but water can easily abstract a proton from chloride without breaking that bond. Perhaps the heterolytic force between a proton and the electron of an ion can be measured by calculating the much higher electron-electron force, adjusting for its ionization and reformation, but this entire process leaves me anxious about the net result.

I find there is considerable variation in the measurement of pKa values if gas phase and different solvents are included. The variations prove that additional interactions must be taking place. The difficulty is how to explain any of the interactions to explain a shift in pKa. For example, if we were to assume the phase phase acidity order for ammonium and methylammonium ions is correct, then how does water result in the relative order found in the lab? I find it far easier to assume the aqueous phase pKa values to represent the relative strength of each conjugate base. Then I may ask whether the variations found in different solvents can be explained. I am not suggesting this is more TRUE, but that it is more expedient. Furthermore, the aqueous and gas phase approximate each other and our expectations of chemical behavior (carbon is a better electron donor than hydrogen). It is easier to observe that replacing a proton with an alkyl group decreases the acidity of an ammonium ion the most. Replacing a second proton has a smaller effect, but seemingly more pronounced with a longer chain. Replacing a third proton no long decreases the acidity and has a slight increase. The difference in acidity noted by the replacement of a proton with a methyl group or longer alkyl group is also more pronounced in trimethylammonium ion. It seems like a smaller hurdle to explain how a methyl group is different than an ethyl group than it is to explain how water or any solvent shifts all acidities.

[1] Data taken indirectly from Hall, H.K., Jr. J. A.m. Chem. Soc. 1957, 79, 5441 via I avoided using other sources as their data may have varied. Unknown whether Hall measured data or consolidated the data from other sources.
[2] Eric V. Anslyn and Dennis A. Dougherty, Modern Physical Organic Chemistry, University Science Books, 2006, p. 284-285.

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