If pH is below pKa, chemical will be protonated: corresponding rule for pKb?

Main Question or Discussion Point

The rule that if the pH of solution is below the pKa of a molecule then that molecule will be protonated is a handy rule. However, I'm finding it difficult to find the pKa of the chemicals I'm working with. This mostly applies to looking at nitrogens in organic compounds.

For example, it is easy to find the pKa of an amine. However, this is usually the pKa for the uncharged species. I don't really care about the hydrogen in NH3 that has a pKa of 35. I want to know the pKa of NH4+ so I can predict whether it will be protonated at physiological pH. The same goes with many compounds like aniline, pyridine, etc. I need to know the pKa of protonated, ammonium group and it is hard to find.

Who cares about the pKa of the uncharged amine in lysine? We care more about the fact that R group with R-NH3+ has a pKa of 10 so it is pretty much always protonated at physiological pH.

Is there a way to use the pKb of a neutral group to predict at what pH that group will grab a proton? This is the only way I can think of to possibly skirt this problem of not knowing pKa values.

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Yes, there is a very easy way: pKa for a protonated species = 14.0 – pKb for the unprotonated species (conjugate base).

Thanks! I actually just worked that out on paper with the henderson hasselbach equation after I posted this and it worked for basic amines.

When I tried to do it with the pKb of arginine though it didn't work. I looked up that the pKb of arginine (uncharged R group) was 11.509, which would suggest that the pKa of the charged species is around 2.5. This is not correct though, since the pKa is really 12.5. What went wrong here?

There are a lot of confusing pK conventions and values tabulated for amino acids, and particularly for multifunctional ones like arginine -- they are connected with the exact way that ionization equations are written, and whether classical or zwitterionic forms are used.

The table that I have (CRC Handbook of Chemistry and Physics, 56th Edition, page C-761) shows the following values for arginine:

Classical: pKa1 = 12.48 pKb1 = 4.96 pKb2 = 11.99
Zwitterionic: pKA1 = 2.01 pKB1 = 1.52 pKb2 = 4.96
Acidic: pKa1 = 2.01 pKa2 = 9.04 pKa3 = 12.48

From this I glean:
H2N-R-COOH --> H2N-R-COO(–) + H(+) pKa = 12.48 pKb = 1.52

H2N-R(+)-COOH --> H2N-R-COOH + H(+) pKa = 9.04 pKb = 4.96

H3N(+)-R(+)-COOH --> H2N-R(+)-COOH + H(+) pKa = 2.01 pKb = 11.99

I think that the values in the middle reaction are the ones that you are really wanting.