[Carnifex]

Just a quick question; I always thought carboxylic acids were more acidic than the ammonium cation group, but in my solution manual, it says the hydrogens on the ⁺NH₃R are more acidic than the hydrogen on the COOH. In the text it even says the pKa of COOH is greater than the ammonium ion, but yet still says the opposite in the solution manual. Is this just a mistake?

[macman104]

You can't just say NH3R is more acidic than COOH, it depends on what is attached to those groups.  But for example, benzoic acid (Ph-COOH, 4.2pKa) is only slightly more acidic than an anilinium cation (Ph-NH3⁺, 4.6pKa)

[Yggdrasil]

Aniline is a very representative example because the basicity of the amine is greatly reduced by conjugation with the benzene ring.  A more generalizable comparision is acetic acid (CH₃CH₂COOH pKa = 4.76) versus the ethylammonium cation (CH₃CH₂NH₃⁺, pKa = 10.7).

[Carnifex]

Ah I apologize. I forgot to mention that these two groups are together in the same compound. The exact compound is H₃N⁺CH₂COOH. The question was "which hydrogen is more acidic.

[azmanam]

The carboxylic acid of glycine is significantly more acidic (lower pka) than the ammonium ion.  pKa carboxylic acid: ~2.3.  pKa ammonium cation: ~9.6

http://courses.cm.utexas.edu/jrobertus/ch339k/overheads-1/table_3-1.jpg
http://dbs.umt.edu/courses/fall2006/bioc380/lectures/008/images/aa-pkas.jpg

But, carboxylic acids are not always more acidic than ammonium cations.  Like macman said, it depends on the substituents on both.