Zwitterions/IEP of glycine at pH 6? (Paradox?)

Question

I am trying to understand an experiment: Some crystalline, solid glycine was solved in water and a pH=6 was measured (also calculable with $\mathrm{pH} =\frac{1}{2}(\mathrm{p}K_\mathrm{a1} + \mathrm{p}K_\mathrm{a2} = \frac{1}{2}(2.34 + 9.6) = 5.97)$

I have tried to explain the acidic pH-value: Solid glycine is in a crystalline structure — all molecules are in a zwitterionic state. If they get solved in neutral water, the crystal-structure is lost and $100~\%$ of zwitterions are dissolved in the neutral solution. The carboxylic and amino group now act as an acid and base in aqueous solution. The acid reaction of the carboxylic group predominates ($\mathrm{p}K_\mathrm{a1} < \mathrm{p}K_\mathrm{a2}$). Some amino acids are now negative ions, some are still zwitterions.

But now is my question (the contradiction?): pH = 6 is also the isoelectric point IP with the definition, that all amino acids are in zwitterionic state. But according to my theory above, some amino acids have already reacted "away" from the zwitterionic state.

Are there flaws in my reasoning — is my explained "paradox" not true?

Answer 1

You need to separate the two concepts.

When dissolving a neutral amino acid in water, a buffered acid-base reaction will take place as you highlighted, giving a certain pH value. In this case, the following equilibrium:

$$\ce{HOOC-CH2-NH3+ <=> ^{-}OOC-CH2-NH3+ <=> ^{-}OOC-CH2-NH2}$$

will be somewhere between the pure second and the pure third species. (The neutral, non-zwitterionic species is neglectable in aquaeous solution.) Superfluous protons liberated into the solution will end up as $\ce{H3O+}$ explaining the overall reduction in pH value when compared to a neutral solution. You won’t notice it unless you perform really accurate experiments, but the solution’s pH value will be a tad higher than the isoelectric point.

If you go on and add external protons, i.e. by carefully adding an acid, you can adjust the overall solution’s pH. Since the glycinide anions are the strongest base present, they will take up the protons first, followed by the zwitterions. At a certain pH value (corresponding to a certain external proton concentration added), the concentrations of glycinide anions and glycinium cations will be identical and we have reached the isoelectric point of glycine. It is, and has to be, slightly different from the pH value obtained by dissolving glycine.

Answer 2

After it dissolves, there will be four species, the zwitter-ion, the positive species, the negative species, and the neutral non-zwitter-ion species.

In the limit that the concentration of amino acid is much greater than the effect of water auto-ionizing to H+ and OH-, there will be equal positive and negative species. The concentration of each of the negative and positive species will be $10^{5.97-9.6}$ times the concentration of the neutral (zwitter-ion + non-zwitterion) species.

If the concentration of amino acid is very low, the pH will be closer to 7 because some of the OH- of water will react with the amino acid to shift the negative species to be greater concentration than the positive species (and [H+] greater than [OH-]).

Overall, for quantitative prediction, you would need to solve for 5 concentrations: H+, OH-, the positive and negative amino acid species, and the sum of the two neutral amino acid species, considering Kw, the 2 "Ka"s, conservation of charge, and the fact that the sum of the amino acid species is a constant. 5 unknowns and 5 equations.