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Assuming a solution of 100 polycationic molecules, each of them carrying 100 amino groups and an apparent pKa of 6.5. Would it mean that, at a pH of 6.5,

  1. 50 molecules will be fully protonated
  2. 50 amino groups of each molecule will be protonated or
  3. 50% of the total amount of amino groups present in solution will be protonated?

The third option would mean that each molecule can have any charge number, from 0 to 100, with 50% of the 10.000 amino groups being protonated.

In other words, is it safe to state that, at a pH below 6.5, all molecules will be mostly protonated?

Edit due to ambiguity:

In other words, is it safe to state that, at a pH below 6.5, all molecules will have more protonated amino groups than unprotonated?

Many thanks in advance!

Ben

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Do a thought experiment: Into your polycationic molecule, insert very large spacers in between the amino groups so that they are far away from each other in terms of covalent connection and in terms of spatial distance. Now, break a bond in the middle of each spacer. Do you think this will influence the protonation state of the amino groups?

If the $\mathrm{pH} = \mathrm{p}K_\mathrm{A}$ for your $100^2$ independent amino groups, half of them will be protonated and half deprotonated. If you randomly pick 100 amino groups and turn them into a molecule by repairing the spacers in our thought experiment, you get a distribution of charges (a Gaussian bell curve centered on 50).

If you lower your pH by one unit, about 91% of amino groups will be protonated and 9% deprotonated, and again there will be a distribution of charges for the polycationic molecule/ion.

If, instead of taking a snapshot at a given time, you ask about average protonation state over a couple of milliseconds, you will have a molecular (or ionic, I guess) charge of 50+ for pH 6.5, and about 91+ for pH 5.5.

If the amino groups are not separated by spacers, they will "talk to each other", like the carboxylate groups in citric acid, for example. For citric acid, three pKa values are given, 3.13, 4.76 and 6.40, even though each group has similar chemistry and two are identical. So in that case, things are more complicated. It also gets more complicated if you bundle species with identical charge when figuring out pKa values theoretically (for citrate, there is one neutral species and one 3- species, but three 1- and three 2- species).

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  • $\begingroup$ This is exactly what I was thinking. Given the random distribution of charges and your example in the last paragraph which basically states that each amino group will have its own pKa (that's why I was speaking of "apparent" (=average) pKa), it is therefore impossible to state that all molecules will be mostly protonated below pH 6.5 since there is the possibility of fully deprotonated molecules, isn't it? $\endgroup$ – Ben Es Jan 31 at 18:37
  • $\begingroup$ And with that said, actually one could only say THAT (some) amino groups (which are not protonated yet) within one particular molecule become (also) protonated at pH 6.5, right? $\endgroup$ – Ben Es Jan 31 at 18:55

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