# Dissociation behaviour of polyelectrolytes

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?

Ben

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).