So we have glutamic acid (HO2C(CH2)2CHCOOHNH2) in solution and we add an equal amt of moles of HCl and we want the final pH. Glutamic acid has three pKas, 2.2, 4.2, and 9.7 and a pHi of 3.2. Here's my reasoning but it's not producing the right answer. What is wrong in my reasoning?:
When we add the glutamic acid to the water, the majority species will charge -1, because at water's pH two of the three H's will dissociate. The only protonated function is the NH3+. So then, when we add equal amount of HCl, its freed protons will attach to the 2.2 pKa functions of the glutamic acid and we'll end up with the zwitterion in H2O. That gives us a final pH of pHi = 3.2.
But the correct answer we're given is that we end up with the same number of moles of a fully protonated (thus charge +1) glutamic acid species and hence the pH is that of a weak acid, .5pKa - .5log[species] etc. What is going on here?