[sharbeldam]

Question:
You are given 500 ml of a mixture of the amino acid glutamine, at a concentraton of 0.2M. It is a given that 17% of the molecules in the mixture freed the proton from the alpha-amino group. How much HCl at a concentration of 0.4M must you add to the mixture, to reach a situation where 50% of the molecules are charged with an extra positive charge?

MY attempt (aka my failure)
They didnt give us any pkas values but i think we need it for this question (Im not sure), the pka1 is 2.16 and the pka2 is 9.1, now at pH of 2.16 or 9.1, half of the molecules would have +1 charge. but i assumed that i need the lower pH since it is asking me about how much HCl I need to add.

moles of amino acid = 0.2*0.5=0.1mole
moles of H+ which the amino acid freed = 17% *0.1 = 0.017moles

Since the pH i require at the end is 2.16 (=pka1 = 50% of molecules have +1 ) then 2.16=-log[H+] and i get that the concentration of the H+ i need at the end is 0.006M and i got stuck :/