The questions is  :

1.812 g of a crystallized α-amino acid (pKa1: 2.4; pKa2; 9.7) has a pH of 10.4 when dissolved in 100 mL of 0.1M NaOH. Calculate the molecular mass of this amino acid.

As usual we can obtain the ratio of the conjugate base and acid around pka2 by using the HH equation. However, once we get the ratio the solutions key says that we know the concentration of [Base] = .1 because all of the OH- reacted with our acid. While I totally agree that all the OH- reacted with the acid, since it is a strong base, how do we know there was no [Base] before the addition of NaOH?Thus making the concentration [Original Base] + .1. Is this because it came from a solid crystal where all of the amino acid was in the acid form?

Thanks!

The questions is:

$1.812\ \mathrm{g}$ of a crystallized α-amino acid ($\mathrm{p}K_\mathrm{a1} = 2.4, \mathrm{p}K_\mathrm{a2} = 9.7$) has a $\mathrm{pH}$ of $10.4$ when dissolved in $100\ \mathrm{mL}$ of $0.1~\mathrm{M}\ \ce{NaOH}$. Calculate the molecular mass of this amino acid.

As usual we can obtain the ratio of the conjugate base and acid around $\mathrm{p}K_\mathrm{a2}$ by using the Henderson-Hasselbalch equation. However, once we get the ratio, the solutions key says that we know $c(\text{Base}) = 0.1$ because all of the $\ce{OH-}$ reacted with our acid. While I totally agree that all the $\ce{OH-}$ reacted with the acid, since it is a strong base, how do we know there was no $c(\text{Base})$ before the addition of $\ce{NaOH}$? Thus making the concentration $c_0(\text{Base}) + 0.1$. Is this because it came from a solid crystal where all of the amino acid was in the acid form?