1.812 g of a crystallized a-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.

Question

1.812 g of a crystallized a-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.

Answer 1

Since we already have the mass of the amino acid, all we need is the number of moles to be able to calculate the molecular mass.

To find the number of moles, the first step will be to visualize the reaction that happens. The amino acid will begin in the zwitterion form (H₃N⁺-CRH-COO^-). Since the amino acid is dissolved in base (deprotonating conditions), the first reaction that will happen is that OH^- will take an H⁺ from the N-terminus, resulting in a negative amino acid (H₂N-CRH-COO^-). The lost H⁺ will combine with OH^- to make an H₂O.

The resulting reaction is as follows:

H₃N⁺-CRH-COO^- (acid) + OH^- --> H₂N-CRH-COO^- (base) + H₂O.

This is the reaction of a weak acid in equilibrium with its conjugate base, meaning that this is a buffer solution. For buffer solutions, we use the Henderson-Hasselbalch Equation to solve:

pH = pKa + log([base]/[acid])

Plugging in our values gives us this:

10.4 = 9.7 + log(0.01/[acid])

1. Where did the 0.01 come from? The amount of OH^- originally in the solution is (0.1L NaOH)(0.1mol/L) = 0.01mol NaOH = 0.01mol OH^-. Since each mole of OH^- will create a mole of base in the reaction above, we know that the moles of base in our equation is 0.01.
2. Why 9.7? the pKa₂ of the amino acid is the pKa of the N-terminus. Since the reaction is happening on the N-terminus, we use that pKa.

Solving this calculation for [acid] gives us 0.002 moles of acid.

The total number of moles of amino acid will equal the sum of the moles of acid and moles of base. Thus, 0.01 + 0.002 = 0.012 moles of amino acid.

Finally, 1.812g/0.012 mol = 151g/mol.