A biochemist adds 1.098 g of a crystalline amino acid to water. After the crysta

Question

A biochemist adds 1.098 g of a crystalline amino acid to water. After the crystalline amino acid dissolves, the biochemist checks the pH and sees that it is the average of pK1 and pK2 (see below). The label on the bottle that contained the amino acid has mostly faded, so the biochemist is not sure which amino acid she is working with, but she was able to read that pK1 = 2.3 and pK2 = 9.51. She adds 0.01 mol of NaOH, which brings the final volume to 50. mL. She also checks the final pH of the solution and sees that it is 10.13. What is the molecular weight of the amino acid? (Hint: it may not be one of the 20 standard amino acids of living organisms.) Report your answer to the nearest ones.

Explanation / Answer

Average of pK1 and pK2 means the first equivalence point for the amino acid

pH at first equivalence point = (2.3 + 9.51)/2 = 5.905

this is when 1 equivalent of NaOH is added

pH = -log[H+] = 5.905

[H+] = 1.24 x 10^-6 M

So molarity of amino acid present = 1.24 x 10^-6 M

when 0.01 M NaOH added, pH = 10.13

pH = pKa + log(base/acid)

10.13 = 9.51 + log(x/1.24 x 10^-6 M x 50 ml- x)

2.6 x 10^-4 - 4.17x = x

x = 5.03 x 10^-5 mmol

So molar mass of amino acid = 1.098 g x 1000/5.03 x 10^-5 mmol = 21829026 g/mol

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