The concentration ratio of conjugate acid to conjugate base for a 20 mM solution at pH 7.0 of an amino acid is 20:1. Required:
a. What is the pK of the side chain?
b. What amino acid might this be?

a. 8.3= pKa of the aminoacid

b. Cysteine

Explanation:

The pH of an acid can be obtained using the H-H equation:

pH = pKa + log [A-] / [HA]

Where pH is the pH of the buffer = 7.0

pKa is the pka of the conjugate acid = ?

[A-] / [HA] is the ratio between conjugate base and conjugate acid. As the ratio of conjugate acid to conjugate base = 20:1, the [A-] / [HA] = 1/20

Replacing:

7 = pKa + log 1/20

7 = pKa - 1.30

7+1.30 = 8.3 = pKa of the aminoacid

The only aminoacid with a side chain with pKa = 8.3 is:

Cysteine. Allowing its identification.