Question

Suppose you are researching a special enzyme named "Generic Enzyme." Generic Enzyme has an amino acid side chain functional group that must be in the protonated form for the enzyme to be active. You have just purified Generic Enzyme and found that 1 in every 4 individual Generic Enzyme molecules is active. Your special Generic Enzyme is at a pH of 7.75. Generic enzyme has a phenolic hydroxyl group which is responsible for its catalytic activity. What is the pKa of this phenolic hydroxyl group?

Answer 1

Given, the ratio of deprotonated : protonated phenolic -OH group of the enzyme = 3 : 1

Given, the pH of the solution = 7.75

From Henderson-Hasselbalch equation,

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

or, pH = pK_a + log([deprotonated hydroxyl]/[protonated hydroxyl])

or, 7.75 = pK_a + log(3/1)

or, 7.75 = pK_a + 0.477

or, pK_a = 7.27

Hence, the pK_a of this phenolic hydroxyl group = 7.27