BR, Gen Chem, Section 4, Passage 13, Question 85

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sillyjoe

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The question reads:

"What is the relationship between the pKa and the pKb for lysine?

A. pKa1 + pKb1 = 14
B. pKa1 +pKb2 = 14
C. pKa2 + pKb2 = 14
D. pKa2 + pKb3 = 14

Choice C is correct. Lysine is a triprotic acid. The first proton released (from the carboxyl terminal) corresponds to the third proton gained by the conjugate base. This means that from a conjugate pair perspective, the pKa-to-pKb relationship is: pKal + pKb3 = 14. This is not one of the answer choices, so we next consider the second proton on lysine. The second proton released (from the amino terminal) corresponds to the second proton gained. Thismeansthatfromaconjugatepairperspective,thepKa-to-pKbrelationshipis:pKa2+pKb2=14. This makes choice C the correct answer; but to finish our discussion of the correlation between pKa and pKb, we must consider the third proton. The third proton released (from the side chain) corresponds to the first proton gained. This means that from a conjugate pair perspective, the pKa-to-pKb relationship is: pKa3 + pKbi = 14."

Can someone please explain this? Why would pKa1 carboxy terminus correspond to the 3rd proton gained from the conjugate base? Why would pKa2 correspond to pKb2? What are the distinctions? I am very confused by this.

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