Question

An amino acid has an alpha-carboxyl, an alpha-aminium group, and a delta-aminium group. The respective pKas of these three groups are 1.96, 8.65, and 10.70. What is the average, net charge of this amino acid when the pH equals pK1 (the pKa of the alpha-carboxyl group)?

0

+2

−2

+0.5

−0.5

−1.5

+1

+1.5

−1

Answer 1

The pK_a values of the amino acid are listed below.

Group	pKa
α-COOH	1.97
α-NH3+	8.65
δ-NH3+	10.70

The isoelectric point is the pH where the amino acid exists as Zwitterion, i.e, the α-COOH group is deprotonated to α-COO^- and the α-NH₃⁺ is protonated. The isoelectric point is the average of the pK_a values that are close to each other, i.e, the average of pK_a2 and pK_a3.

Therefore,

pI = ½*(pK_a2 + pK_a3) = ½*(8.65 + 10.70) = 9.675.

When the pH of the solution is less than the pI, the amino acid is positively charged while when the pH is greater than the pI, the amino acid has a net negative charge.

When pH = pK_a1, half the α-COOH groups are protonated while the other half is deprotonated. The protonated half has a charge of 0 while the deprotonated half has a charge -1. Hence, in collection of say 100 amino acids, 50% will have charge 0 while the remaining 50% will have charge -1.

The pKa₂ and pK_a3 are well above the pH and hence will each have charge +1. Find the charge on each group.

Group	Charge on Group
α-COOH (50% protonated)	0
α-COOH (50% deprotonated)	-1
α-NH3+	+1
δ-NH3+	+1

The charge on the amino acid is (0 + 1 + 1) = +2 (all protonated) and (-1 + 1 + 1) = +1 (50% deprotonated). The average charge on the amino acid = ½*(2 + 1) = ½*3 = 1.50 (ans)

Hence, the correct answer is +1.50 (ans).