The dissociation constant for a previously uncharacterized racemic acid discovered in a meteor have been determined to be pk1=2.0, pk2=3.5, pk3=6.3, pk4=8.0, pk5=9.8, and pk7 = 10.9. What would be its approximate net charge on this amino acid at a pH of 2?

According to Henderson-Hasselbalch equation,

pH = pKa+ log (α/1- α)

Given pH =2

Calculate α = degree of dissociation = 1/ 10^(pKa-pH) +1

Given pKa1 = 2; α = 0.5; upon deprotonation, charge on carboxyl will change to -1.

pKa2 = 3.5; α = 0.031;

pKa3 = 6.3; α = 0.00005~1

pKa4 = 8.0; α = 0.0000009~1; upon deprotonation, charge on amino group will become +1.

pKa5 = 9.8; α = ~1

pKa7 = 10.9; α = ~1

So, the total charge on this amino acid at pH 2 =∑ (charge on the group upon deprotonation* degree of deprotonation/protonation)

= (-1)*0.5 +(-1)*0.031 + (-1)*1+ (+1)*(1-1) + (+1)*(1-1) + (+1)*(1-1)

~ -0.5 – 0.031 – 1 + 0 + 0 + 0

~ -1.5

Actually, the charge should be around -1. (Because for pK_a = 3, 4, 5 and 7, we have used approximate values of 1).