HOOC CH(CH2CH2SCH3)NH3+ , the
amino acid methionine, has pKa1 = 2.2 and pKa2 = 9.1. If this amino acid is represented by H2L+, what is the major species at pH 6?
Here is how you do this type.
alphao = (H2L) = (H^+)^2/D
alpha1 = ((HL^-) = k1*(H^+)/D
alpha2 = (L^-2) = k1k2/D
where D (denominator) is
(H^+)^2 + k1*(H^+)^ + k1k2
Plug in 1 x 10^-6 for (H^+) and evalueate alphao, alpha1 and alpha2.
You can go through the math (I did) and approximations are
alphao = (H2L) = 0.0002
alpha1 = (HL^-) = 0.95
alpha2 = (L^-2) = 0.0009
Those numbers aren't exact and you should do it to determine the exact values (these are fractions in the form shown); however, you can see that the majority of the H2L is in the form of HL^-