Problem Statement: At pH=7, what fraction of alanine has no net charge (i.e., electrically neutral)? Set up the equations.
Solution:
An amino acid acts as a zwitterion, i.e., it can be either:
1) positively charged in an acid solution
2) negatively charged in an alkaline solution, or
3) neutral at the isoelectric point.
Zwitterion Reaction:
NH3+-CHR-COOH ----> NH3+-CHR-COO- + H+
NH3+-CHR-COO- ----> NH2-CHR-COO- + H+
which can be abbreviated as:
A+ ----> A + H+
A ----> A- + H+
The Dissociation constants for these steps are:
Dissociation constant #1: pK1=2.34=-log([A][H+]/[A+]) eq. (1)
Dissociation constant #2: pK2=9.69=-log([A-][H+]/[A]) eq. (2)
Add one more equation to find the fraction:
[A+] + [A] + [A-] = 1 eq. (3)
From three eqs (1)--(3), solve for three unknowns ([A+], [A], [A-])
at pH=7 (i.e., [H+]=10-7)
Actual numerical solution:
A closely related example with MATLAB, which was a problem solved in CHBE250.
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