Calculating acid to base/ base to acid ratios based on amino acids pka and given pH

Question

When we are calculating the ratio of acid to base or base to acid for the amino acids do we do them 2 or 3 times depending on whether a side chain is involved? If so, would you just calculate each one separately using the (Ka/H3O+) equation and then write the ratios separately for each group? Can you also give an example?

Answer 1

Yes, when calculating the ratio of acid to base or base to acid for amino acids, we must consider the ionization of the amino and carboxyl groups. In some cases, we also need to consider the ionization of the side chain. Therefore, we may need to calculate the ratio two or three times, depending on the amino acid and its side chain.

To calculate the ratio of acid to base or base to acid for each ionizable group, we use the Henderson-Hasselbalch equation (Think of this equation when dealing with amino acids/proteins):

pH = pKa + log [A-]/[HA] or pH = pKa + log [Base]/[Acid] depending on which ionizable part of the molecule you are looking at. If you are looking at the C terminal: COOH <==> COO- + H+. pKa = X. If you are looking at the amino group: NH2 + H2O <===> NH3+ pKa = Y.

Where pH is the pH of the solution, pKa is the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid. Note that in the case of the amino group, the acid is NH3+ and the conjugate base is NH2, while in the case of the carboxyl group, the acid is COOH and the conjugate base is COO-.

Let's take the example of glycine, which has a pKa of 2.35 for the carboxyl group and a pKa of 9.78 for the amino group. Suppose we have a solution of glycine with a pH of 7.4. We can calculate the ratios of acid to base or base to acid for each ionizable group as follows:

For the carboxyl group:

pH = pKa + log [A-]/[HA] 7.4 = 2.35 + log [COO-]/[COOH] log [COO-]/[COOH] = 7.4 - 2.35 = 5.05 [COO-]/[COOH] = 10^5.05 = 113,000

Therefore, the ratio of base to acid for the carboxyl group in glycine is 113,000 to 1.

For the amino group:

pH = pKa + log [A-]/[HA] 7.4 = 9.78 + log [NH2]/[NH3+] log [NH2]/[NH3+] = 7.4 - 9.78 = -2.38 [NH2]/[NH3+] = 10^-2.38 = 0.004

Therefore, the ratio of acid to base for the amino group in glycine is 0.004 to 1.



In this case, glycine does not have an ionizable side chain, so we only need to calculate the ratios for the carboxyl and amino groups separately. If there were an ionizable side chain, we would need to calculate the ratio for that group as well. When/if you take organic chemistry- it will become apparent why the H side-chain in glycine is not ionizable.