# Constants of acidity and isoelectric point of amino acids

We find the isoelectric point by averaging the $ pK_a $ of the different pairs formed by an amino acid:

## Example 1: Glycine

*Demonstration:*
Since species II is neutral and I and III have opposite signs, it is necessary to find the pH for which [I] = [III]

(1) $\frac{[H_3O^+][II]}{[I]}=10^{-2.4}$
(2) $\frac{[H_3O^+][III]}{[II]}=10^{-9.6}$
(3) $[III]=[I]$
By multiplying (1) by (2) and introducing (3), we find: $[H_3O^+]^2= 10^{-12}$, hence the result!

## Example 2: Aspartic acid

*Demonstration:*
At $ pH = 2.9 $ , species IV has a negligible concentration, indeed
$\frac{10^{-2.9}[IV]}{[III]}=10^{-9.2}$
We can therefore neglect it and proceed as for the preceding example!

## Example 3: Lysine

*Demonstration:*
At $pH =9.7$, species I has a negligible concentration, indeed
$\frac{10^{-9.7}[II]}{[I]}=10^{-2.2}$
We can therefore neglect it and proceed as for the preceding example!