 Glycine speciation model

In an ideal aqueous chemical solution, set $h=[{\mathrm{H}}_3{\mathrm{O}}^{+}]/c^{\circ }=10^{-\mathrm{pH}}$, with $c^{\circ }=1\mathrm{mol}{\mathrm{L}}^{-1}$, and approximate activity coefficients by one. Put $K_1=10^{-2.35}$ and $K_2=10^{-9.78}$ for the stipulated dimensionless acid dissociation constants. The Henderson-Hasselbalch equation gives the adjacent-state ratiosWith analytical concentration $C_T=[G^{+}]+[G^0]+[G^{-}]$, normalization gives the three fractions and mean electric charge in units of the elementary charge:All three fractions are nonnegative and sum to one. At pH $7$, the model gives about $99.832\%$ zwitterion, $0.00224\%$ cation and $0.1657\%$ anion; $\bar{z}\approx -0.00163$. Predominantly zwitterionic therefore need not mean exactly at the isoelectric point.

Setting $\bar{z}=0$ requires $h^2=K_1{K}_2$. Taking the logarithm yieldsAt this model isoelectric point, ${\alpha }_{+}={\alpha }_{-}\approx 0.0001927$ and ${\alpha }_0\approx 0.9996146$: about $0.0193\%$ of each charged form remains. At either pKa, the relevant adjacent fractions are equal, but the third fraction is not mathematically zero. This three-state model neglects the minor uncharged form ${\mathrm{H}}_2\mathrm{N}-\mathrm{C}{\mathrm{H}}_2-\mathrm{COOH}$; macroscopic pKa values alone do not determine its fraction separately from the zwitterion.