In diprotic systems, compounds can exist in three distinct forms: the acidic form (H₂A), the intermediate form (HA^-), and the basic form (A^2-). The dissociation of these forms is characterized by two acid dissociation constants, K_a1 and K_a2. When the first acidic hydrogen is removed, the reaction produces hydronium ions (H₃O⁺) and the intermediate form, with K_a1 governing this equilibrium. The expression for this equilibrium can be represented as:

$$ K_{a1} = \frac{[H_3O^+][HA^-]}{[H_2A]} $$

Rearranging this allows us to isolate the concentration of the intermediate form (HA^-), which can be expressed as:

$$ [HA^-] = \frac{[H_2A] \cdot K_{a1}}{[H_3O^+]} $$

From the intermediate form, the second acidic hydrogen can be lost, resulting in more hydronium ions and the basic form (A^2-). By substituting the expression for the intermediate form into the equilibrium for the second dissociation, we can derive the concentration of the basic form as:

$$ [A^{2-}] = \frac{[H_2A] \cdot K_{a1} \cdot K_{a2}}{[H_3O^+]^2} $$

The formal concentration (C) of the diprotic acid system can be expressed in terms of the concentrations of the three forms. The mass balance equation states:

$$ C = [H_2A] + [HA^-] + [A^{2-}] $$

By substituting the expressions for the concentrations of the intermediate and basic forms into this equation, we can calculate the new concentrations of each form. It is important to note that all three forms share the same denominator in their respective expressions.

When analyzing the relationship between pH and the concentrations of these forms, a fraction versus pH chart can be utilized. The intersection points on this chart correspond to specific pH values: at pH = pK_a1, the concentrations of the acidic and intermediate forms are equal, while at pH = pK_a2, the concentrations of the intermediate and basic forms are equal. As pH increases, the proportion of the basic form increases, although even at high pH levels, a small amount of the acidic form remains present. This illustrates that all three forms coexist in varying proportions across different pH levels.

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