In the study of polyprotic acids, understanding the relationship between their various forms and the corresponding equilibrium constants is crucial. A polyprotic acid can lose multiple protons, and each step of deprotonation is associated with a specific acid dissociation constant, denoted as K_a1, K_a2, and K_a3. Conversely, when protons are added back, the base dissociation constants are represented as K_b1, K_b2, and K_b3.

For instance, when the fully protonated form, H₃A, loses its first acidic hydrogen, it involves K_a1. The second loss corresponds to K_a2, and the third to K_a3. The reverse process, where protons are added, utilizes the base constants. Notably, there are overlapping relationships between these constants, leading to the equations: K_a1 × K_b3 = K_w, K_a2 × K_b2 = K_w, and K_a3 × K_b1 = K_w, where K_w is the ion product of water.

When analyzing the fully protonated form, it can be treated similarly to a monoprotic acid using K_a1. In contrast, the fully deprotonated form, A³⁻, behaves as a base, utilizing K_b1. For the first intermediate, where one acidic hydrogen has been lost, the concentration of H⁺ can be calculated using the formula:

[H⁺] = \frac{K_a1 \times K_a2 \times [C₀] + K_a1 \times K_w}{K_a1 + [C₀]}

For the second intermediate, the equation becomes:

[H⁺] = \frac{K_a2 \times K_a3 \times [C₀] + K_a2 \times K_w}{K_a2 + [C₀]}

In summary, when dealing with polyprotic acids, it is essential to recognize the four possible forms: the fully acidic form, the fully basic form, and the two intermediate forms. Each form requires specific approaches to determine pH or H⁺ concentration, often involving ICE (Initial, Change, Equilibrium) tables for the acid and base forms, while the intermediate forms can be calculated directly using the established formulas.