Diprotic buffers are characterized by their ability to donate two protons (H⁺) due to the presence of two acidic hydrogens, each associated with its own dissociation constant (K_a). The general formula for a diprotic acid can be represented as H₂A, where the two acidic hydrogens can be sequentially lost, leading to distinct forms: the acidic form (H₂A), the intermediate form (HA^-), and the basic form (A^2-).

The first dissociation step involves the loss of the first acidic hydrogen, represented by the equilibrium constant K_a1:

H₂A ⇌ HA^- + H⁺ (K_a1)

In the second dissociation step, the intermediate form can lose its second acidic hydrogen, represented by K_a2:

HA^- ⇌ A^2- + H⁺ (K_a2)

Conversely, these forms can also accept protons. The basic form (A^2-) can gain a proton to become the intermediate form (HA^-), represented by K_b1:

A^2- + H⁺ ⇌ HA^- (K_b1)

Then, the intermediate form can accept another proton to revert to the acidic form (H₂A), represented by K_b2:

HA^- + H⁺ ⇌ H₂A (K_b2)

The relationships between these constants are defined by the water dissociation constant (K_w):

K_a1 × K_b2 = K_w and K_a2 × K_b1 = K_w.

The Henderson-Hasselbalch equation is crucial for calculating the pH of buffer solutions. For diprotic buffers, there are two equations corresponding to the two dissociation steps. The first equation relates the pH to the first dissociation constant:

pH = pK_a1 + log(HA^-/H₂A)

In this equation, HA^- represents the base (intermediate form) and H₂A represents the acid (acidic form). The second equation addresses the second dissociation constant:

pH = pK_a2 + log(A^2-/HA^-)

Here, A^2- is the base (basic form) and HA^- is the acid (intermediate form). The intermediate form can act as either an acid or a base, depending on the context of the reaction, making it a versatile component in diprotic buffer systems.