= Diprotic acid
A diprotic <acid (chemistry)> can donate two <protons> per molecule through successive acid-base steps. The name counts ionizable protons in the stated chemistry, rather than all hydrogen atoms in a molecular formula. The intermediate after the first loss is itself able to act as an <acid (chemistry)> in the second step. <Carbonic acid> and <sulfuric acid> provide examples with different dissociation strengths.<Chemistry 2e by Paul Flowers and others>[Section 14.5, diprotic acids and stepwise carbonic/sulfuric acid ionization]{ref}
For $\mathrm{H_2A}$ in water, write the equilibria as $\mathrm{H_2A\rightleftharpoons H^++HA^-}$ and $\mathrm{HA^-\rightleftharpoons H^++A^{2-}}$, suppressing the explicit water/hydronium notation. There are two <acid dissociation constants>, $K_1$ and $K_2$. In an ideal dilute approximation let $h$ be hydrogen-ion concentration divided by the standard concentration, so
$$
\frac{[\mathrm{HA^-}]}{[\mathrm{H_2A}]}=\frac{K_1}{h},\qquad
\frac{[\mathrm{A^{2-}}]}{[\mathrm{HA^-}]}=\frac{K_2}{h}.
$$
Square brackets denote <concentrations>. With total acid concentration $C_T=[\mathrm{H_2A}]+[\mathrm{HA^-}]+[\mathrm{A^{2-}}]$, the fractions in the three forms are
$$
(\alpha_0,\alpha_1,\alpha_2)
=\frac{(h^2,K_1h,K_1K_2)}{h^2+K_1h+K_1K_2}.
$$
Their sum is one by construction; this is a species balance, not a claim that every molecule has already released both protons.
For illustrative constants $K_1=10^{-3}$ and $K_2=10^{-6}$, a maintained $h=10^{-4}$ gives fractions approximately $(0.0901,0.9009,0.00901)$. The singly deprotonated form dominates in this chosen regime. These are stipulated parameters, not measured constants for the named example acids.
If the acid is placed in initially pure water, $h$ is generally unknown: species balance must be combined with <charge neutrality>, water ionization and any other ions. Holding <pH> fixed, as in the example, is a different boundary condition. Likewise, two available protons do not imply two resolved features in every <acid-base titration>: the separation of the two dissociation steps and the experimental conditions determine how distinguishable they are.
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