= Dicarboxylic acid
{title2=$\mathrm{R(COOH)_2}$}
A \b[<dicarboxylic acid>] is a <carboxylic acid> containing two <carboxyl groups>. The groups may be attached to an aliphatic framework, as in <malonic acid>, or an aromatic framework, as in <terephthalic acid>.<Dicarboxylic acid in ChEBI>[CHEBI:35692, Definition and ontology]{ref} The definition counts functional groups rather than specifying chain length, ring substitution or acid strength.
A <dicarboxylic acid> can supply two acidic <protons> through its <carboxyl groups>. In the simplest <diprotic acid> model, write the successive equilibria
$$
\mathrm{H_2A\rightleftharpoons H^++HA^-},\qquad
\mathrm{HA^-\rightleftharpoons H^++A^{2-}}.
$$
The two <acid dissociation constants> $K_1$ and $K_2$ characterize different equilibria. Two chemically similar groups do not justify treating the two proton-removal steps as identical. Other ionizable groups, if present, require additional equilibria.
For an original ideal dilute-solution example, use concentration-form constants $K_1=10^{-3}\,\mathrm{mol\,L^{-1}}$, $K_2=10^{-5}\,\mathrm{mol\,L^{-1}}$ and hydrogen-ion concentration $H=10^{-4}\,\mathrm{mol\,L^{-1}}$. Mass balance and the two equilibrium relations give species fractions
$$
\alpha_0=\frac{H^2}{D},\quad
\alpha_1=\frac{K_1H}{D},\quad
\alpha_2=\frac{K_1K_2}{D},\qquad
D=H^2+K_1H+K_1K_2.
$$
Here $(\alpha_0,\alpha_1,\alpha_2)=(1,10,1)/12$. The average charge is $-1$ per acid-derived species even though only $5/6$ of the molecules are monoanions: equal neutral and dianion populations balance around that mean. The constants are stipulated for illustration, not assigned to a particular compound. Precise thermodynamic calculations use activities rather than equating them with concentrations.
A <titration> that fully removes both carboxyl protons consumes two moles of hydroxide per mole of initially neutral <dicarboxylic acid>, in the absence of other reactions. For example, 0.50 mmol requires 1.00 mmol hydroxide by stoichiometry. Two stoichiometric equivalents do not guarantee two separately resolved features on a <titration curve>; the <acid dissociation constants> and measurement conditions determine their separation.
Two <carboxyl groups> also provide two possible connections in <esterification>. <Terephthalic acid> and a diol can therefore build a <polyester>, illustrating how the same functional-group count matters both to acid-base measurements and to polymer connectivity.<Organic Chemistry by John McMurry>[Section 31.4, Step-Growth Polymers, terephthalic acid and ethylene glycol]{ref}
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