= Weak acid dissociation fraction
{title2=$\alpha=[\mathrm A^-]/C_T$}
For a <monoprotic acid> with <analytical concentration> $C_T=[\mathrm{HA}]+[\mathrm A^-]$, define the <dimensionless> <weak acid dissociation fraction>
$$
\alpha=\frac{[\mathrm A^-]}{C_T},\qquad 1-\alpha=\frac{[\mathrm{HA}]}{C_T}.
$$
This counts acid units in the <conjugate base> form. Identifying it with $[\mathrm H_3\mathrm O^+]/C_T$ additionally requires negligible <self-ionization of water> and no other sources of <electric charge>. In the ideal dilute <chemical solution> model, with $h=[\mathrm H_3\mathrm O^+]/c^\circ$, the <acid dissociation constant> gives $\alpha=K_a/(K_a+h)$. Thus lowering <hydronium> <thermodynamic activity> favors the <conjugate base>.
\Image[/weak-acid-dissociation-dilution.png]
{title=<Dilution> increases the <weak acid dissociation fraction> while raising <pH> in a synthetic aqueous <chemical equilibrium>}
{id=weak-acid-dilution-equilibrium}
The diagram uses stipulated <dimensionless> <acid dissociation constant> $K_a=10^{-5}$ and <self-ionization of water> ion product $K_w=10^{-14}$ at fixed <temperature>; these are model inputs, not measurements of a named substance. It solves the <weak acid mass and charge balances>. At $C_T=0.010\,\mathrm{mol\,L^{-1}}$, the calculated <weak acid dissociation fraction> is about $3.11\%$ and <pH> about $3.51$; at $C_T=10^{-4}\,\mathrm{mol\,L^{-1}}$, they are about $27.0\%$ and $4.57$. More acid units are dissociated as a fraction of the total, yet fewer <hydronium> <ions> occur per <volume (thermodynamics)>.
At extreme <dilution>, <self-ionization of water> makes $h$ approach $\sqrt{K_w}$, so <pH> approaches $7$ for the chosen model. The limiting <weak acid dissociation fraction> is $K_a/(K_a+\sqrt{K_w})\approx0.9901$, rather than exactly one. The calculation assumes pure added <water>, a neutral <monoprotic acid>, and no competing <chemical reactions>; actual contamination becomes increasingly important as $C_T$ falls.
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