Fraction dissociated calculator

A fraction dissociated calculator turns two standard acid-base inputs—the acid dissociation constant Ka and the initial molar concentration—into the equilibrium fraction of molecules that have ionized. Enter Ka and c₀ in mol/L; the tool returns α from the Ostwald relation Ka equals c₀ times alpha squared over one minus alpha, percent dissociation, equilibrium concentrations of undissociated HA and of H+ and A−, a readable reaction model, and ordered substitution steps you can check by hand. Homework checks, weak-acid ICE-table shortcuts, exam prep, and coding kata expected values all need that same closed form without opening a computer-algebra system.

What fraction dissociated means for a weak acid

The fraction dissociated α—also called the degree of dissociation—is the fraction of the original undissociated acid that has ionized at equilibrium. For a monoprotic weak acid written HA goes to H+ plus A−, if the initial concentration of HA is c₀ and a fraction α has dissociated, the equilibrium amounts under the usual dilute, one-to-one ICE-table assumptions are [HA] equals c₀ times one minus α, and [H+] equals [A−] equals c₀ times α, ignoring water autodissociation when it is negligible.

The acid dissociation constant is then Ka equals [H+] times [A−] over [HA], which simplifies to Ka equals c₀ times α squared over one minus α. That identity is Ostwald’s dilution law for a binary dissociation, inverted here so that α is the unknown and Ka and c₀ are known.

When Ka is much smaller than c₀, α is small and the familiar approximation α approximately equals the square root of Ka over c₀ holds; when Ka is larger relative to c₀, α grows toward one and the full quadratic solution is required.

Solving Ka equals c₀ α squared over one minus α for α yields the quadratic equation c₀ α squared plus Ka α minus Ka equals zero, whose physical root is α equals negative Ka plus the square root of Ka squared plus four c₀ Ka, all over two c₀. Teachers and automated graders care about the negative-Ka rejection as much as the numerical answer: a student who reports a negative dissociation constant has left the domain of the definition, and a silent absolute-value clamp would hide that mistake.

Practical tips, limits, and related searches

Keep Ka non-negative and c₀ strictly positive so the mass-action model stays physically interpretable for dilute aqueous monoprotic acids. Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern.

Remember that this landing targets people searching for a fraction dissociated calculator, degree of dissociation from Ka, or alpha from acid dissociation constant online; it is not a polyprotic stepwise solver, not a buffer pH calculator, and not the reverse map that builds Kc from a measured α and c₀. Prefer this capability when you already have Ka and the analytical concentration and only need α, percent dissociation, and the matching equilibrium concentrations; if your source lists pKa, convert with Ka equals ten to the minus pKa first.

Round-trip checks are easy: recompute c₀ times alpha times alpha over one minus alpha by hand and confirm it equals the published ka within the same twelve-decimal rounding, and confirm that equilibrium HA plus either product equals c₀ within that same rounding.