pKa Calculator

Solved from the exact quadratic, so you can see how far the usual square-root shortcut drifts.

pKa4.757Acetic acid

Ka1.75 × 10⁻⁵

pH of this solution2.8814from the exact quadratic, at 0.1 mol/L

Hydrogen ion concentration1.3142 × 10⁻³ mol/L

Percent ionised1.3142%

The usual approximation gives2.8785out by 0.0029 pH units here

pKb of the conjugate base9.243pKa and pKb sum to pKw, which is 14 only at 25 °C

pH if diluted tenfold3.3876and 4.097% ionised — a LARGER share

Diluting a weak acid raises the fraction that dissociates even as it lowers the hydrogen ion concentration. Both are true at once, and Ostwald's dilution law is the statement that the first rises roughly as the square root of the dilution.

The formula

pKa = -log10(Ka) ; [H+] solved from x^2 + Ka x - Ka C = 0

A number that does not depend on concentration

Ka is an equilibrium constant, so it describes the acid itself rather than any particular solution of it. Diluting a weak acid changes its pH but not its pKa. That is what makes pKa the useful figure to tabulate, and the pH of a solution something you calculate from it.

Solved exactly, not approximated

The textbook shortcut takes the hydrogen ion concentration as the square root of Ka times C, which assumes the acid barely dissociates and the concentration is essentially unchanged. That holds well for acetic acid, where the error is 0.003 pH units. It holds less well for hydrofluoric acid, where nearly eight per cent dissociates and the shortcut is 0.018 units out. This page solves the quadratic instead and shows both, so the size of the approximation is visible rather than assumed.

Weaker acids ionise proportionally more when dilute

Dilute a weak acid tenfold and the fraction that dissociates rises by roughly the square root of ten. The absolute hydrogen ion concentration still falls and the pH still rises — but a larger share of the acid present has given up its proton. Ostwald called this the dilution law, and it is the reason a very dilute weak acid behaves more like a strong one than intuition suggests.

Which denominator?

Most of the confusion in solution work is not arithmetic but bookkeeping. Molarity divides by the volume of the finished solution; molality divides by the mass of the solvent; percent by mass divides by the mass of the solution again. The three agree closely in dilute water and diverge sharply in concentrated acid, which is why a bottle labelled 98 % is also labelled 18.4 M without contradiction.