Acid Dissociation Constant Ka

Ka = [H+][A−]/[HA] is the equilibrium constant for a weak acid's ionization, and it measures how strong that weak acid is.

K_a = \frac{[H^+][A^-]}{[HA]}

Ka = [H+] [A-] / [HA]

What it means

Ka applies the equilibrium-constant idea to a weak acid breaking into ions: HA ⇌ H⁺ + A⁻, so Ka = [H⁺][A⁻]/[HA]. A larger Ka means the acid ionizes more, so it is stronger; a smaller Ka means it barely ionizes. Chemists often flip it to pKa = −log Ka, on which a smaller number means a stronger acid — strong enough acids (like HCl) ionize so completely that Ka is not even useful.

Variables

Symbol	Name	Unit	Meaning
$[H⁺]$	Hydrogen ion concentration	mol/L (M)	The molar concentration of hydrogen ions produced by the acid's ionization at equilibrium.
$[A⁻]$	Conjugate base concentration	mol/L (M)	The molar concentration of the conjugate base formed alongside H⁺ at equilibrium.
$[HA]$	Un-ionized acid concentration	mol/L (M)	The molar concentration of the intact, un-ionized weak acid remaining at equilibrium.
$Ka$	Acid dissociation constant	mol/L (M), often treated as dimensionless	The equilibrium constant of ionization; bigger Ka means a stronger weak acid.

Assumptions

The acid is weak — strong acids ionize essentially completely and have no meaningful Ka.
The solution is dilute enough that concentration approximates activity.
The ionization has reached equilibrium at constant temperature.
The solvent is water (aqueous solution).

Worked example

Problem

A 0.100 M solution of acetic acid (Ka = 1.8 × 10⁻⁵) ionizes as CH3COOH ⇌ H⁺ + CH3COO⁻. Estimate [H⁺] and the pH.

Given:

Ka = 1.8 × 10⁻⁵ for acetic acid
Initial [CH3COOH] = 0.100 M
Equilibrium: CH3COOH ⇌ H⁺ + CH3COO⁻

For a weak acid, [H⁺] ≈ √(Ka × C) = √(1.8 × 10⁻⁵ × 0.100).
Multiply inside the root: 1.8 × 10⁻⁵ × 0.100 = 1.8 × 10⁻⁶.
Take the root: √(1.8 × 10⁻⁶) = √1.8 × 10⁻³ = 1.34 × 10⁻³ M.
Validate the approximation: 1.34 × 10⁻³ / 0.100 = 1.34%, under 5%, so it is valid.
pH = −log(1.34 × 10⁻³) = −(0.127 − 3) = 2.87.

[H⁺] = 1.34 × 10⁻³ M; pH = 2.87

Only about 1.3% of the acid ionized — exactly what a small Ka promises — and the pH of 2.87 confirms a weak-acid solution.