What is percent ionization?

Percent ionization (also called percent dissociation) is the fraction of weak acid or base molecules that have ionized at equilibrium, expressed as a percentage: (x / C₀) × 100%, where x is the equilibrium concentration of ions produced and C₀ is the initial concentration.

Why use the quadratic formula instead of the 5% approximation?

The approximation x ≈ √(K·C) assumes x is negligible compared to C, which is only accurate when ionization is below ~5%. This calculator always uses the exact quadratic solution, so it works correctly even for highly ionized or very dilute solutions.

Does percent ionization increase or decrease with dilution?

Percent ionization increases when you dilute a weak acid or base. The equilibrium shifts to produce more ions, so a higher fraction of molecules ionize even though the absolute ion concentration drops.

What is the difference between Ka and Kb calculations here?

For a weak acid, x represents [H⁺] = [A⁻] and the equilibrium is HA ⇌ H⁺ + A⁻. For a weak base, x represents [OH⁻] = [BH⁺] and the equilibrium is B + H₂O ⇌ BH⁺ + OH⁻. The quadratic form is identical in both cases; only the species labels differ.

What Ka and Kb values are typical?

Weak acids have Ka roughly 10⁻² to 10⁻¹⁴ (e.g., acetic acid Ka = 1.8×10⁻⁵). Weak bases have Kb in a similar range (e.g., ammonia Kb = 1.8×10⁻⁵). If Ka or Kb is greater than ~1, the substance is essentially a strong acid or strong base and is fully ionized.

Can I use this for polyprotic acids?

Yes, for each dissociation step individually. Enter Ka1 to find the percent ionization from the first step. Subsequent steps contribute negligibly to [H⁺] for most polyprotic acids and can be treated as separate equilibria.

Percent Ionization Calculator

Name: Percent Ionization Calculator
Availability: InStock
Author: Nham Vu

Enter Ka or Kb and initial concentration to instantly find percent ionization, equilibrium concentrations, and whether the 5% approximation holds.

Parameters

Type

Acid Dissociation Constant (Ka)

× 10 (exponent)

Example: acetic acid Ka = 1.8 × 10⁻⁵

Initial Concentration C₀ (mol/L)

mol/L

Quick Presets

Results

Enter K and concentration, then click Calculate.

How the Math Works

Equilibrium (acid)

HA ⇌ H⁺ + A⁻

Ka = x² / (C − x)

Quadratic Form

x² + K·x − K·C = 0

x = (−K + √(K² + 4KC)) / 2

Percent Ionization

% = (x / C) × 100

5% rule: valid when % < 5

Summary

Enter Ka or Kb and initial concentration to instantly find percent ionization, equilibrium concentrations, and whether the 5% approximation holds.

How it works

Select whether you are working with a weak acid (Ka) or weak base (Kb).
Enter the dissociation constant (Ka or Kb) using mantissa × 10^exponent notation.
Enter the initial concentration of the acid or base in mol/L.
The calculator solves the quadratic x² + K·x − K·C = 0 for x (the ionized amount).
Percent ionization is displayed as (x / C) × 100%, along with equilibrium concentrations.
A note tells you whether the 5% approximation is valid for this scenario.

Use cases

Verify percent ionization in general chemistry homework problems.
Check whether the 5% rule applies before simplifying equilibrium calculations.
Find equilibrium concentrations for weak acid or base buffer preparation.
Compare ionization across different concentrations or dissociation constants.
Understand the relationship between Ka, concentration, and solution pH.
Double-check results from ICE table calculations.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu