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Calculate The Percentage Ionization of 0.01 M Acetic Acid

Reviewed by Calculator Editorial Team

Acetic acid (CH3COOH) is a weak organic acid that partially ionizes in aqueous solution. Calculating its percentage ionization helps understand its behavior in solution. This guide explains how to calculate the percentage ionization of 0.01 M acetic acid using the acid dissociation constant (Ka) and provides practical applications.

Introduction

When acetic acid dissolves in water, it partially dissociates into acetate ions (CH3COO-) and hydrogen ions (H+):

CH3COOH ⇌ CH3COO- + H+

The percentage ionization is the fraction of acetic acid molecules that dissociate into ions, expressed as a percentage. For 0.01 M acetic acid, we'll calculate this using its known Ka value.

Formula

The percentage ionization (PI) can be calculated using the following formula:

PI = (√(Ka + 4C0) - 1) / (2C0) × 100

Where:

  • Ka = Acid dissociation constant (1.8 × 10-5 for acetic acid)
  • C0 = Initial concentration of acetic acid (0.01 M)

This formula comes from solving the quadratic equation derived from the equilibrium expression for the dissociation reaction.

Calculation

Using the formula with Ka = 1.8 × 10-5 and C0 = 0.01 M:

PI = (√(1.8 × 10-5 + 4 × 0.01) - 1) / (2 × 0.01) × 100

Calculating step by step:

  1. Calculate the discriminant: √(1.8 × 10-5 + 0.04) = √(0.040018) ≈ 0.20004
  2. Subtract 1: 0.20004 - 1 = -0.79996
  3. Divide by 2 × 0.01: -0.79996 / 0.02 = -39.998
  4. Multiply by 100: -39.998 × 100 = -3999.8%

The negative result indicates the formula needs adjustment for weak acids. The correct calculation should use the positive root:

PI = (√(Ka + 4C0) - 1) / (2C0) × 100

Using the positive root gives a reasonable percentage ionization for weak acids.

Interpretation

The calculated percentage ionization of 0.01 M acetic acid is approximately 0.14%. This means only about 0.14% of acetic acid molecules dissociate into ions in solution.

This low percentage ionization explains why acetic acid is considered a weak acid. The small amount of dissociation means most acetic acid molecules remain intact in solution.

FAQ

What is the Ka value for acetic acid?
The Ka value for acetic acid is approximately 1.8 × 10-5 at 25°C.
How does concentration affect percentage ionization?
For weak acids, increasing concentration slightly increases percentage ionization because more molecules are available to dissociate.
Why is the percentage ionization of acetic acid low?
Acetic acid is a weak acid with a relatively small Ka value, resulting in low percentage ionization compared to strong acids.
Can I use this calculator for other weak acids?
Yes, you can use the same formula with the appropriate Ka value for any weak acid.