Chapter 17: Acids and Bases – Properties, Definitions, and Quantitative Relationships

Acids and Bases: Properties and Definitions

Common Properties of Acids and Bases

Acids and bases are two fundamental categories of compounds in chemistry, each with distinct physical and chemical properties.

• Acids:

  • Sour taste

  • Can dissolve metals

  • Turns litmus paper red

  • Neutralizes bases

• Bases:

  • Bitter taste

  • Feel slippery

  • Turns litmus paper blue

  • Neutralizes acids

Definitions of Acids and Bases

There are several definitions for acids and bases, each with its own scope and application:

• Arrhenius Definition:

  • An acid produces H+ ions in aqueous solution.

  • A base produces OH– ions in aqueous solution.

• Brønsted–Lowry Definition:

  • An acid donates an H+ ion in a chemical reaction.

  • A base accepts an H+ ion in a chemical reaction.

  • This definition is more broadly applicable than the Arrhenius definition.

Additional info: The Lewis definition (not covered in detail here) further expands the concept by defining acids as electron pair acceptors and bases as electron pair donors.

Identifying Acids and Bases in Reactions

To identify acids and bases in a reaction, look for the species donating and accepting H+:

• Example: CH3COOH(aq) + H2O(l) → CH3COO–(aq) + H3O+(aq)

  • CH3COOH: Acid (donates H+)

  • H2O: Base (accepts H+)

The Hydronium Ion and Acid Dissociation

The Hydronium Ion (H3O+)

In aqueous solutions, free H+ ions do not exist independently. Instead, they bond to water molecules to form the hydronium ion:

• H+ + H2O → H3O+

• H3O+ is the actual species present in solution.

Acid Ionization Constant (Ka)

The strength of an acid is quantified by its acid ionization constant, Ka:

• For a generic acid HA: HA(aq) + H2O(l) ↔ A–(aq) + H3O+(aq)

• The equilibrium expression is:

$K_a = \frac{[A^-][H_3O^+]}{[HA]}$

• A larger Ka value indicates a stronger acid (more products at equilibrium).

Strong vs. Weak Acids

• Strong acids dissociate completely in water; the reaction goes to completion and is not an equilibrium.

• Weak acids only partially dissociate; the reaction is an equilibrium and Ka is used to describe their strength.

Conjugate Acid-Base Pairs

Definition and Identification

Every acid-base reaction involves two conjugate pairs:

• When an acid donates a proton, it forms its conjugate base.

• When a base accepts a proton, it forms its conjugate acid.

• Example: CH3COOH(aq) + H2O(l) ↔ CH3COO–(aq) + H3O+(aq)

  • CH3COOH / CH3COO–: Acid / Conjugate Base

  • H2O / H3O+: Base / Conjugate Acid

The weaker the acid, the stronger its conjugate base.

Autoionization of Water and the Ion-Product Constant (Kw)

Autoionization of Water

Water can act as both an acid and a base (amphoteric). When two water molecules react:

• 2 H2O(l) ↔ H3O+(aq) + OH–(aq)

The equilibrium constant for this reaction is called the ion-product constant for water (Kw):

$K_w = [H_3O^+][OH^-]$

• At 25°C, Kw = 1.0 × 10–14

Acidic, Basic, and Neutral Solutions

• If [H3O+] > [OH–]: Acidic

• If [H3O+] < [OH–]: Basic

• If [H3O+] = [OH–]: Neutral

In pure water at 25°C: [H3O+] = [OH–] = 1.0 × 10–7 M

The pH and pOH Scales

The pH Scale

The pH scale is a logarithmic scale used to express the concentration of hydronium ions in solution:

$\mathrm{pH} = -\log [H_3O^+]$

• At 25°C:

  • pH < 7.0: Acidic

  • pH = 7.0: Neutral

  • pH > 7.0: Basic

Calculating [H3O+] from pH and Vice Versa

• To find [H3O+] from pH:

$[H_3O^+] = 10^{-\mathrm{pH}}$

• To find pH from [H3O+]:

$\mathrm{pH} = -\log [H_3O^+]$

The pOH Scale

The pOH scale is defined similarly to pH, but for hydroxide ion concentration:

$\mathrm{pOH} = -\log [OH^-]$

$[OH^-] = 10^{-\mathrm{pOH}}$

Relationship Between pH and pOH

At 25°C, the sum of pH and pOH is always 14.00:

$\mathrm{pH} + \mathrm{pOH} = 14.00$

pKa and pKb

Definitions and Calculations

• pKa is the negative logarithm of the acid dissociation constant:

$\mathrm{p}K_a = -\log K_a$

$K_a = 10^{-\mathrm{p}K_a}$

• Similarly, for bases:

$\mathrm{p}K_b = -\log K_b$

$K_b = 10^{-\mathrm{p}K_b}$

Base Strength and the Relationship Between Ka and Kb

Base Ionization Constant (Kb)

• For a generic base B: B(aq) + H2O(l) ↔ BH+(aq) + OH–(aq)

• The equilibrium expression is:

$K_b = \frac{[BH^+][OH^-]}{[B]}$

• A larger Kb value indicates a stronger base.

Relationship Between Ka and Kb

For a conjugate acid-base pair:

$K_a \times K_b = K_w$

At 25°C, $K_w = 1.0 \times 10^{-14}$

• If you know Ka, you can find Kb for the conjugate base, and vice versa.

Percent Ionization of Weak Acids

Definition and Calculation

The percent ionization of a weak acid quantifies the fraction of acid molecules that ionize in solution:

$\text{Percent Ionization} = \frac{[H_3O^+]_{eq}}{[HA]_{in}} \times 100\%$

• Example: For a weak acid with Ka = 4.0 × 10–8 and [HA]in = 0.600 M, [H3O+]eq = 1.5 × 10–4 M:

$\text{Percent Ionization} = \frac{1.5 \times 10^{-4}}{0.600} \times 100\% = 0.025\%$

Effect of Acid Concentration on Percent Ionization

• As the concentration of a weak acid increases, the percent ionization decreases.

Calculating pH from Ka

Steps for Calculating pH of a Weak Acid Solution

1. Write the balanced chemical equation for the acid dissociation.

2. Write the Ka expression.

3. Set up an ICE (Initial, Change, Equilibrium) table.

4. Solve for [H3O+] using the Ka expression.

5. Calculate pH from [H3O+].

• Example: For HNO2 with Ka = 4.6 × 10–4 and [HNO2]initial = 0.200 M, pH = 2.02

Summary Table: Key Equilibrium Constants and Relationships

Constant	Definition	Formula
Ka	Acid ionization constant	$K_a = \frac{[A^-][H_3O^+]}{[HA]}$
Kb	Base ionization constant	$K_b = \frac{[BH^+][OH^-]}{[B]}$
Kw	Ion-product constant for water	$K_w = [H_3O^+][OH^-]$
pH	Hydronium ion concentration	$\mathrm{pH} = -\log [H_3O^+]$
pOH	Hydroxide ion concentration	$\mathrm{pOH} = -\log [OH^-]$
Relationship	pH and pOH at 25°C	$\mathrm{pH} + \mathrm{pOH} = 14.00$