Acid-Base Equilibria: Concepts, Calculations, and Applications

Chapter 16: Acid-Base Equilibria

16.1 Acids and Bases – A Brief Review

This section introduces the fundamental definitions of acids and bases, highlighting the differences between the Arrhenius, Brønsted-Lowry, and Lewis concepts. Understanding these definitions is essential for classifying substances and predicting their behavior in chemical reactions.

• Arrhenius Definition: Acids produce H+ ions in aqueous solution; bases produce OH- ions.

• Brønsted-Lowry Definition: Acids are proton (H+) donors; bases are proton acceptors. This definition is broader than Arrhenius and does not require water as a solvent.

• Lewis Definition: Acids are electron pair acceptors; bases are electron pair donors. This is the most general definition.

• Examples:

  • Monoprotic acid: HCl, HNO3

  • Diprotic acid: H2SO4

  • Triprotic acid: H3PO4

  • Strong base: NaOH, KOH

16.2 Brønsted-Lowry Acids and Bases

The Brønsted-Lowry theory expands the concept of acids and bases to include proton transfer reactions. This section covers the identification of acids, bases, and their conjugate pairs.

• Acid: Substance that donates a proton (H+).

• Base: Substance that accepts a proton (H+).

• Conjugate Acid-Base Pair: Two species that differ by one proton.

• Example: In the reaction $\mathrm{NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^-}$, NH3 is a base, H2O is an acid, NH4+ is the conjugate acid, and OH- is the conjugate base.

• Hydrolysis of water: $\mathrm{H_2O + H_2O \rightleftharpoons H_3O^+ + OH^-}$

Conjugate Acid-Base Pairs Table

Acid	Conjugate Base
HCl	Cl-
H2SO4	HSO4-
NH4+	NH3
H2O	OH-

16.3 The Autoionization of Water

Water can act as both an acid and a base, undergoing autoionization to produce hydronium and hydroxide ions. The equilibrium constant for this process is known as the ion-product constant for water, $K_w$.

• Autoionization Reaction: $\mathrm{2H_2O \rightleftharpoons H_3O^+ + OH^-}$

• Ion-Product Constant: $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$ at 25°C

• Neutral Solution: $[H_3O^+] = [OH^-] = 1.0 \times 10^{-7}$ M

• Acidic Solution: $[H_3O^+] > [OH^-]$

• Basic Solution: $[H_3O^+] < [OH^-]$

Summary Table: Water Autoionization

Condition	[H3O+]	[OH-]	Solution Type
Neutral	$1.0 \times 10^{-7}$	$1.0 \times 10^{-7}$	Neutral
Acidic	>$1.0 \times 10^{-7}$	<$1.0 \times 10^{-7}$	Acidic
Basic	<$1.0 \times 10^{-7}$	>$1.0 \times 10^{-7}$	Basic

16.4 The pH Scale

The pH scale is a logarithmic measure of the hydrogen ion concentration in a solution. It is widely used to express the acidity or basicity of aqueous solutions.

• Definition: $\mathrm{pH = -\log[H^+]}$

• pOH: $\mathrm{pOH = -\log[OH^-]}$

• Relationship: $\mathrm{pH + pOH = 14.00}$ at 25°C

• Neutral Solution: pH = 7.00

• Acidic Solution: pH < 7.00

• Basic Solution: pH > 7.00

• Calculating [H+] from pH: $[H^+] = 10^{-\mathrm{pH}}$

• Calculating pH from [H+]: $\mathrm{pH = -\log[H^+]}$

• Significant Figures: The number of decimal places in pH equals the number of significant figures in [H+].

pH Scale Table

pH	[H+]	Solution Type
0	$1.0 \times 10^0$	Strongly Acidic
7	$1.0 \times 10^{-7}$	Neutral
14	$1.0 \times 10^{-14}$	Strongly Basic

• Measuring pH: pH can be measured using indicators (color change), pH paper, or electronic pH meters.

• Examples of Indicators: Methyl red (pH 4.4–6.0), Bromothymol blue (pH 6.0–7.6), Phenolphthalein (pH 8.2–10.0).

16.5 Strong Acids and Bases

Strong acids and bases dissociate completely in aqueous solution. This section lists common strong acids and bases and provides guidance for calculations involving their solutions.

• Strong Acids: HCl, HBr, HI, HNO3, HClO4, H2SO4 (first dissociation only)

• Strong Bases: Group 1A and 2A metal hydroxides (e.g., NaOH, KOH, Ca(OH)2)

• Calculation Example: For 0.10 M HCl, $[H^+] = 0.10$ M, so $\mathrm{pH = -\log(0.10) = 1.00}$

Table: Common Strong Acids and Bases

Strong Acids	Strong Bases
HCl	NaOH
HBr	KOH
HI	Ca(OH)2
HNO3	Ba(OH)2
HClO4	Sr(OH)2
H2SO4 (1st dissociation)	LiOH

16.6 Weak Acids

Weak acids only partially dissociate in solution. The extent of dissociation is described by the acid dissociation constant, $K_a$.

• General Dissociation: $\mathrm{HA \rightleftharpoons H^+ + A^-}$

• Acid Dissociation Constant: $K_a = \frac{[H^+][A^-]}{[HA]}$

• Smaller $K_a$: Indicates a weaker acid (less dissociation).

• Example: Acetic acid, $K_a = 1.8 \times 10^{-5}$

Table: Relative Strengths of Acids (Inferred)

Acid	$K_a$	Strength
HCl	Very large	Strong
Acetic acid	$1.8 \times 10^{-5}$	Weak
HF	$6.8 \times 10^{-4}$	Weak

Additional info: The notes also include practice problems and visual aids for pH measurement, as well as a summary of the relationships between acid/base strength and their conjugate pairs.