Acids and Bases: Definitions, Properties, and Calculations

Chapter 17: Acids and Bases

Definitions of Acids and Bases

Understanding acids and bases is fundamental in chemistry. Several definitions exist, each broadening the scope of what constitutes an acid or a base.

Arrhenius Acids and Bases

• Arrhenius Acid: A substance that, when dissolved in water, increases the concentration of hydrogen ions (H+).

• Arrhenius Base: A substance that, when dissolved in water, increases the concentration of hydroxide ions (OH−).

• Example: HCl is an Arrhenius acid because it dissociates in water to produce H+ and Cl− ions. NaOH is an Arrhenius base because it dissociates to produce Na+ and OH− ions.

Hydrogen Ion and Hydronium Ion

• In aqueous solution, the hydrogen ion (H+) does not exist freely but bonds to water to form the hydronium ion (H3O+).

• For simplicity, H+(aq) and H3O+(aq) are used interchangeably.

• Neutralization Reaction: H+(aq) + OH−(aq) → H2O(l)

Lewis Acids and Bases

• Lewis Acid: An electron pair acceptor.

• Lewis Base: An electron pair donor.

• Many metal ions act as Lewis acids due to their empty orbitals.

• Example: NH3 (Lewis base) donates a pair of electrons to BF3 (Lewis acid) to form an adduct.

Brønsted-Lowry Acids and Bases

• Brønsted-Lowry Acid: A proton (H+) donor.

• Brønsted-Lowry Base: A proton (H+) acceptor.

• Acid-base reactions always involve a pair: one species donates a proton, the other accepts it.

• These reactions can occur in aqueous and non-aqueous solutions, and even in the gas phase.

• Example: NH3(aq) + H2O(l) ⇌ NH4+(aq) + OH−(aq)

The Conjugate Acid-Base Concept

• Every acid forms a conjugate base after donating a proton.

• Every base forms a conjugate acid after accepting a proton.

• Acid + Base ⇌ Conjugate Base + Conjugate Acid

Water as a Solvent

Auto-Ionization of Water

• Water is amphoteric: it can act as both an acid and a base.

• Water undergoes auto-ionization (self-ionization):

$\mathrm{H_2O(l) + H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)}$

• Or simply: $\mathrm{H_2O(l) \rightleftharpoons H^+(aq) + OH^-(aq)}$

Ion-Product Constant of Water, Kw

• The equilibrium constant for water is:

$\mathrm{K_w = [H_3O^+][OH^-] = [H^+][OH^-]}$

• At 25°C, $K_w = 1.0 \times 10^{-14}$

• In neutral water: $[H_3O^+] = [OH^-] = 1.0 \times 10^{-7}$ M

pKw, pH, and pOH

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

• pOH: $\mathrm{pOH = -\log[OH^-]}$

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

• As [H3O+] increases, pH decreases (more acidic).

pH Scale and Measurements

The pH scale is a logarithmic scale used to express the acidity or basicity of a solution.

• pH normally ranges from 0 (very acidic) to 14 (very basic), but values outside this range are possible.

• Each unit change in pH represents a tenfold change in [H+].

• pOH is used similarly for hydroxide ion concentration.

• Example: If [OH−] = 1.0 × 10−6 M, then pOH = 6.00.

• pH + pOH = 14.00 at 25°C.

pH Measurements

• pH is measured using a pH meter, which uses a glass electrode sensitive to [H3O+].

• Less accurate methods include pH paper and indicators.

Weak Acids (Monoprotic): Acid Dissociation Constant (Ka), % Ionization, and pH Calculations

Strong Acids

• Strong acids ionize completely in water; [H+] equals the acid's molarity.

• Example: 0.10 M HCl yields [H3O+] = 0.10 M, so pH = 1.00.

• Common strong acids: HCl, HBr, HI, HNO3, HClO4, HClO3, H2SO4 (first proton only).

Weak Acids

• Weak acids ionize only partially in water.

• General reaction: HA(aq) + H2O(l) ⇌ H3O+(aq) + A−(aq)

• The acid dissociation constant (Ka) quantifies acid strength:

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

• Larger Ka = stronger acid; smaller Ka = weaker acid.

• pKa = −log Ka; smaller pKa = stronger acid.

% Ionization of a Weak Acid

• % Ionization = ([H3O+]eq / [HA]i) × 100

• As acid is diluted, % ionization increases.

Calculating pH of a Weak Acid Solution

• Set up an ICE table (Initial, Change, Equilibrium) for the reaction.

• Assume x (amount ionized) is small if % ionization ≤ 5%.

• Solve for x using Ka expression; x = [H3O+].

• Calculate pH: pH = −log [H3O+].

• If % ionization > 5%, use the quadratic formula for accuracy.

• Example: For 0.15 M acetic acid (Ka = 1.8 × 10−5):

$\mathrm{K_a = \frac{x^2}{0.15} = 1.8 \times 10^{-5} \implies x = 1.6 \times 10^{-3}}$

• % Ionization = (1.6 × 10−3 / 0.15) × 100 = 1.1%

• pH = −log(1.6 × 10−3) = 2.80

Summary Table: Acid Dissociation Constants for Selected Weak Acids

Acid	Formula	Structural Formula	Conjugate Base	Equilibrium Reaction	Ka
Hydrofluoric acid	HF	H–F	F−	HF(aq) + H2O(l) ⇌ H3O+(aq) + F−(aq)	6.8 × 10−4
Nitrous acid	HNO2	H–O–N=O	NO2−	HNO2(aq) + H2O(l) ⇌ H3O+(aq) + NO2−(aq)	4.5 × 10−4
Benzoic acid	C6H5COOH	Ph–COOH	C6H5COO−	C6H5COOH(aq) + H2O(l) ⇌ H3O+(aq) + C6H5COO−(aq)	6.3 × 10−5
Acetic acid	CH3COOH	CH3–COOH	CH3COO−	CH3COOH(aq) + H2O(l) ⇌ H3O+(aq) + CH3COO−(aq)	1.8 × 10−5
Hypochlorous acid	HClO	H–Cl–O	ClO−	HClO(aq) + H2O(l) ⇌ H3O+(aq) + ClO−(aq)	3.0 × 10−8
Hydrocyanic acid	HCN	H–C≡N	CN−	HCN(aq) + H2O(l) ⇌ H3O+(aq) + CN−(aq)	4.9 × 10−10
Phenol	C6H5OH	Ph–OH	C6H5O−	C6H5OH(aq) + H2O(l) ⇌ H3O+(aq) + C6H5O−(aq)	1.3 × 10−10