Acid-Base Equilibria: Definitions, Calculations, and Examples

Acid-Base Equilibria

Definitions of Acids and Bases

Acids and bases are fundamental concepts in chemistry, with several definitions that describe their behavior in different contexts:

• Arrhenius Definition: Acids produce H+ ions (or H3O+) in aqueous solution, while bases produce OH– ions.

• Brønsted-Lowry Definition: Acids are proton donors; bases are proton acceptors.

• Lewis Definition: Acids accept electron pairs; bases donate electron pairs.

Arrhenius Acids and Bases

Arrhenius acids and bases are defined by their ability to increase the concentration of H+ or OH– ions in water:

• Strong Acids: Completely dissociate in water. Examples: HCl, HBr, HI, HNO3, H2SO4, HClO4.

• Weak Acids: Partially dissociate; not on the strong acid list.

• Strong Bases: Completely dissociate in water. Examples: LiOH, NaOH, KOH, Ca(OH)2, Sr(OH)2, Ba(OH)2.

• Weak Bases: Partially dissociate; often increase OH– indirectly (e.g., NH3).

Hydronium Ion Formation

H+ ions are unstable in water and react to form hydronium ions (H3O+):

• Hydronium Ion: The H3O+ ion formed when an acid reacts with water.

• H+ and H3O+ are often used interchangeably.

Acid-Base Neutralization

Acid-base neutralization reactions produce water and a salt:

• General Reaction: Acid + Base → Water + Salt

• Example: HNO3 (aq) + KOH (aq) → H2O (l) + KNO3 (aq)

• Salt: An ionic compound formed from the cations and anions remaining after water is produced.

Brønsted-Lowry Acids and Bases

Brønsted-Lowry theory focuses on proton transfer:

• Acid: Proton donor (e.g., HCl, H2SO4, HC2H3O2).

• Base: Proton acceptor (e.g., OH–, NH3).

• Amphiprotic: Water can act as either an acid or a base depending on the reaction.

Conjugate Acid-Base Pairs

Acid-base reactions create pairs that differ by one proton:

• Conjugate Acid: Formed when a base gains a proton.

• Conjugate Base: Formed when an acid loses a proton.

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

Autoionization of Water and Ion Product (Kw)

Water undergoes autoionization, producing H+ and OH– ions:

• Reaction: H2O (l) ⇌ H+ (aq) + OH– (aq)

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

• Kw: The equilibrium constant for water's autoionization.

Calculating [H+] and [OH–]

Knowing one ion concentration allows calculation of the other:

• Formula: $[H^+][OH^-] = 1.0 \times 10^{-14}$

• Example: If [H+] = 1.8 × 10–5 M, then [OH–] = $\frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.6 \times 10^{-10}$ M

Equilibrium in Pure Water

In pure water, [H+] = [OH–], and the solution is neutral:

• Calculation: $x^2 = 1.0 \times 10^{-14}$, so $x = 1.0 \times 10^{-7}$ M

• Neutral Solution: pH = 7

pH Scale and Calculations

The pH scale is a convenient way to express acidity and basicity:

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

• Neutral: pH = 7

• Acidic: pH < 7

• Basic: pH > 7

• Significant Figures: Only digits to the right of the decimal in pH are significant.

pOH and pKw

pOH is analogous to pH for hydroxide ions, and pKw relates both:

• Definition: $\text{pOH} = -\log [OH^-]$

• pKw: $\text{pK}_w = -\log K_w = 14.00$

• Relationship: $\text{pH} + \text{pOH} = \text{pK}_w = 14.00$

• Example: If pH = 10.0, pOH = 4.0

Strong Acids and Bases: pH Calculations

For strong acids and bases, the ion concentration equals the solute concentration:

• Example: 0.0142 M HBr → [H+] = 0.0142 M, pH = $-\log(0.0142) = 1.848$

• Example: 1.5 M Sr(OH)2 → [OH–] = 3.0 M (since 2 OH– per formula unit)

Weak Acids and Bases: Equilibrium Calculations

Weak acids and bases do not fully dissociate; equilibrium expressions are used:

• Acid Dissociation: $\text{HC}_2\text{H}_3\text{O}_2 (aq) \rightleftharpoons H^+ (aq) + \text{C}_2\text{H}_3\text{O}_2^- (aq)$

• Ka (acid dissociation constant): $K_a = \frac{[H^+][C_2H_3O_2^-]}{[HC_2H_3O_2]}$

• Base Dissociation: $\text{NH}_3 (aq) + H_2O (l) \rightleftharpoons \text{NH}_4^+ (aq) + OH^- (aq)$

• Kb (base dissociation constant): $K_b = \frac{[NH_4^+][OH^-]}{[NH_3]}$

Polyprotic Acids

Polyprotic acids can donate more than one proton, each with its own dissociation constant:

• Example: H2SO4 and H3PO4 have multiple dissociation steps.

• Ka values: Each step has a unique Ka, decreasing with each proton removed.

Summary Table: Strong Acids and Bases

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

Summary Table: pH, pOH, and Ion Concentrations

[H3O+] (M)	[OH–] (M)	pH	pOH	Sample Solution
10–1	10–13	1	13	1 M HCl
10–7	10–7	7	7	Pure water
10–14	10–1	14	0	1 M NaOH
Additional info: See image_3 for more sample solutions and their pH values.