Acid-Base Equilibria and Strengths in GOB Chemistry

Acid-Base Equilibria

Acid Dissociation Constant (Ka)

The acid dissociation constant, Ka, quantifies the strength of a weak acid in water. It is defined for the ionization of a monoprotic acid (HA) as follows:

• Ionization equation: HA (aq) + H2O (l) → A- (aq) + H3O+ (aq)

• Equilibrium expression:

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

• Ka measures the strength of weak acids; higher Ka means a stronger acid.

• For weak bases, the analogous constant is Kb (base dissociation constant).

Relationship Between Ka and Kb

The relationship between the acid dissociation constant (Ka) and the base dissociation constant (Kb) for a conjugate acid-base pair is given by:

$K_w = K_a \times K_b$

• Kw is the ion-product constant for water ($K_w = 1.0 \times 10^{-14}$ at 25°C).

• pKa and pKb are related by: $pK_a + pK_b = 14$

• Strong acids have Ka >> 1; weak acids have Ka < 1.

Strengths of Acids and Bases

The strength of an acid or base is determined by its ability to donate or accept protons. The following generalizations apply:

• The higher the Ka, the stronger the acid and the greater the concentration of H3O+.

• The lower the pKa, the stronger the acid.

• The higher the Kb, the stronger the base and the greater the concentration of OH-.

Conjugate Acid-Base Pairs

Every acid has a conjugate base, and every base has a conjugate acid. The strength of a conjugate base is inversely related to the strength of its acid:

• A strong acid has a weak conjugate base.

• A weak acid has a relatively stronger conjugate base.

Practice Problems and Examples

• Determining Ka from Kb: If the Kb of NH3 is $1.76 \times 10^{-5}$, the acid dissociation constant of its conjugate acid (NH4+) can be found using $K_a = \frac{K_w}{K_b}$.

• Comparing Acid Strengths: Knowing that HF has a higher Ka than CH3COOH, HF is the stronger acid. The equilibrium for the reaction HF (aq) + CH3COO- (aq) → F- (aq) + CH3COOH (aq) lies to the right, favoring the formation of the weaker acid and base.

Table: Acid and Base Strengths

The following table summarizes the Kb values for several Bronsted-Lowry bases and Ka values for acids, as referenced in the practice questions:

Base	Kb
C5H5N	8.3 × 10-9
C6H7N	1.7 × 10-9
C7H9N	1.0 × 10-9
C8H11N	3.5 × 10-9
C9H13N	3.9 × 10-11

Acid	Ka
HCNO	2.0 × 10-4
HF	3.5 × 10-4
HNO2	2.5 × 10-5
HCO2H	4.3 × 10-4

Key Practice Concepts

• Greatest concentration of hydroxide ions: The base with the highest Kb will produce the most OH- ions in solution.

• Weakest conjugate base: The acid with the highest Ka is the strongest acid and thus has the weakest conjugate base.

Summary Table: Acid and Base Strength Relationships

Property	Strong Acid	Weak Acid
Ka	High	Low
pKa	Low	High
Conjugate Base Strength	Weak	Stronger

Example Calculation:

• Given Kb for NH3 is $1.76 \times 10^{-5}$, calculate Ka for NH4+:

$K_a = \frac{K_w}{K_b} = \frac{1.0 \times 10^{-14}}{1.76 \times 10^{-5}} = 5.68 \times 10^{-10}$

Additional info: The notes also reference equilibrium positions and how acid/base strength affects the direction of equilibrium in reactions between acids and bases.