Acid-Base Equilibria: Ka, Kb, pKa, and pKb

Acid-Base Equilibria

Ka and Kb: Acid and Base Dissociation Constants

The strength of acids and bases is quantitatively described by their dissociation constants, Ka for acids and Kb for bases. These equilibrium constants measure the extent to which an acid or base dissociates in water.

• Ka (Acid Dissociation Constant): Measures the strength of an acid in solution.

• Kb (Base Dissociation Constant): Measures the strength of a base in solution.

Stronger acids have larger Ka values, while stronger bases have larger Kb values. The dissociation of weak acids and bases is incomplete, resulting in equilibrium between the undissociated and dissociated forms.

Key Equilibrium Expressions

Equilibrium Constant (K)	Example Equilibrium Expressions	Acid/Base Strength
Ka (acid dissociation constant)	$\mathrm{HA} + \mathrm{H_2O} \rightleftharpoons \mathrm{H_3O^+} + \mathrm{A^-}$ $K_a = \frac{[\mathrm{H_3O^+}][\mathrm{A^-}]}{[\mathrm{HA}]}$	Stronger Acid: Larger $K_a$ Weaker Acid: Smaller $K_a$
Kb (base dissociation constant)	$\mathrm{B} + \mathrm{H_2O} \rightleftharpoons \mathrm{HB^+} + \mathrm{OH^-}$ $K_b = \frac{[\mathrm{HB^+}][\mathrm{OH^-}]}{[\mathrm{B}]}$	Stronger Base: Larger $K_b$ Weaker Base: Smaller $K_b$

Relationship Between Acid/Base Strength and Ka/Kb

• Strong acids and bases dissociate completely in water (very large Ka or Kb).

• Weak acids and bases only partially dissociate (small Ka or Kb).

Example: Comparing Acid Strengths

Identify the strongest acid from the following list of weak acids based on their Ka values (at 25°C):

• a) HCN, $K_a = 4.9 \times 10^{-10}$

• b) HIO, $K_a = 2.3 \times 10^{-11}$

• c) HNO2, $K_a = 4.6 \times 10^{-4}$

• d) HCrO4-, $K_a = 1.6 \times 10^{-6}$

Solution: The strongest acid is the one with the largest Ka value. Thus, HNO2 ($K_a = 4.6 \times 10^{-4}$) is the strongest acid among the options.

Practice Problems

• Given: Hypochlorous acid ($K_a = 3.2 \times 10^{-8}$) and hydrocyanic acid ($K_a = 4.9 \times 10^{-10}$). Which is the stronger acid? Answer: Hypochlorous acid, because it has a larger Ka value.

• Identify the Bronsted-Lowry acid with the weakest conjugate base: a) HF, $K_a = 6.8 \times 10^{-4}$ b) HCOOH, $K_a = 1.8 \times 10^{-4}$ c) HCN, $K_a = 4.9 \times 10^{-10}$ Answer: HF, because the strongest acid has the weakest conjugate base.

pKa and pKb: Logarithmic Measures of Acid and Base Strength

Definitions and Relationships

The pKa and pKb values are logarithmic expressions of Ka and Kb, respectively, and provide a convenient way to compare acid and base strengths.

• pKa: $pK_a = -\log K_a$

• pKb: $pK_b = -\log K_b$

• Lower pKa or pKb values indicate stronger acids or bases, respectively.

Relationship Between Ka, Kb, pKa, and pKb

Formula	Application
$K_w = K_a \times K_b$	Relates the dissociation constants of a conjugate acid-base pair ($K_w = 1.0 \times 10^{-14}$ at 25°C)
$14 = pK_a + pK_b$	Relates the pKa and pKb of a conjugate acid-base pair at 25°C

pKa and pKb Strength Trends

• Smaller pKa = Stronger acid

• Smaller pKb = Stronger base

• Larger pKa = Weaker acid

• Larger pKb = Weaker base

Example: Calculating pKa

Aspirin (acetylsalicylic acid) has $K_a = 3.3 \times 10^{-4}$. Calculate the pKa of acetylsalicylic acid.

• $pK_a = -\log(3.3 \times 10^{-4})$

• $pK_a \approx 3.48$

Practice Problems

• Which of the following acids is the strongest? a) Acetic acid pKa = 4.76 b) Formic acid pKa = 3.75 c) Ammonium pKa = 9.25 Answer: Formic acid (lowest pKa).

• Determine the pKa given Ka: a) $K_a = 1.3 \times 10^{-5}$ $pK_a = -\log(1.3 \times 10^{-5}) \approx 4.89$

Additional info: The relationship between Ka, Kb, pKa, and pKb is fundamental for predicting the direction of acid-base reactions and for calculating the strengths of conjugate acids and bases. These concepts are essential for understanding chemical equilibria in aqueous solutions.