Ka and Kb / Weak Acids and Bases
Related Examples and Practice Problems
Topic Summary & Highlights
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Core Concept
Weak Acids: Acids that only partially dissociate into $\text{H}^+$ (or $\text{H}_3\text{O}^+$) and their conjugate base in solution.
Example: Acetic acid ($\text{CH}_3\text{COOH}$) dissociates as: $\text{CH}_3\text{COOH} \rightleftharpoons \text{H}^+ + \text{CH}_3\text{COO}^-$
Weak Bases: Bases that only partially accept protons ($\text{H}^+$) in solution.
Example: Ammonia ($\text{NH}_3$) reacts with water as: $\text{NH}_3 + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4^+ + \text{OH}^-$
Practice Tips
Weak acids and bases do not fully dissociate; equilibrium must be considered.
$K_a$ and $K_b$ are measures of acid and base strength, respectively:
Larger $K_a$ or $K_b$: Stronger acid or base.
Smaller $K_a$ or $K_b$: Weaker acid or base.
Approximations simplify calculations, but always verify assumptions.
Use Ka ⋅ Kb = Kw to relate conjugate pairs.
Key Characteristics
| Property | Weak Acids | Weak Bases |
|---|---|---|
| Dissociation | Partial dissociation | Partial proton acceptance |
| Equilibrium | Establish equilibrium between dissociated and undissociated forms | Establish equilibrium between protonated and unprotonated forms |
| Ion Concentration | Produces fewer \( H^+ \) ions compared to strong acids | Produces fewer \( OH^- \) ions compared to strong bases |
| Conductivity | Poor conductor due to low ion concentration | Poor conductor due to low ion concentration |
| Strength Indicator | Measured by \( K_a \) | Measured by \( K_b \) |
Particle Level Diagram
Dissociation Constants
Acid Dissociation Constant (Ka)
Represents the strength of a weak acid: $$K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$$
[$H^+$]: Concentration of hydrogen ions.
[$\text{A}^-$]: Concentration of the conjugate base.
[$\text{HA}$]: Concentration of the undissociated acid.
Base Dissociation Constant (Kb)
Represents the strength of a weak base: $K_b = \frac{[\text{BH}^+][\text{OH}^-]}{[\text{B}]}$
Where:
$[\text{BH}^+]$: Concentration of the conjugate acid.
$[\text{OH}^-]$: Concentration of hydroxide ions.
$[\text{B}]$: Concentration of the unreacted base.
Relationship Between Ka, Kb, and Kw
For a conjugate acid-base pair: Ka⋅Kb=KwK_a \cdot K_b = K_wKa⋅Kb=Kw
Kw=1.0×10−14K_w = 1.0 \times 10^{-14}Kw=1.0×10−14 at 25°C.
Example:
For acetic acid (Ka=1.8×10−5K_a = 1.8 \times 10^{-5}Ka=1.8×10−5) and acetate ion: Kb=KwKa=1.0×10−141.8×10−5=5.6×10−10K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.6 \times 10^{-10}Kb=KaKw=1.8×10−51.0×10−14=5.6×10−10