Ka and Kb / Weak Acids and Bases

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Core Concept

Weak Acids: Acids that only partially dissociate into H+H^+H+ (or H3O+H_3O^+H3​O+) and their conjugate base in solution.

  • Example: Acetic acid (CH_3COOH) dissociates as: CH_3COOH \rightleftharpoons H^+ + CH_3COO^-

Weak Bases: Bases that only partially accept protons (H^+) in solution.

  • Example: Ammonia (NH3NH_3NH3​) reacts with water as: NH3+H2O⇌NH4++OH−NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^-NH3​+H2​O⇌NH4+​+OH−

Practice Tips

  • Weak acids and bases do not fully dissociate; equilibrium must be considered.

  • Ka​ and Kb​ are measures of acid and base strength, respectively:

    • Larger Ka​ or Kb​: Stronger acid or base.

    • Smaller Ka or Kb​: Weaker acid or base.

  • Approximations simplify calculations, but always verify assumptions.

  • Use Ka ⋅ Kb = Kw to relate conjugate pairs.

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Key Characteristics

Weak Acids vs Weak Bases
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 Ka Measured by Kb

Particle Level Diagram

Dissociation Constants

Acid Dissociation Constant (Ka​)

  • Represents the strength of a weak acid: Ka=[H+][A−][HA]K_a = \frac{[H^+][\text{A}^-]}{[\text{HA}]}Ka​=[HA][H+][A−]​

    • [H+]: Concentration of hydrogen ions.

    • [A−]: Concentration of the conjugate base.

    • [HA]: Concentration of the undissociated acid.

Base Dissociation Constant (Kb​)

  • Represents the strength of a weak base: Kb=[BH+][OH−][B]K_b = \frac{[\text{BH}^+][OH^-]}{[\text{B}]}Kb​=[B][BH+][OH−]​

    • [BH+][\text{BH}^+][BH+]: Concentration of the conjugate acid.

    • [OH−][OH^-][OH−]: Concentration of hydroxide ions.

    • [B][\text{B}][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​=Ka​Kw​​=1.8×10−51.0×10−14​=5.6×10−10

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