Acid and Base Dissociation Constants (Ka and Kb)

Jul 25, 2024

Acid and Base Dissociation Constants (Ka and Kb)

Acid Dissociation Constant (Ka)

  • Definition: Measures how much acid molecules dissociate in a water solution.

  • Expression: For an acid HA, dissociating in water:

    $$HA \leftrightharpoons H^+ + A^-$$

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

  • Interpretation:

    • Larger $K_a$ value: Stronger acid (more dissociation).
    • Smaller $K_a$ value: Weaker acid (less dissociation).

Using Data to Calculate Ka

  • Use equilibrium concentrations (final data), not initial data.
  • Example: If $[H^+] = 0.2$, $[A^-] = 0.2$, and $[HA] = 0.8$, then use these in the $K_a$ expression.

Exercises

  1. Write dissociation reactions and $K_a$ expressions:

    • Nitrous acid (HNO_2):

      $$HNO_2 \leftrightharpoons H^+ + NO_2^-$$

      $$K_a = \frac{[H^+][NO_2^-]}{[HNO_2]}$$

    • Acetic acid (CH_3COOH):

      $$CH_3COOH \leftrightharpoons H^+ + CH_3COO^-$$

      $$K_a = \frac{[H^+][CH_3COO^-]}{[CH_3COOH]}$$

    • Phosphoric acid (H_3PO_4):

      $$H_3PO_4 \leftrightharpoons H^+ + H_2PO_4^-$$

      $$K_{a1} = \frac{[H^+][H_2PO_4^-]}{[H_3PO_4]}$$

      • Only the first proton dissociation is considered here for $K_{a1}$.

  2. Identify the weakest acid:

    • Compare $K_a$ values; the smallest $K_a$ indicates the weakest acid.
    • Example: Acetic acid $K_a = 1.8 \times 10^{-5}$ (weak acid).

Base Dissociation Constant (Kb)

  • Definition: Measures how much base molecules dissociate in a water solution.

  • Expression: For a base B, dissociating in water:

    $$B + H_2O \leftrightharpoons BH^+ + OH^-$$

    $$K_b = \frac{[BH^+][OH^-]}{[B]}$$

  • Interpretation:

    • Larger $K_b$ value: Stronger base.
    • Smaller $K_b$ value: Weaker base.

  • Example: Formate ion ($HCOO^-)$:

    $$HCOO^- + H_2O \leftrightharpoons HCOOH + OH^-$$

    $$K_b = \frac{[HCOOH][OH^-]}{[HCOO^-]}$$

Ion Product Constant (Kw)

  • Expression:

    $$K_w = [H^+][OH^-] = 1.0 \times 10^{-14}$$ at 25°C.

  • Implications:

    • Neutral solution: $[H^+] = [OH^-] = 1.0 \times 10^{-7}$ (pH 7).
    • Acidic solution: $[H^+] > [OH^-]$.
    • Basic solution: $[H^+] < [OH^-]$.

Example Calculations

  1. Given: $[OH^-] = 1.0 \times 10^{-5}$ at 25°C.

  2. Find: $[H^+]$.

  3. Solution:

    $$[H^+] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-5}} = 1.0 \times 10^{-9}$$

  4. Interpretation:

    • Higher $[OH^-]$ than $[H^+]$: Basic solution.

  5. Neutral Solution Criteria: $[H^+] = [OH^-] = 1.0 \times 10^{-7}$ at 25°C.