Ionization Constants ($K_a$ & $K_b$)
Strength of Acids and Bases | Ionic Equilibrium
1. What is an Ionization Constant?
Strong electrolytes dissociate completely, but weak electrolytes dissociate only partially. The equilibrium constant for this dissociation is called the Ionization Constant. It measures the strength of a weak acid or base.
2. Acid Dissociation Constant ($K_a$)
For a weak acid $HA$ dissociating in water:
$$ HA(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + A^-(aq) $$
$$ K_a = \frac{[H_3O^+][A^-]}{[HA]} $$
- Significance: Larger $K_a$ $\Rightarrow$ Stronger Acid $\Rightarrow$ Higher $[H^+]$.
- pKa Scale: $pK_a = -\log_{10} K_a$. (Smaller $pK_a$ $\Rightarrow$ Stronger Acid).
3. Base Dissociation Constant ($K_b$)
For a weak base $B$ ionizing in water:
$$ B(aq) + H_2O(l) \rightleftharpoons BH^+(aq) + OH^-(aq) $$
$$ K_b = \frac{[BH^+][OH^-]}{[B]} $$
- Significance: Larger $K_b$ $\Rightarrow$ Stronger Base $\Rightarrow$ Higher $[OH^-]$.
- pKb Scale: $pK_b = -\log_{10} K_b$. (Smaller $pK_b$ $\Rightarrow$ Stronger Base).
4. Relationship for Conjugate Acid-Base Pairs
For any conjugate pair (e.g., $HA$ and $A^-$):
$$ \text{Acid (HA)}: K_a \quad \text{and} \quad \text{Base (A}^-): K_b $$
$$ K_a \times K_b = K_w $$
$$ pK_a + pK_b = pK_w = 14 \, (\text{at } 25^\circ C) $$
Conclusion: A strong acid has a weak conjugate base, and a weak acid has a strong conjugate base.
5. Ostwald's Dilution Law
For a weak electrolyte ($HA$) with concentration $C$ and degree of ionization $\alpha$:
$$ K_a = \frac{C\alpha \cdot C\alpha}{C(1-\alpha)} = \frac{C\alpha^2}{1-\alpha} $$Since $\alpha \ll 1$ for weak electrolytes, $(1-\alpha) \approx 1$.
$$ K_a \approx C\alpha^2 \quad \Rightarrow \quad \alpha = \sqrt{\frac{K_a}{C}} $$
This shows that the degree of ionization ($\alpha$) increases upon dilution (as $C$ decreases).
Practice Quiz
Test your knowledge on Ionization Constants.
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