Ka and Kb values

1. Introduction

• $K_a$ (Acid Dissociation Constant) measures the strength of an acid in solution.
• $K_b$ (Base Dissociation Constant) measures the strength of a base in solution.
• Both are equilibrium constants used to describe the extent of ionisation in water.

2. Ionisation of Acids and Bases

For Acids:

• A weak acid $(HA)$ partially ionises in water: $HA + H_2O \rightleftharpoons H_3O^+ + A^-$

• Ka expression: $K_a = \frac{[H_3O^+][A^-]}{[HA]}$

• Strength of an acid:

  • Strong acids → High $K_a$ value (more ionisation).
  • Weak acids → Low $K_a$ value (less ionisation).

For Bases:

• A weak base $(B)$ partially ionises in water: $B + H_2O \rightleftharpoons BH^+ + OH^-$

• Kb expression: $K_b = \frac{[BH^+][OH^-]}{[B]}$

• Strength of a base:

  • Strong bases → High $K_b$ value (more ionisation).
  • Weak bases → Low $K_b$ value (less ionisation).

3. Relationship Between Acid and Base Strength

• Stronger acid → Weaker conjugate base.
• Stronger base → Weaker conjugate acid.
• The relationship between Ka and Kb for a conjugate acid-base pair: $K_a \times K_b = K_w$

where $K_w$ is the ionisation constant of water ( $1.0 \times 10^{-14}$ at $25°C$).

4. Application in $pH$ Calculations

• Acids with higher $K_a$ values produce more $H_3O^+$, leading to lower $pH.$
• Bases with higher $K_b$ values produce more $OH−OH^-$, leading to higher $pH.$

5. Example Comparison of Base Strength

Base	$K_b$ Value	Strength
Ammonia $(NH₃)$	$1.8 \times 10^{-5}$	Weak
Hydroxylamine $(HONH₂)$	$9.1 \times 10^{-9}$	Weaker
Ethylamine $(C₂H₅NH₂)$	$4.3 \times 10^{-4}$	Stronger

• The larger the $K_b$, the stronger the base.

6. Key Takeaways

• Higher $K_a$ = Stronger Acid.
• Higher $K_b$ = Stronger Base.
• Ka and $K_b$ are inversely related for conjugate acid-base pairs.
• $pH$ and $pOH$ are influenced by $K_a$ and $K_b$ values.