Acid/base Dissociation Constants and Kw
HSC Chemistry Syllabus
- calculate and apply the dissociation constant (Ka) and pKa (pKa = –log10 (Ka)) to determine the difference between strong and weak acids (ACSCH098)
Kw (equilibrium constant of the self-ionisation of water) is the product of Ka of a weak acid and Kb of its conjugate base
$$K_w = K_a \times K_b$$
Derivation (do not memorise): For a generic acid-base system,
$$\boldsymbol{Acid}: \hspace{0.5cm} HA_{(aq)} + H_2O_{(l)} \leftrightharpoons A^-_{(aq)} + H_3O^+_{(aq)} \hspace{0.5cm} K_a = \frac{[A^-][H_3O^+]}{[HA]}$$
$$\boldsymbol{Base}: \hspace{0.5cm} A^-_{(aq)} + H_2O_{(l)} \leftrightharpoons HA_{(aq)} + OH^-_{(aq)} \hspace{0.5cm} K_b = \frac{[HA][OH^-]}{[A^-]}$$
$$K_a \times K_b = \frac{[{A^-}][H_3O^+]}{[HA]} \times \frac{[HA][OH^-]}{[A^-]}$$
$$K_a \times K_b = [H_3O^+_{(aq)}][OH^-_{(aq)}] = 1.0 \times 10^{-14}$$
This means at 25℃ (298 K):
$$ K_a = \frac{10^{-14}}{K_b} \hspace{3cm} K_b = \frac{10^{-14}}{K_a}$$
The mathematical implication of this relationship between acid and base dissociation constants is that:
|
Weak acid |
Conjugate weak base |
High Ka & low pKa |
High strength |
Low strength |
Low Ka & high pKa |
Low strength |
High strength |
|
Weak base |
Conjugate weak acid |
High Kb & low pKb |
High strength |
Low strength |
Low Kb & high pKb |
Low strength |
High strength |