Acid/base Dissociation Constants and Kw

This is part of the HSC Chemistry course under the topic Quantitative Analysis.

HSC Chemistry Syllabus

calculate and apply the dissociation constant (K_a) and pK_a(pK_a = –log10 (K_a)) to determine the difference between strong and weak acids (ACSCH098)

K_w(equilibrium constant of the self-ionisation of water) is the product of K_a of a weak acid and K_b 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 K_a & low pK_a	High strength	Low strength
Low K_a & high pK_a	Low strength	High strength

	*Weak base*	*Conjugate weak acid*
High K_b & low pK_b	High strength	Low strength
Low K_b & high pK_b	Low strength	High strength