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 (Ka) and pK(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