Acid dissociation constant

In this lesson, we will learn:

• To recall the equilibrium ionization expressions for weak acids and bases.
• How to relate K_a and K_b for conjugate acid/base pairs.
• How to calculate concentration of aqueous ions in weak acid/base solutions.

• In Autoionization of water, we looked at the equilibrium:
  
  2 H₂O_(l) $\, \rightleftharpoons \,$ H₃O⁺ _(aq) + OH^- _(aq)
  The equilibrium constant was expressed as:
  
  K_w = [H₃O⁺] [OH^-] = 1 * 10 ^-14 at 25^oC
  We saw the effect of adding strong acids/bases to equilibrium concentrations of water and dissolved ions. That was straightforward because strong acids and bases experience 100% dissociation in water.
  We also saw in
• In strong and weak acids and bases that weak acids and bases do not experience 100% dissociation. This makes expressions for their dissociation in water more complicated.
  
  
• Every weak acid has an acid dissociation constant, K_a and a weak base a base dissociation constant, K_b. These are equilibrium constants showing how much the acid/base dissociates when dissolved in water (aqueous solution).
  For a weak acid HX dissolved in water:
  
  K_a = $\frac{[H_3O^{+}] [X^{-}]}{[HX]}$
  For a weak base B dissolved in water:
  
  K_b = $\frac{[HB^{+}] [OH^{-}]}{[B]}$
  
  • Just like in the ionization of water and other equilibria; this is an equilibrium constant expression. This means that the higher the K_a/K_b value, the greater the degree of dissociation (because the concentrations of the dissociated ions, in the numerator, are larger values) and therefore the stronger the acid or base.
  • Remember that for strong acids and bases K_a/K_b values are not normally used. This is because in the K_a expression, their [HX] or [B] is equal to or almost zero due to complete dissociation, so the values are incredibly large.
  • For strong acids, pK_a is used instead of K_a. pK_a is the negative logarithm of the K_a value and is more appropriate to use for strong acids, instead of the extremely large K_a values they have.
  
  
• In Conjugate acids and bases, we learned in a conjugate pair that a stronger conjugate acid will have a weaker the conjugate base. This relationship affects the concentration of aqueous ions and therefore affects the K_a and K_b values for a conjugate acid/base pair!
  Consider the equations for the conjugate pair acid-base pair HX and X^-:
  
  Conjugate acid: $\qquad$ HX + H₂O $\, \rightleftharpoons \,$ X^- + H₃O⁺ $\qquad$
  K_a = $\frac{[H_3O^{+}] [X^{-}]}{[HX]}$
  Conjugate base: $\qquad$ X^- + H₂O $\, \rightleftharpoons \,$ HX + OH^- $\qquad$
  K_b = $\frac{[HX] [OH^{-}]}{[X^{-}]}$
  
  • Both equations depend on [X^-] and [HX] so K_a and K_b themselves can be related, and terms cancelled out:
    
    
    As you can see, the result is the product of [H₃O⁺] and [OH^-] which is the expression for K_w. Therefore for a conjugate pair:
    
    K_a * K_b = K_w