Weak acid base equilibrium

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  • For a generic monoprotic weak acid H, A with conjugate base A, start superscript, minus, end superscript, the equilibrium constant has the form:
K, start subscript, a, end subscript, equals, start fraction, open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket, open bracket, A, start superscript, minus, end superscript, close bracket, divided by, open bracket, H, A, close bracket, end fraction
  • The acid dissociation constant K, start subscript, a, end subscript quantifies the extent of dissociation of a weak acid. The larger the value of K, start subscript, a, end subscript, the stronger the acid, and vice versa.
  • For a generic weak base B with conjugate acid B, H, start superscript, plus, end superscript, the equilibrium constant has the form:
K, start subscript, b, end subscript, equals, start fraction, open bracket, B, H, start superscript, plus, end superscript, close bracket, open bracket, O, H, start superscript, minus, end superscript, close bracket, divided by, open bracket, B, close bracket, end fraction
  • The base dissociation constant (or base ionization constant) K, start subscript, b, end subscriptquantifies the extent of ionization of a weak base. The larger the value of K, start subscript, b, end subscript, the stronger the base, and vice versa.

Strong vs. weak acids and bases

Strong acids and strong bases refer to species that completely dissociate to form ions in solution. By contrast, weak acids and bases ionize only partially, and the ionization reaction is reversible. Thus, weak acid and base solutions contain multiple charged and uncharged species in dynamic equilibrium.
In this article, we will discuss acid and base dissociation reactions and the related equilibrium constants: K, start subscript, a, end subscript, the acid dissociation constant, and K, start subscript, b, end subscript, the base dissociation constant.

Weak acids and the acid dissociation constant, K, start subscript, a, end subscript

Weak acids are acids that don't completely dissociate in solution. In other words, a weak acid is any acid that is not a strong acid.
The strength of a weak acid depends on how much it dissociates: the more it dissociates, the stronger the acid. In order to quantify the relative strengths of weak acids, we can look at the acid dissociation constant K, start subscript, a, end subscript, the equilibrium constant for the acid dissociation reaction.
For a generic monoprotic weak acid H, A, the dissociation reaction in water can be written as follows: 
H, C, l
H, start subscript, 2, end subscript, S, O, start subscript, 4, end subscriptH, start subscript, 2, end subscript, S, O, start subscript, 4, end subscriptleft parenthesis, H, start subscript, 3, end subscript, P, O, start subscript, 4, end subscript, right parenthesis
\text{HA}(aq)+\text{H}_2\text{O}(l)\rightleftharpoons\text{H}_3\text{O}^+(aq)+\text{A}^-(aq)
Based on this reaction, we can write our expression for equilibrium constant K, start subscript, a, end subscript:
common weak acids malic acid
The table below lists some more examples of weak acids and their K, start subscript, a, end subscript values.
NameFormulaK, start subscript, a, end subscript, left parenthesis, 25, space, degree, C, right parenthesis
AmmoniumN, H, start subscript, 4, end subscript, start superscript, plus, end superscript5, point, 6, times, 10, start superscript, minus, 10, end superscript
Chlorous acidH, C, l, O, start subscript, 2, end subscript1, point, 2, times, 10, start superscript, minus, 2, end superscript
Hydrofluoric acidH, F7, point, 2, times, 10, start superscript, minus, 4, end superscript
Acetic acidC, H, start subscript, 3, end subscript, C, O, O, H1, point, 8, times, 10, start superscript, minus, 5, end superscript

Weak bases and K, start subscript, b, end subscript

Let's now examine the base dissociation constant (also called the base ionization constant) K, start subscript, b, end subscript. We can start by writing the ionization reaction for a generic weak base B in water. In this reaction, the base accepts a proton from water to form hydroxide and the conjugate acid, B, H, start superscript, plus, end superscript:
\text{B}(aq)+\text{H}_2\text{O}(l)\rightleftharpoons\text{BH}^+(aq)+\text{OH}^-(aq)

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