5.3.2 Ka, pH & Kw

Weak acids

• A weak acid is an acid that partially (or incompletely) dissociates in aqueous solutions
  • Eg. most organic acids (ethanoic acid), HCN (hydrocyanic acid), H₂S (hydrogen sulfide) and H₂CO₃ (carbonic acid)

• The position of the equilibrium is more over to the left and an equilibrium is established

The diagram shows the partial dissociation of a weak acid in aqueous solution

• As this is an equilibrium we can write an equilibrium constant expression for the reaction

• This constant is called the acid dissociation constant, K_a, and has the units mol dm^-3
• Values of K_a are very small, for example for ethanoic acid K_a = 1.74 x 10^-5 mol dm^-3 
• When writing the equilibrium expression for weak acids, the following assumptions are made:
  • The concentration of hydrogen ions due to the ionisation of water is negligible

• The value of K_a indicates the extent of dissociation
  • The higher the value of K_a the more dissociated the acid and the stronger it is
  • The lower the value of K_a the weaker the acid

pK_a

• The range of values of K_a is very large and for weak acids, the values themselves are very small numbers

Table of K_a values

• For this reason it is easier to work with another term called pK_a
• The pK_a  is the negative log of the K_a value, so the concept is analogous to converting [H⁺] into pH values

pK_a = -logK_a

• Looking at the pK_a values for the same acids:

Table of pK_a values

• The range of pK_a values for most weak acids lies between 3 and 7

pH

• The acidity of an aqueous solution depends on the number of H⁺ (H₃O⁺) ions in solution
• The pH is defined as:

pH = -log[H⁺]

• • where [H⁺] is the concentration of hydrogen ions in mol dm^–3

• Similarly, the concentration of H⁺ of a solution can be calculated if the pH is known by rearranging the above equation to:

[H⁺] = 10^-pH

• The pH scale is a logarithmic scale with base 10
• This means that each value is 10 times the value below it. For example, pH 5 is 10 times more acidic than pH 6.
• pH values are usually given to 2 decimal places
• The relationship between concentration is easily seen on the following table

pH & [H+] Table

The ionic product of water, K_w

• In all aqueous solutions, an equilibrium exists in water where a few water molecules dissociate into protons and hydroxide ions
• We can derive an equilibrium constant for the reaction:

• This is a specific equilibrium constant called the ionic product for water
• The product of the two ion concentrations is always 1 x 10^-14 mol² dm^-6
• This makes it straightforward to see the relationship between the two concentrations and the nature of the solution:

[H⁺] & [OH^–] Table