Buffer and Buffer Capacity

Buffers are formed by the combination of either a weak acid and the salt of its conjugate base or vice versa. They resist a change in pH against the addition of a small amount of acid or base.

The pH of a buffer is calculated by using the Henderson equation.

pH = pKa + log [Salt]

                         [Acid]

                                 or

pH = pKw - pKb + log [Base]

                                      [Salt]

 Where,

              pKa = Logarithmic dissociation constant of acid
              pKb= Logarithmic dissociation constant of base
              pKw= pKa x pKb
              [Acid]= Concentration of acid in moles
              [Salt]= Concentration of salt in moles

 Buffer capacity is the measure of the extent to which a buffer can resist a change in pH. It is represented by grams equivalent of the acid or base that is required to change the pH of one liter of the solution by one unit.

The Buffer capacity is usually calculated by the following equation,

Buffer capacity = 2.3 C   Ka [H3O+]

                                         ( Ka + [H3O+] )2

Where,

                       C = [Acid] + [Salt]

                       Ka= Dissociation constant of acid

                       [H3O+]= -log(-pH)
                       C = moles of salt / Liter + moles of acid / Liter 

Buffer and buffer capacity is a very useful tool for formulation development. Especially for the development of ophthalmic preparations, it is crucial to maintain the pH of the solution or suspension in the required range.

Example,

Use Borax and Boric acid to prepare the buffer for an ophthalmic solution. If 7 g of Boric acid is added in 500 mL solution, how much Sodium borate would be required to produce a buffer of 7.7 pH?. If pKa and Ka values of boric acid are 9.27 and 5.8x10-10 respectively, calculate the buffer capacity of this solution.

Lets use The Henderson equation,

pH = pKa + log [Salt]

                         [Acid]

By putting the values in this equation,

7.7 = 9.27 + log [Salt]

                                                                              [0.113]     (7g Boric acid = 0.113 moles)

Solving this equation gives,

                                                  [Salt] = 1.159 g of Borax     (0.003 moles of Borax = 1.159 g)

Calculate buffer capacity by using the following formula,

Buffer capacity = 2.3 C   Ka [H3O+]

                                         ( Ka + [H3O+] )2

Buffer capacity = 2.3 x 0.232 x  5.8x10-10 x 1.99x10-8
                                                  (5.8x10-10 + 1.99x10-8)2

Buffer capacity = 0.014

Note: For ophthalmic preparations, buffer capacity is usually adjusted between 0.01 - 0.1.