Buffer Solution - Buffer Capacity

Buffer Capacity

Buffer capacity, β, is a quantitative measure of the resistance of a buffer solution to pH change on addition of hydroxide ions. It can be defined as follows.

where dn is an infinitesimal amount of added base and d(p) is the resulting infinitesimal change in the cologarithm of the hydrogen ion concentration. With this definition the buffer capacity of a weak acid, with a dissociation constant K_a, can be expressed as

where C_A is the analytical concentration of the acid. pH is approximately equal to -log₁₀.

There are three regions of high buffer capacity.

• At very low p the first term predominates and β increases in proportion to the hydrogen ion concentration. This is independent of the presence or absence of buffering agents and applies to all solvents.
• In the region p = pK_a ± 2 the second term becomes important. Buffer capacity is proportional to the concentration of the buffering agent, C_A, so dilute solutions have little buffer capacity.
• At very high p the third term predominates and β increases in proportion to the hydroxide ion concentration. This is due to the self-ionization of water and is independent of the presence or absence of buffering agents.

The buffer capacity of a buffering agent is at a maximum p = pK_a. It falls to 33% of the maximum value at p = pK_a ± 1 and to 10% at p = pK_a ± 1.5. For this reason the useful range is approximately pK_a ± 1.