(Eqn
2)
Most biological systems will function only within a quite narrow range of conditions, and their activity can vary widely within that range. The acidity, or free proton concentration, of the environment is an important parameter. To prevent the proton concentration of a solution from changing, compounds can be added to a solution that "buffer" or minimize such changes. A compound will act as a proton concentration buffer if it limits changes in proton concentration by binding protons when the proton concentration of the solution increases and releasing bound protons when the proton concentration decreases (Eqn 1).
Buffer×H+ <=> H+ + Buffer (Eqn 1)
Unfortunately, any one compound will be effective as a buffer only for a limited range of proton concentrations, and so the first step in preparing a buffer is deciding which buffer to use. Since a buffer is most effective when about half is in the acid form (Buffer× H+) and half in the base form (Buffer), i.e., when half of its proton binding sites are filled, a buffer should be chosen that will be about half filled at the proton concentration desired.
The affinity of a compounds for protons is often expressed as its acid dissociation constant (Ka), defined in Eqn 2. This is convenient because, as can be seen from Eqn 2, the value of the acid dissociation constant is equivalent to the proton concentration of a solution at which the compound will have half of its proton binding sites filled, i.e. [Buffer] = [Buffer ×H+].
(Eqn
2)
If the proton concentration and the acid dissociation constant are both expressed as their negative log, Eqn 2 becomes;
(Eqn 3)
and if, for reasons largely historical, the negative log operator is called "p", the expression becomes;
(Eqn 4)
The ratio of [Buffer] /[Buffer×H +] can be obtained by rearranging Eqn 4 and inserting the values for the pH and pKa;
(Eqn 5)
Further rearranging of Eqn 5 gives Eqn 6;
(Eqn
6)
After choosing a buffer, the next step is to decide its concentration. The buffer concentration must be sufficient to maintain the pH within acceptable limits with the changes in proton concentration expected to occur. For biological systems, this generally means that the total buffer concentration ([Buffer]total) is within a range from 1 mM to 200 mM. Knowing that the total buffer concentration is equal to the sum of the concentrations of its forms;
(Eqn 7)
by substituting for the [Buffer] term in Eqn 7 with its equivalent from Eqn 6, we see;
(Eqn 8)
and by rearranging,
(Eqn 9)
So for any pH we choose, by finding a buffer whose pKa is within around one pH unit of that pH, and choosing [Buffer]total , we can use Eqns 7 and 9 to solve for the concentrations of [Buffer] and [Buffer×H+] at that pH. More importantly, we can prepare a solution with that pH by adding the right amounts of the acid (Buffer×H+ ) and base (Buffer) forms of the buffer to give the concentrations of [Buffer] and [Buffer×H+] we calculated.
