## Preparation of Aqueous Buffer Solutions

James Richard Fromm

There are several methods used to prepare aqueous buffer solutions, but the basic principle of all of them is the same: the solution must contain both the acid and the base of a conjugate pair, in reasonably similar and in reasonably high concentrations. Only then can the buffer solution properly perform its task of maintaining solution pH when small amounts of strong acid or strong base are added or formed by other chemical reactions. The preparation of buffer solutions is shown in the following examples.

Example. Let us work out the experimental directions for making up one liter of an aqueous buffer solution of pH 7.0. First, we select an acid-base conjugate pair such that its pKa is about 7.0. For the phosphoric acid system:

K1 = [H3O+][H2PO4-]/[H3PO4] = 7.11 x 10-3

K2 = [H3O+][HPO42-]/[H2PO4-] = 6.23 x 10-8

The value of K2 is reasonably close to 1 x 10-7. When pH = 7.0, [H3O+] = 1.0 x 10-7, so using

K>2 (thereby ignoring K1 and K3, which is approximate but legitimate - one can, in dealing with polyprotic acids, generally treat the different constants as independent unless two of them have very similar values):

6.23 x 10-8 = [1 x 10-7][HPO42-]/[H2PO4-]

[HPO42-]/[H2PO4-] = 0.623, reasonably close to 1.

Now let us set the concentration of one component at an arbitrary but reasonably high value, such as [H2PO4-] = 1 x 10-2 molar. Then 0.623 = [HPO42-]/1 x 10-2, and [HPO42-] = 6.23 x 10-3 molar.

We now need one liter of a solution which is both 6.23 x 10-3 molar in HPO42- and 1.0 x 10-2 molar in H2PO4-. This requires 1.0 L x 6.23 x 10-3 mol/L HPO42- = 6.23 x 10-3 mol HPO42- and 1.0 L x 1.0 x 10-2 mol/L H2PO4- = 1.0 x 10-2 mol H2PO4-. Since it is physically impossible to add single ions to solutions, we have to add compounds. Choosing the sodium salts because they are reasonably easily available specifies Na2HPO4 (molar mass = 142 g/mol) and NaH2PO4 (molar mass = 120 g/mol).

6.23 x 10-3 mol Na2HPO4 x 142 g/mol Na2HPO4 = 0.885 g Na2HPO4

1.0 x 10-2 mol NaH2PO4 x 120 g/mol NaH2PO4 = 1.20 g NaH2PO4

The overall instructions for the preparation of one liter of aqueous buffer of pH 7.00 are: "Weigh out 1.20 g NaH2PO4 solid and 0.885 g Na2HPO4 solid and dilute with water to one liter in a volumetric flask to get a buffer of pH 7.0."