Calculating pH of a diprotic weak acid solution

A diprotic acid (H₂A)  ionizes when dissolved in water in two steps. The first step produces a hydronium ion (H₃O⁺) and the monoprotic base (HA^-). The monorptic base (HA^-) can act as an acid or it can act as a base (ampholyte). When the monoprotic acid (HA^-) acts as an acid, it further dissociates (the second step) to produce  another hydronium ion (H₃O⁺) and the base (A^-2).

At equilibrium, each of the two steps has an  ionization constant as summarized by the following:

                                                            H₂A + H₂O ↔ H₃O⁺ + HA^-

                                                             

                                                             HA^- + H₂O ↔ H₃O⁺ + A^-2

Calculating the pH of a solution of a diprotic acid involves the use of a cubic equation which can be simplified by making the assumption that K1 is much greater than K2. This assumption is valid if K1 is more than 100 folds greater than K2. For example carbonic acid has K1 =  4.31× 10^-7  and K2 =  4.7 × 10^-11 (K1 is much greater than K2). Accordingly, the second ionization can be neglected and the acid is assumed to have a single ionization step (K1). Thus the equation used would be the following:

Where Ca is the concentration of the diprotic acid.

For example if we have 0.001 M solution of carbonic acid (K1 =  4.31× 10^-7  and K2 =  4.7 × 10^-11 ) then we ignore K2 (K1 is much greater than K2) and by applying the above equation we get pH = 4.69.

When using an online pH calculator just assume that we have a monoprotic acid and use K1 instead of Ka.

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