Question 8.10: What is the pH of a phosphate buffer solution containing 1.0...
What is the pH of a phosphate buffer solution containing 1.0 mol/L of sodium dihydrogen phosphate, NaH_{2}PO_{4}, and 0.50 mol/L of sodium hydrogen phosphate, Na_{2}HPO_{4}?
Strategy
Use the Henderson-Hasselbalch equation to determine the pH. You must know either the number of moles of both the conjugate acid and base or the concentrations of the conjugate acid or base. Divide the conjugate base by the conjugate acid, take the log of that ratio, and add it to the pK_{a} of the conjugate acid.
The weak acid in this problem is H_{2}PO_{4}^{-}; its ionization produces HPO_{4} ^{2-}. The pK_{a} of this acid is 7.21 (from Table 8.3). Under the weak acid and its
conjugate base are shown their concentrations.
Substituting these values in the Henderson-Hasselbalch equation gives a pH of 6.91.
| Formula | Name | K_{a} | pK_{a} |
|
| H_{3}PO_{4} | Phosphoric acid | 7.5 × 10^{-3} | 2.12 | |
| HCOOH | Formic acid | 1.8 × 10 ^{-4} | 3.75 | |
| CH_{3}CH(OH)COOH | Lactic acid | 1.4 × 10 ^{-4} | 3.86 | |
| CH_{3}COOH | Acetic acid | 1.8 × 10^{-5} | 4.75 | |
| H_{2}CO_{3} | Carbonic acid | 4.3× 10 ^{-7}4.3×10^{-7} | 6.37 | |
| H_{2}PO_{4}^{-} | Dihydrogen phosphate ion | 6.2 × 10^{-8} | 7.21 | |
| H_{3}BO_{3} | Boric acid | 7.3 × 10^{-10} | 9.14 | |
| NH_{4}^{+} | Ammonium ion | 5.6 × 10^{-10} | 9.25 | |
| HCN | Hydrocyanic acid | 4.9 × 10^{-10} | 9.31 | |
| C_{6}H_{5}OH | Phenol | 1.3 × 10^{-10} | 9.89 | |
| HCO_{3}^{-} | Bicarbonate ion | 5.6 × 10^{-11} | 10.25 | |
| HPO_{4}^{2-} | Hydrogen phosphate ion | 2.2 × 10^{-13} | 12.66 |
