This is an example calculation about the phosphate buffer system from my Biochemistry textbook. 1. The problem statement, all variables and given/known data If the total cellular concentration of phosphate is 20 mM (millimolar) and the pH is 7.4, the distribution of the major phosphate species is given by pH = pKa + log_{10} [HPO_{4}^{2-}] / [H_{2}PO_{4}^{-}] 7.4 = 7.20 + log_{10} [HPO_{4}^{2-}] / [H_{2}PO_{4}^{-}] [HPO_{4}^{2-}] / [H_{2}PO_{4}^{-}] = 1.58 Thus, if [HPO_{4}^{2-}] + [H_{2}PO_{4}^{-}] = 20 mM, then [HPO_{4}^{2-}] = 12.25 mM and [H_{2}PO_{4}^{-}] = 7.75 mM 2. Relevant equations pH = pKa + log_{10} [A^{-}] / [HA] pH = -log_{10} [H^{+}] 3. The attempt at a solution I understand everything up until they provide the concentrations of each phosphate species. Since their ratio as shown in the equation is 1.58, one can clearly assume that [HPO_{4}^{2-}] > [H_{2}PO_{4}^{-}]. But the fact that no explanation is provided for arriving at their specific concentrations is driving me insane. The Henderson-Hasselbalch equation shows that, when [HPO_{4}^{2-}] / [H_{2}PO_{4}^{-}] = 1, pH = pKa. But since we are at pH = 7.4, they obviously can't be equal. I think the solution must involve taking the 0.2 difference into account somehow.
Wow. I stared at that problem for 2 hours...I can't believe the answer was right there. Thanks for clearing that up.