This is an example calculation about the phosphate buffer system from my Biochemistry textbook.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Henderson-Hasselbalch & phosphate buffers

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