Buffers

A buffer solution consists of a weak acid and the salt form of its conjugate base. Buffer solutions can be made at a specific pH, and then small amounts of strong acids or bases can be added to the solution, and the pH will not change measurably. The acids and bases in the buffer react with the outside materials to maintain equilibrium.

If large quantities of strong acid or base are added to the solution, the equilibrium reaction will drive toward completion, and the solution is said to have exceeded its buffer capacity.

Generally, we have the acid-base reaction

\[ \ce{HA_{(aq)} + H2O_{(l)} \rightleftharpoons A^{-}_{(aq)} + H+_{(aq)}},\]

where \( \ce{HA} \) is the acid and \( \ce{A-} \) is the conjugate base.

We have then \( K_{a} = \dfrac{[A^{-}][H+]}{[HA]} .\)

From this, we obtain

\[ \begin{align} [H^+] &= K_a \cdot \dfrac{[HA]}{[A^{-}]}\\ -\log [H+] &= -\log K_a - \log \left( \dfrac{[HA]}{[A^{-}]}\right)\\ pH &= \boxed{pK_a + \log \left( \dfrac{[A^-]}{[HA]}\right)}. \end{align} \]

This is what is known as Henderson Hasselbach equation.

Human blood is a solution that must be maintained in a narrow pH range, between 7.35 and 7.45 in a healthy person. The lungs and kidneys work together to maintain this acid-base balance and provide several examples of buffer systems.

One buffer in the blood is hemoglobin (Hb), the molecule within red blood cells that transports oxygen throughout the body. When hemoglobin unloads oxygen in the tissues, it can bind to hydrogen, decreasing the pH of the blood:

\[\begin{align} \ce{Hb*O2} &\longrightarrow \ce{Hb + O2}\\ \ce{Hb + H+} &\longrightarrow \ce{Hb*H}. \end{align}\]

This is useful, because carbon dioxide is a major waste product in human tissues, and it is converted to bicarbonate and hydrogen ions through the following two-step process:

\[\ce{CO2 +H2O <-> H2CO3 <-> HCO3^- + H+}.\]

Once the hemoglobin molecules reach the lungs, the reactions reverse. Hydrogen is released, and the hemoglobin binds a new oxygen molecule to deliver to the tissues.

Carbon dioxide and its conjugate base, bicarbonate, work together to make another buffer system in the blood. Ions convert easily between the acid and the base to maintain the proper pH, and excess molecules of \(\ce{CO2}\) are excreted through the lungs while \(\ce{HCO3-}\) is removed by the kidneys.