Acid/base chemistry: How do organisms maintain a constant pH range?

Controlling the environmental pH is important for living systems as many organisms can only exist within in a narrow pH range. Human plasma, for example, must be maintained at a pH within half a pH unit of $7.4$‍. One such mechanism that helps humans accomplish this is the phosphate buffer system inside the cytoplasm of cells. This buffer system consists of dihydrogen phosphate ions $({\text{H}}_2{\text{PO}}_4^{-})$‍ as hydrogen-ion donor (acid) and hydrogen phosphate ions $(\text{H}{\text{PO}}_4^{2-})$‍ as hydrogen-ion acceptor (base). These two ions are in equilibrium with each other as indicated by the chemical equation in Figure 1.

Figure 1. The phosphate buffer system

${\text{H}}_2{\text{PO}}_4^{-}(aq)$‍ ⇌ ${\text{H}}^{+}(aq)$‍ + $\text{H}{\text{PO}}_4^{2-}(aq)$‍

If additional hydrogen ions enter the cellular fluid, they are consumed in the reaction with $\text{H}{\text{PO}}_4^{2-}$‍, and the equilibrium shifts to the left. If additional hydroxide ions enter the cellular fluid, they react with ${\text{H}}_2{\text{PO}}_4^{-}$‍, producing $\text{H}{\text{PO}}_4^{2-}$‍, and shifting the equilibrium to the right. This behavior allows the pH of an aqueous buffer solution to change only slightly after drops of acid or base are added. The equilibrium-constant expression for this equilibrium is shown in Figure 2.

Figure 2. The value of ${\text{K}}_a$‍ for this equilibrium is $6.23\times {10}^{-8}$‍ at $25°C$‍, which yields a ${\text{pK}}_a$‍ of $7.21$‍.

This equation can be reorganized in the form of the Henderson-Hasselbalch equation:

$\text{pH}$‍ $=$‍ ${\text{pK}}_a$‍ + $\text{log}$‍ $([\text{H}{\text{PO}}_4^{2-}]/[{\text{H}}_2{\text{PO}}_4^{-}])$‍

In order to make a buffer, a weak acid must be chosen that has a ${\text{pK}}_a$‍ value within one unit of the the desired pH. This weak acid is then mixed with its conjugate base in equal concentration amounts. Table 1 lists a series of weak acids and conjugate bases, along with the ${\text{pK}}_a$‍ values for each acid.

Table 1.