# 20.3 Biological Acids and the Henderson-Hasselbalch Equation

Objectives

After completing this section, you should be able to

1. identify the form that carboxylic acids take within living cells.
2. use the Henderson‑Hasselbalch equation to calculate the percentages of dissociated and undissociated acids [A] and [HA]  in a solution, given the pKa value of the acid and the pH of the solution.
3. explain why cellular carboxylic acids are always referred to by the name of their anion.

Key Terms

Make certain that you can define, and use in context, the key terms below.

• Henderson‑Hasselbalch equation
• physiological pH

#### Organic molecules in buffered solution:  The Henderson-Hasselbalch equation

The environment inside a living cell, where most biochemical reactions take place, is an aqueous buffer with pH ~ 7 (or sometimes referred to as the physiological pH). Recall from your General Chemistry course that a buffer is a solution of a weak acid and its conjugate base.  The key equation for working with buffers is the Henderson-Hasselbalch equation:

The Henderson-Hasselbalch equation:

The equation tells us that if our buffer is an equimolar solution of a weak acid and its conjugate base, the pH of the buffer will equal the pKa of the acid (because the log of 1 is equal to zero).  If there is more of the acid form than the base, then of course the pH of the buffer is lower than the pKa of the acid.

Exercise 7.2.4

What is the pH of an aqueous buffer solution that is 30 mM in acetic acid and 40 mM in sodium acetate? The pKa of acetic acid is 4.8.

Solution

The Henderson-Hasselbalch equation is particularly useful when we want to think about the protonation state of different biomolecule functional groups in a pH 7 buffer. When we do this, we are always assuming that the concentration of the biomolecule is small compared to the concentration of the buffer components.  (The actual composition of physiological buffer is complex, but it is primarily based on phosphoric and carbonic acids.).

Imagine an aspartic acid residue located on the surface of a protein in a human cell.  Being on the surface, the side chain is in full contact with the pH 7 buffer surrounding the protein. In what state is the side chain functional group: the protonated state (a carboxylic acid) or the deprotonated state (a carboxylate ion)? Using the Henderson-Hasselbalch equation, we fill in our values for the pH of the buffer and a rough pKa approximation of pKa = 5 for the carboxylic acid functional group. Doing the math, we find that the ratio of carboxylate to carboxylic acid is about 100 to 1: the carboxylic acid is almost completely ionized (in the deprotonated state) inside the cell. This result extends to all other carboxylic acid groups you might find on natural biomolecules or drug molecules: in the physiological environment, carboxylic acids are almost completely deprotonated. Indeed, often cellular carboxylic acids are often referred to by the name of their anion. So rather than pyruvic acid, or acetic acid or lactic acid, it is pyruvate, acetate or lactate.

While we are most interested in the state of molecules at pH 7, the Henderson-Hasselbalch equation can of course be used to determine the protonation state of functional groups in solutions buffered to other pH levels.  The exercise below provide some practice in this type of calculation.

Exercise 7.2.6

What is the ratio of acetate ion to neutral acetic acid when a small amount of acetic acid (pKa =  4.8) is dissolved in a buffer of pH 2.8? pH 3.8? pH 4.8? pH 5.8? pH 6.8?

Solution