Amino Acids and Henderson-Hasselbalch: Videos & Practice Problems

The Henderson-Hasselbalch equation is a fundamental tool in understanding the behavior of amino acids in solution, particularly in relation to their ionizable groups. This equation establishes a crucial relationship between the pH of a solution and the pKa of an ionizable group, which is essential for predicting the state of an amino acid in different pH environments.

The equation is expressed as:

\( \text{pH} = \text{pKa} + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \

In this formula, \([\text{A}^-]\) represents the concentration of the conjugate base, while \([\text{HA}]\) denotes the concentration of the conjugate acid. The Henderson-Hasselbalch equation serves two primary purposes: it can be used to determine the final pH of a weak acid solution at equilibrium, or it can help calculate the ratio of the concentrations of conjugate base to conjugate acid when the pH is known.

When applying this equation to amino acids, it is important to recognize that each ionizable group within the amino acid can be analyzed independently. This means that the Henderson-Hasselbalch equation can be utilized for each group to ascertain the average net charge of the amino acid at a given pH. Understanding these concepts is vital for solving practice problems related to amino acids and their behavior in various pH conditions.

As you engage with practice problems, remember that the ability to manipulate the Henderson-Hasselbalch equation will enhance your understanding of amino acid chemistry and its applications in biochemistry and molecular biology.

To determine the percentage of the protonated amino group (NH₃⁺) in the R group of lysine at a pH of 9.8, we can utilize the Henderson-Hasselbalch equation. The pK_a of lysine's R group is given as 10.8. The goal is to find the ratio of the concentration of the conjugate base (CB) to the concentration of the conjugate acid (CA) at the specified pH.

The Henderson-Hasselbalch equation is expressed as:

\[\text{pH} = \text{pK}_a + \log\left(\frac{[\text{CB}]}{[\text{CA}]}\right)\]

Substituting the known values into the equation:

\[9.8 = 10.8 + \log\left(\frac{[\text{CB}]}{[\text{CA}]}\right)\end{p}

To isolate the log term, we subtract 10.8 from both sides:

\[9.8 - 10.8 = \log\left(\frac{[\text{CB}]}{[\text{CA}]}\right)\]

\[-1 = \log\left(\frac{[\text{CB}]}{[\text{CA}]}\right)\end{p}

Next, we eliminate the logarithm by taking the antilog of both sides:

\[\frac{[\text{CB}]}{[\text{CA}]} = 10^{-1} = \frac{1}{10}\end{p}

This ratio indicates that for every 1 molecule of the conjugate base, there are 10 molecules of the conjugate acid. Therefore, the total number of molecules is 11 (10 conjugate acids + 1 conjugate base).

To find the percentage of the protonated amino group, we calculate the ratio of the conjugate acid to the total number of molecules:

\[\text{Percentage} = \left(\frac{10}{11}\right) \times 100\% \approx 90.909\% \approx 91\%\end{p}

This result indicates that approximately 91% of the amino groups in the R group of lysine will be protonated at a pH of 9.8. This calculation highlights the importance of understanding the relationship between pH, pK_a, and the ionization states of amino acids in biochemical contexts.