Problem 133 - Chemistry An Atoms First Approach

Question

All amino acids have at least two functional groups with acidic or basic properties. In alanine, the carboxylic acid group has \(K_{a}=4.5 \times 10^{-3}\) and the amino group has \(K_{b}=7.4 \times 10^{-5}.\) Three ions of alanine are possible when alanine is dissolved in water. Which of these ions would predominate in a solution with \(\left[\mathrm{H}^{+}\right]=1.0 \mathrm{M} ?\) In a solution with \(\left[\mathrm{OH}^{-}\right]=1.0 \mathrm{M} ?\)

Step-by-Step Solution

Answer

In a solution with \(\left[\mathrm{H}^{+}\right]=1.0 \mathrm{M}\), the predominant ion of alanine is \(NH_3^+CH_2COOH\), and in a solution with \(\left[\mathrm{OH}^{-}\right]=1.0 \mathrm{M}\), the predominant ion of alanine is \(NH_2CH_2COO^-\).

Step 1: 1. Converting Ka and Kb to pKa and pKb

First, convert the given \(K_a\) and \(K_b\) values to pKa and pKb by using the equations: \(pK_{a} = -\log_{10}{K_{a}}\) and \(pK_{b} = -\log_{10}{K_{b}}\) For alanine, \(pK_{a} = -\log_{10}{(4.5 \times 10^{-3})} = 2.35\) \(pK_{b} = -\log_{10}{(7.4 \times 10^{-5})} = 4.13\)

Step 2: 2. Calculate pH values for both solutions

This can be done using the equations: \(pH = -\log_{10}{[\mathrm{H}^{+}]}\) for the first solution, and \(pOH = -\log_{10}{[\mathrm{OH}^{-}]}\) and \(pH + pOH = 14\) for the second solution. For the first solution: \(pH = -\log_{10}{(1.0 \mathrm{M})} = 0\) For the second solution: \(pOH = -\log_{10}{(1.0 \mathrm{M})} = 0\) Since \(pH + pOH = 14\), \(pH = 14\)

Step 3: 3. Compare pH values with pKa and pKb to determine predominant ions

Now, we'll compare the pH values of the solutions to the pKa and pKb values. For the first solution with \(pH = 0\): Since \(pH < pK_a\), the carboxylic acid group will donate a proton, and alanine will be in its cationic form: \(NH_3^+CH_2COOH\). For the second solution with \(pH = 14\): Since \(pH > pK_b\), the amino group will gain a proton, and alanine will be in its anionic form: \(NH_2CH_2COO^-\). So, in a solution with \(\left[\mathrm{H}^{+}\right]=1.0 \mathrm{M}\), the predominant ion of alanine is \(NH_3^+CH_2COOH\), and in a solution with \(\left[\mathrm{OH}^{-}\right]=1.0 \mathrm{M}\), the predominant ion of alanine is \(NH_2CH_2COO^-\).

Key Concepts

Understanding pKa and pKb

Amino acids have both acidic and basic properties due to their functional groups. For alanine, these are the carboxylic acid group and the amino group. To measure how acidic or basic a substance is, we use values called pKa and pKb. These values are derived from Ka and Kb, which represent the acid dissociation constant and the base dissociation constant, respectively.

Here's how you calculate them:

• Convert Ka to pKa using the formula: \(pK_{a} = -\log_{10}{K_{a}}\)
• Convert Kb to pKb using the formula: \(pK_{b} = -\log_{10}{K_{b}}\)

For alanine, the pKa is 2.35 and the pKb is 4.13. These values indicate how easily the amino acid can donate or accept protons.

A low pKa value means the carboxylic acid group will easily give up a proton, making the solution acidic. Conversely, a low pKb means the amino group can easily accept a proton, increasing the basicity.

Ionic Forms of Amino Acids

In different pH environments, amino acids can exist in multiple ionic forms. This involves either gaining or losing protons (H⁺ ions). When dissolved in water, alanine can take on different forms depending on the balance of acidic and basic conditions.

• In a strongly acidic environment (like a solution with \( \left[\mathrm{H}^{+}\right]=1.0 \mathrm{M} \)), alanine's carboxylic acid group will remain protonated, leading to the cationic form \(NH_3^{+}CH_2COOH\).
• In a strongly basic environment (like a solution with \( \left[\mathrm{OH}^{-}\right]=1.0 \mathrm{M} \)), the amino group remains unprotonated, resulting in the anionic form \(NH_2CH_2COO^-\).

Understanding these forms helps predict the behavior and charges of amino acids under different conditions. This knowledge is crucial for studying proteins and biochemical reactions.

Acid-Base Equilibrium in Amino Acids

Acid-base equilibrium is a dynamic balance of protonation and deprotonation among amino acids in solution. This balance depends on the pH of the environment compared to the pKa and pKb values of the amino acids.

• When the pH is less than the pKa, the acidic group tends to donate protons, leading to a positively charged form.
• When the pH exceeds the pKb, the basic group accepts protons, resulting in a negatively charged form.

For alanine, the equilibrium shifts to favor certain ionic forms depending on the pH:

- A low pH (acidic conditions) means more protons are available, pushing alanine to its protonated form \(NH_3^{+}CH_2COOH\).

- A high pH (basic conditions) means fewer protons, promoting deprotonation and forming \(NH_2CH_2COO^-\).

This concept is key for understanding how amino acids interact and function within biological systems.