Question

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

Short answer

In a solution with \(\left[\mathrm{H}^{+}\right]=1.0 \mathrm{M}\), the cation species (C) would predominate. In a solution with \(\left[\mathrm{OH}^{-}\right]=1.0 \mathrm{M}\), the anion species (A) would predominate.

Step-by-step solution

Determine the balance equation of alanine species and their pK values

Since we have the \(K_{\mathrm{a}}\) and \(K_{\mathrm{b}}\) values for the carboxylic acid and amino groups, respectively, we can determine their pK values: \(pK_{\mathrm{a}} = -\log_{10}(K_{\mathrm{a}}) = -\log_{10}(4.5 \times 10^{-3}) \) \(pK_{\mathrm{b}} = -\log_{10}(K_{\mathrm{b}}) = -\log_{10}(7.4 \times 10^{-5}) \) Now, let's find the pH and pOH for the given solution concentrations: \(pH = -\log_{10}([\mathrm{H}^{+}])\) \(pOH = -\log_{10}([\mathrm{OH}^{-}])\) For both \([\mathrm{H}^{+}]=1.0M\) and \([\mathrm{OH}^{-}]=1.0M\) solutions, we can calculate the pH and pOH and compare them with the pKa and pKb values to determine the predominant alanine species.

Calculate pH and pOH for the given solutions

Now let's calculate the pH and pOH for the given solutions: Solution with \([\mathrm{H}^{+}]=1.0\mathrm{M}\): \(pH = -\log_{10}(1.0) = 0\) \(pOH = 14 - pH = 14\) Solution with \([\mathrm{OH}^{-}]=1.0\mathrm{M}\): \(pOH = -\log_{10}(1.0) = 0\) \(pH = 14 - pOH = 14\)

Compare pH, pOH with pKa, pKb and determine the predominant alanine species

Now, let's compare the pH with pKa and pKb values: Solution with \([\mathrm{H}^{+}]=1.0\mathrm{M}\): - Since pH is 0 and pKa < pH < pKb, the cation species (C) will predominate. Solution with \([\mathrm{OH}^{-}]=1.0\mathrm{M}\): - Since pH is 14 and pKb < pH, the anion species (A) will predominate. Now, we have determined which alanine species predominate in the given solutions: For a solution with \(\left[\mathrm{H}^{+}\right]=1.0 \mathrm{M}\), the cation species (C) would predominate. For a solution with \(\left[\mathrm{OH}^{-}\right]=1.0 \mathrm{M}\), the anion species (A) would predominate.

Key concepts

Amino Acids

Amino acids are the fundamental components of proteins, which are essential biological molecules present in every living organism. Each amino acid has a similar structure, consisting of a central carbon atom connected to an amino group (-NH₂), a carboxylic acid group (-COOH), a hydrogen atom, and a distinctive "R" group, which varies among different amino acids.
This R group determines the specific properties of each amino acid and contributes to the protein's overall structure and function.
Alanine, for example, has a simple side chain, a methyl group (-CH₃), which makes it one of the nonpolar amino acids.
Acidic or basic properties of amino acids come from their functional groups. Each can donate or accept protons (H⁺ ions), making them reactive and versatile in different pH environments.

pKa and pKb Values

The terms pKa and pKb are critical to understanding the acid and base behavior of amino acids like alanine.
They are logarithmic measures of the strength of an acid or a base, respectively, calculated as the negative log of the dissociation constants (Ka for acids and Kb for bases).
Specifically for alanine:

• The carboxylic acid group has a pKa value, which is \(-\log_{10}(4.5 \times 10^{-3})\).
• The amino group, on the other hand, has a pKb value \(-\log_{10}(7.4 \times 10^{-5})\), indicating how readily it acts as a base.

The pKa and pKb values help predict the prevalent form of alanine under varying pH levels. When the pH of the environment approaches the pKa or pKb, the corresponding alanine group is more likely to donate or accept a proton.
Hence, understanding these values provides insight into the acid-base behavior and the predominant species of alanine in solution.

Acid-Base Equilibrium

Acid-base equilibrium refers to the balance reached between the acidic or basic forms of molecules in solution.
For amino acids like alanine, this balance is influenced by the surrounding pH relative to their pKa and pKb values.
When dissolved in water, the carboxylic group ( -COOH ) can lose a proton to form a carboxylate ion ( -COO⁻ ).
The amino group (-NH₂) can gain a proton to form an ammonium ion (-NH₃⁺ ).

• At low pH (acidic conditions), the solution is rich in H⁺ ions, leading to a predominance of the cationic form of alanine, where the amino group is protonated.
• At high pH (basic conditions), with more OH⁻ ions, the anionic form dominates, as the carboxylic group loses a proton.

Acid-base equilibrium is crucial for determining how the amino acid will interact and stabilize in different environments, affecting protein structure and function extensively.

Predominant Species

The term "predominant species" refers to the major ionic form of a molecule present in solution at a given pH.
For alanine, this is determined by comparing the solution's pH to the amino acid’s pKa and pKb values.

• In a strongly acidic solution where [H⁺] = 1.0 M, the pH is 0. This environment favors the protonated, positively charged cation form of alanine, since the pKa of the carboxylic group is above this pH level, meaning it will hold onto its proton.
• In a strongly basic solution where [OH⁻] = 1.0 M, the pH is 14. Here, the anionic form of alanine is predominant, as the amino group gives up its proton.

By knowing the pH, one can accurately predict which form of the amino acid will dominate in solution, which is essential for understanding reactions in both biological systems and laboratory conditions.