Question

The amino acid glycine \(\left(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}\right)\) can participate in the following equilibria in water: \(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{H}_{2} \mathrm{O}=\) \(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COO}^{-}+\mathrm{H}_{3} \mathrm{O}^{+} \quad K_{a}=4.3 \times 10^{-3}\) \(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\) \({ }^{+} \mathrm{H}_{3} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{OH}^{-} \quad K_{b}=6.0 \times 10^{-5}\) (a) Use the values of \(K_{a}\) and \(K_{b}\) to estimate the equilibrium constant for the intramolecular proton transfer to form a zwitterion: \(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH} \rightleftharpoons{ }^{+} \mathrm{H}_{3} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COO}^{-}\) What assumptions did you need to make? (b) What is the pH of a \(0.050 \mathrm{M}\) aqueous solution of glycine? (c) What would be the predominant form of glycine in a solution with pH 13? With pH 1?

Short answer

The equilibrium constant for zwitterion formation is \(2.33 \times 10^{-12}\). The pH of a 0.050 M aqueous solution of glycine is approximately 2.49. At pH 13, the predominant form of glycine is the anionic form with \(\mathrm{COO^-}\) and \(\mathrm{NH_2}\) groups, while at pH 1, it is the cationic form with the \(\mathrm{NH_3^+}\) and \(\mathrm{COOH}\) groups.

Step-by-step solution

Find the equilibrium constant for zwitterion formation

To find the equilibrium constant for zwitterion formation, we can use the relationship \(K_w = K_a \times K_b\), where \(K_w\) is the ionic product of water, \(K_a\) is the acid dissociation constant of the carboxyl group, and \(K_b\) is the base dissociation constant of the amino group. We are given the values of \(K_a\) and \(K_b\), and we know the value of \(K_w\) is \(1.0 \times 10^{-14}\). Calculate the equilibrium constant for zwitterion formation using this relationship: \[K_z = \frac{K_w}{K_a} \]

Calculate the equilibrium constant for zwitterion formation

Now, use the values we have for \(K_a\), \(K_b\), and \(K_w\) to find the value of \(K_z\): \[K_z = \frac{1.0 \times 10^{-14}}{4.3 \times 10^{-3}} = 2.33 \times 10^{-12} \] The equilibrium constant for zwitterion formation is \(2.33 \times 10^{-12}\).

Calculate the pH of a 0.050 M aqueous solution

We need to find the concentration of \(H_3O^+\) ions in the solution. To do so, we can use the \(K_a\) value. Let's denote the concentration change using x: \[\frac{(x)(x)}{(0.050 - x)} = 4.3 \times 10^{-3}\] Solve the equation above for x, which represents the concentration of \(H_3O^+\) ions (\([H_3O^+]\)). Assume that x is much smaller than 0.050 and simplify the equation: \[x^2 = (0.050)(4.3 \times 10^{-3})\]

Find the concentration of \(H_3O^+\) and calculate pH

Solve for x: \[x = \sqrt{(0.050)(4.3 \times 10^{-3})} \approx 3.26 \times 10^{-3} \] Now that you have the concentration of \(H_3O^+\) ions, you can calculate the pH: \[pH = -\log{(3.26 \times 10^{-3})} \approx 2.49 \] The pH of the 0.050 M aqueous solution of glycine is approximately 2.49.

Predominant form at pH 13 and pH 1

To determine the predominant form of glycine at different pH values, we need to compare the pH to the pKa and pKb values. Calculate the pKa and pKb: \[pK_a = -\log{(4.3 \times 10^{-3})} \approx 2.37 \] \[pK_b = -\log{(6.0 \times 10^{-5})} \approx 4.22 \] When pH is 13 which is greater than both pKa and pKb, the solution is mostly deprotonated, and the predominant form would be anionic – the form with \(\mathrm{COO^-}\) and \(\mathrm{NH_2}\) groups. When pH is 1, which is less than both pKa and pKb, the solution is acidic, and the predominant form would be the cationic form with the \(\mathrm{NH_3^+}\) and \(\mathrm{COOH}\) groups.

Key concepts

Amino Acids

Amino acids are the building blocks of proteins, critical to life processes. They consist of a central carbon atom (the α-carbon) bonded to four groups: an amino group ( ext{NH}_{2}), a carboxyl group ( ext{COOH}), a hydrogen atom, and an R group, which varies for each amino acid. This structure results in diverse properties and functions that cater to various biochemical processes.
- The R group, or side chain, determines the characteristics and role of each amino acid in protein structure and function. Glycine, for example, has a hydrogen atom as its R group, making it the simplest amino acid.
- Amino acids can be categorized based on their side chains into groups like polar, nonpolar, acidic, and basic. This categorization affects their interaction in proteins and other molecules. Glycine participates in chemical equilibria in water, where it can exist in different ionization states due to its amino and carboxyl groups' reactivity.
Understanding amino acids' properties is crucial for exploring their functions within proteins and their behavior in different environmental conditions.

Acid-Base Reactions

Acid-base reactions involve the transfer of protons (H⁺ ions) between molecules, which is a fundamental chemical process that affects molecular interactions and equilibria in biological systems. In the context of amino acids, acid-base reactions are essential for the formation and behavior of amino acids in solution.
- Glycine, like other amino acids, has both an amino group that can accept a proton and a carboxyl group that can donate a proton. This dual reactivity makes amino acids amphoteric, allowing them to act as both acids and bases in reactions.
- The Ka (acid dissociation constant) and Kb (base dissociation constant) values for glycine reveal how easily a proton can be transferred from its carboxyl group or amino group. The Ka value reflects the acid's strength as it dissociates to form H_3O^+ in solution, while the Kb value indicates the amino group's ability to accept protons.
These constants are integral to predicting the behavior of glycine in different environments, such as biological systems or various pH conditions. Understanding acid-base reactions in amino acids like glycine helps in predicting protein behavior and stability, impacting fields like biochemistry and pharmacology.

Zwitterion Formation

Zwitterion formation in amino acids is an important characteristic that affects their solubility and behavior in aqueous environments. Zwitterions are molecules with both positive and negative charges, but overall electrically neutral.
In the case of glycine, zwitterion formation occurs through an intramolecular proton transfer where the amino group ( NH_2) accepts a proton from the carboxyl group ( COOH), creating a molecule with an NH_3^+ group and a COO^- group. This form is predominant in neutral pH.
- Zwitterionic molecules balance the charged groups within the molecule, stabilizing it in water, which is crucial for biological functions like protein interaction and solubility.
- The equilibrium constant for this process can be calculated using the given Ka and Kb values, demonstrating the tendency of glycine to form a zwitterion in water.
The understanding of zwitterion formation provides insight into how amino acids behave under different pH levels and environments, which is crucial for applications such as drug formulation and protein engineering.