Problem 114 - Chemistry The Central Science In Si Units

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: \(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\) $$ \mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COO}^{-}+\mathrm{H}_{3} \mathrm{O}^{+} \quad K_{\mathrm{a}}=4.3 \times 10^{-3} $$$$ \begin{aligned} \mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \\ &{ }^{+} \mathrm{H}_{3} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{OH}^{-} \quad K_{\mathrm{b}}=6.0 \times 10^{-5} \end{aligned} $$ (a) Use the values of \(K_{a}\) and \(K_{b}\) to estimate the equilibrium constant for the intramolecular proton transfer to form a zwitterion: $$ \mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH} \rightleftharpoons{ }^{+} \mathrm{H}_{3} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COO}^{-} $$ (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 \(\mathrm{pH} 13\) ? With \(\mathrm{pH} 1\) ?

Step-by-Step Solution

Answer

Use Ka, Kb, and Kw to calculate equilibrium constants and assess conditions based on pH values.

Step 1: Understanding the Zwitterion Formation

The task asks us to find the equilibrium constant for the reaction where glycine transforms into its zwitterionic form. For the intramolecular proton transfer: \[ \mathrm{H}_{2} \mathrm{N}-\mathrm{CH}_{2}-\mathrm{COOH} \rightleftharpoons{ }^{+} \mathrm{H}_{3} \mathrm{N}-\mathrm{CH}_{2}-\mathrm{COO}^{-} \]we can write the equilibrium constant as: \[ K_{zw} = \frac{{[^{+} \mathrm{H}_{3} \mathrm{N}-\mathrm{CH}_{2}-\mathrm{COO}^{-}]}}{{}\mathrm{[H}_{2} \mathrm{N}-\mathrm{CH}_{2}-\mathrm{COOH}]} \]This can be expressed as the product of Ka and Kb divided by the ionic product of water, Kw, as this formation is an internal acid-base reaction.Therefore: \[ K_{zw} = \frac{{K_a \cdot K_b}}{{K_w}} \]

Key Concepts

Amino Acids

Amino acids are the building blocks of proteins and play crucial roles in various biological processes. They are organic compounds, each containing both an amino group \(\mathrm{(-NH}_2)\) and a carboxyl group \(\mathrm{(-COOH)}\).
Their structure generally includes a central carbon atom to which the amino group, carboxyl group, a hydrogen atom, and a side chain (R) are bonded. This side chain varies among different amino acids, giving each one unique characteristics.
Glycine is the simplest amino acid with the chemical formula \(\mathrm{H}_2\mathrm{N}-\mathrm{CH}_2-\mathrm{COOH}\). Due to its simple structure, glycine does not have a side chain, making it flexible in protein structures. Apart from providing structural components for proteins, amino acids are also involved in metabolism and as precursors for biosynthesis of various biological molecules.

Zwitterion Formation

Zwitterions are molecules with both positive and negative charges but remain overall electrically neutral. For amino acids, zwitterion formation is a significant characteristic, especially in aqueous environments. This occurs when the amino acid contains an \(\mathrm{NH}_3^+\) group (positive) and a \(\mathrm{COO}^-\) group (negative) within the same molecule.
In the case of glycine, when in solution, an internal proton transfer occurs within the molecule. The carboxylic acid group donates a proton to the amino group, resulting in the zwitterionic form \(\mathrm{H}_3\mathrm{N}^+-\mathrm{CH}_2-\mathrm{COO}^-\). The equilibrium constant for this reaction, \(K_{zw}\), is derived from the acid dissociation constant \(K_a\) and the base dissociation constant \(K_b\), adjusted for the ionic product of water \(K_w\). This ability to form zwitterions is essential for the stability and function of amino acids in physiological pH conditions.

Acid-Base Reactions

An acid-base reaction involves the transfer of protons between reactants, often resulting in the formation of water and salts. In the context of amino acids like glycine, these reactions are crucial for understanding how they interact in different environments.
Glycine can react with bases, losing a proton from its carboxyl group to form a carboxylate anion, or with acids, gaining a proton on its amino group to form an ammonium cation. The \(K_a\) represents the equilibrium constant for the acid reaction, while \(K_b\) is for the base reaction.
These reactions describe the amino acid's behavior in different pH environments. For instance, under acidic conditions, glycine is more likely to gain protons, forming cations, while in basic conditions, it becomes an anion. Understanding these reactions helps predict the predominant ionic form of an amino acid under varying pH conditions, vital for biochemical processes.

Equilibrium Constants

Equilibrium constants provide a crucial understanding of how far a reaction will proceed before reaching equilibrium. They are represented by \(K_a\) for acid dissociations, \(K_b\) for base dissociations, and in the case of zwitterion formation, \(K_{zw}\).
For glycine, the given \(K_a = 4.3 \times 10^{-3}\) and \(K_b = 6.0 \times 10^{-5}\) illustrate how glycine can act as both an acid and a base. The intramolecular proton transfer to form a zwitterion has its specific equilibrium constant \(K_{zw} = \frac{{K_a \cdot K_b}}{{K_w}}\), where \(K_w\) is the ionic product of water, generally \(1.0 \times 10^{-14}\) at room temperature.
By determining these constants, one can calculate the concentration of different forms of glycine at equilibrium, helping to predict reactions in different environmental conditions, such as varying pH.