Problem 103 - General Chemistry: Principles and Modern Applications

Question

In your own words, define or explain the following terms or symbols: (a) \(K_{\mathrm{w}} ;\) (b) \(\mathrm{pH} ;\) (c) \(\mathrm{p} K_{\mathrm{a}} ;\) (d) hydrolysis; (e) Lewis acid.

Step-by-Step Solution

Answer

\(K_{\mathrm{w}}\) is the ion product of water, pH is a measure of acidity or alkalinity of a solution, \(\mathrm{p}K_{\mathrm{a}}\) is a measure of the strength of an acid in solution, Hydrolysis is a type of chemical reaction that involves the breaking of a bond using water and Lewis acid is a substance that can accept an electron pair.

Step 1: Define \(K_{\mathrm{w}}\)

\(K_{\mathrm{w}}\) represents the ion product of water. It is the equilibrium constant for the self-ionization of water and its value at 25°C is \(1.0 \times 10^{-14}\). It is defined by the equation \(K_{\mathrm{w}} = [H^+][OH^-]\) where [H+] and [OH-] are the concentrations of hydrogen and hydroxide ions respectively.

Step 2: Define pH

pH is a measure of acidity or alkalinity of a solution. It is the negative logarithm (base 10) of the concentration of H+ ions in a solution. Mathematically, \(\mathrm{pH} = -\log[H^+]\), where [H+] stands for the concentration of H+ ions in the solution.

Step 3: Define \(\mathrm{p}K_{\mathrm{a}}\)

\(\mathrm{p}K_{\mathrm{a}}\) is the negative logarithm (base 10) of the acid dissociation constant (Ka). It provides a measure of the strength of an acid in solution. A lower pKa value indicates a stronger acid.

Step 4: Explain Hydrolysis

Hydrolysis is a type of chemical reaction that involves the breaking of a bond in a molecule using water. In the process, water molecule itself splits into H+ and OH- ions.

Step 5: Define Lewis Acid

Lewis acid is a substance that can accept an electron pair. This definition is based on the Lewis concept of acids and bases, where acids are electron pair acceptors and bases are electron pair donors.

Key Concepts

Water Ionization Constant

The water ionization constant, often denoted as \(K_{\mathrm{w}}\), plays a crucial role in the chemistry of water. It describes the equilibrium constant for the self-ionization of water, a process where water molecules break apart into hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\). At 25°C, the value of this constant is \(1.0 \times 10^{-14}\).

• This means that in pure water, the product of the concentrations of hydrogen and hydroxide ions is always \(1.0 \times 10^{-14}\).
• This constant helps us understand the balance between acids and bases in water-based solutions.
• A change in temperature can alter \(K_{\mathrm{w}}\), affecting the concentrations of \([H^+]\) and \([OH^-]\).

Understanding \(K_{\mathrm{w}}\) is essential for calculating the pH of solutions and predicting the direction of acid-base reactions. It also helps in understanding the nature of neutral, acidic, and basic solutions.

pH Scale

The pH scale is a measuring tool that tells us how acidic or basic a solution is. The scale ranges from 0 to 14, where lower values correspond to acidic solutions, higher values indicate basic solutions, and a pH of 7 represents a neutral solution.

• The pH is calculated as \(\text{pH} = -\log[H^+]\), where \([H^+]\) is the concentration of hydrogen ions in the solution.
• An acidic solution has a high concentration of hydrogen ions, leading to a lower pH.
• A basic solution has a low concentration of hydrogen ions, leading to a higher pH.

The pH scale is logarithmic, meaning each whole number change represents a tenfold change in hydrogen ion concentration. For example, a decrease in pH from 6 to 5 means the hydrogen ion concentration increases by ten times. Using this scale, scientists can easily compare the acidity or basicity of different solutions.

Acid Dissociation Constant

The acid dissociation constant, represented by \(K_{\mathrm{a}}\), measures the strength of an acid in a solution. It quantifies how effectively an acid donates protons to water molecules.

• The equation for \(K_{\mathrm{a}}\) is derived from the equilibrium expression for the dissociation of an acid: \(\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-\).
• Higher \(K_{\mathrm{a}}\) values signify stronger acids, as they dissociate more completely.
• A related term is \(\mathrm{p}K_{\mathrm{a}}\), which is the negative logarithm of \(K_{\mathrm{a}}\). Lower \(\mathrm{p}K_{\mathrm{a}}\) values indicate stronger acids.

Understanding the acid dissociation constant is crucial for predicting how acids will behave in different chemical environments. It also helps in determining the pH of solution mixtures involving acids and their conjugate bases.

Chemical Hydrolysis

Chemical hydrolysis involves breaking down a compound by using water. In this reaction, water molecules split and contribute to the formation of new products.

• During hydrolysis, water breaks a bond in the substrate molecule, forming two or more products.
• Common examples include the conversion of esters into acids and alcohols, and the breakdown of proteins into amino acids.
• In biological systems, enzymes often catalyze hydrolysis reactions.

This process is crucial in both natural and industrial settings, playing a significant role in digestion, the breakdown of minerals, and in the recycling of biomolecules. By understanding hydrolysis, one can better grasp how additives react in solutions and how complex molecules are broken down into simpler forms.

Lewis Acids and Bases

The Lewis theory of acids and bases broadens the definition of acid-base reactions. According to this theory, a Lewis acid is a compound that accepts an electron pair, whereas a Lewis base donates an electron pair.

• Traditional acids, which release hydrogen ions, are often considered Lewis acids because they can accept electron pairs to form bonds.
• Lewis acids often include compounds with empty orbitals, such as \(\text{AlCl}_3\) and \(\text{BF}_3\).
• This concept expands the understanding of chemical reactivity and interaction beyond hydrogen ion transfer.

The Lewis concept allows chemists to explore a wider array of reactions, including those in coordination chemistry, catalysis, and enzyme function. It provides a framework that enhances the understanding of molecular interactions and reactivity.