Acids and Bases: Principles, Calculations, and Applications

Chapter 10: Acids and Bases

Introduction to Acids and Bases

Acids and bases are fundamental chemical species that participate in a wide range of chemical reactions. Their behavior in aqueous solutions is essential for understanding chemical equilibria, biological systems, and industrial processes.

• Acid: A substance that donates protons (H+) in a chemical reaction.

• Base: A substance that accepts protons (H+).

• Bronsted-Lowry Acid: Proton donor.

• Bronsted-Lowry Base: Proton acceptor.

• Conjugate Acid-Base Pair: Two species that differ by a single proton.

• Amphiprotic: A substance that can act as both an acid and a base (e.g., H2O).

Strengths of Acids and Bases

The strength of an acid or base is determined by its ability to donate or accept protons. Strong acids and bases dissociate completely in water, while weak acids and bases only partially dissociate.

• Strong Acid: Completely donates its proton in water (e.g., HCl).

• Weak Acid: Partially donates its proton (e.g., acetic acid).

• Strong Base: Completely accepts protons (e.g., NaOH).

• Weak Base: Partially accepts protons (e.g., NH3).

Acid Dissociation Constant (Ka)

The acid dissociation constant quantifies the extent to which an acid dissociates in water.

• Formula:

$K_a = \frac{[H_3O^+][A^-]}{[HA]}$

• Interpretation: Larger Ka values indicate stronger acids.

Ion Product Constant for Water (Kw)

Water can act as both an acid and a base, leading to the autoionization equilibrium:

$H_2O(l) + H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)$

$K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$ at 25°C

• Acidic solution: $[H_3O^+] > 1.0 \times 10^{-7}$ M, $[OH^-] < 1.0 \times 10^{-7}$ M

• Basic solution: $[H_3O^+] < 1.0 \times 10^{-7}$ M, $[OH^-] > 1.0 \times 10^{-7}$ M

• Neutral solution: $[H_3O^+] = [OH^-] = 1.0 \times 10^{-7}$ M

pH and pOH Calculations

pH is a measure of the hydrogen ion concentration in a solution. It is defined as:

$\text{pH} = -\log[H_3O^+]$

Similarly, pOH is defined as:

$\text{pOH} = -\log[OH^-]$

• Relationship: $\text{pH} + \text{pOH} = 14$ (at 25°C)

• Acidic solution: pH < 7

• Neutral solution: pH = 7

• Basic solution: pH > 7

Calculating [H3O+] from pH

To find the hydronium ion concentration from pH:

$[H_3O^+] = 10^{-\text{pH}}$

• Example: If pH = 2.34, $[H_3O^+] = 10^{-2.34} = 4.6 \times 10^{-3}$ M

Normality and Equivalents

Normality (N) is a measure of concentration based on the equivalents of acid or base per liter of solution.

• Normality of acid: Molarity of acid × Number of H+ ions produced per formula unit

• Normality of base: Molarity of base × Number of OH- ions produced per formula unit

• Formula:

$\text{Normality (N)} = \frac{\text{Equivalents of acid or base}}{\text{Liters of solution}}$

Neutralization Reactions and Titrations

Neutralization occurs when an acid reacts with a base to produce water and a salt. Titration is a technique used to determine the concentration of an acid or base in solution.

• General reaction: $H_3O^+(aq) + OH^-(aq) \rightarrow 2H_2O(l)$

• Titration formula:

$M_{acid} V_{acid} = M_{base} V_{base}$

• Application: Used to calculate unknown concentrations in acid-base titrations.

Buffer Solutions

Buffers are solutions that resist changes in pH upon addition of small amounts of acid or base. They are typically composed of a weak acid and its conjugate base.

• Buffer equation (Henderson-Hasselbalch):

$\text{pH} = \text{p}K_a + \log\left(\frac{[A^-]}{[HA]}\right)$

• Effective pH range: Depends on the pKa of the acid and the ratio of acid to conjugate base.

• Examples:

  • Carbonic acid-bicarbonate buffer: $H_2CO_3/HCO_3^-$, pKa = 6.37

  • Dihydrogen phosphate-hydrogen phosphate buffer: $H_2PO_4^-/HPO_4^{2-}$, pKa = 7.21

Indicators and pH Measurement

Indicators are substances that change color depending on the pH of the solution. Universal indicators provide a range of colors for different pH values.

• pH scale: Ranges from 0 (strongly acidic) to 14 (strongly basic).

• Blood pH: The concentration of $[H_3O^+]$ in blood is about $4 \times 10^{-8}$ M, corresponding to pH ≈ 7.4.

Summary Table: Acid and Base Properties

Type	Definition	Example
Strong Acid	Completely dissociates in water	HCl, HNO3
Weak Acid	Partially dissociates in water	CH3COOH
Strong Base	Completely dissociates in water	NaOH, KOH
Weak Base	Partially dissociates in water	NH3
Buffer	Resists pH change	H2CO3/HCO3-

Key Equations and Concepts

• $K_a = \frac{[H_3O^+][A^-]}{[HA]}$

• $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$

• $\text{pH} = -\log[H_3O^+]$

• $\text{pOH} = -\log[OH^-]$

• $\text{pH} + \text{pOH} = 14$

• $\text{Normality (N)} = \frac{\text{Equivalents}}{\text{Liters of solution}}$

• $M_{acid} V_{acid} = M_{base} V_{base}$

• $\text{pH} = \text{p}K_a + \log\left(\frac{[A^-]}{[HA]}\right)$

Additional info:

• Water is amphiprotic, meaning it can act as both an acid and a base depending on the reaction context.

• Buffer systems are crucial in biological systems, such as blood, to maintain a stable pH.

• Indicators are used in titrations to determine the endpoint of acid-base reactions.