Notes on Acid-Base Equilibria

Chapter 18: Acid-Base Equilibria

Introduction

• Many important chemical reactions are classified as acid-base reactions.

• Substances have been recognized for their acid-base properties since ancient times, but clear definitions were established only in the late 19th century by Svante Arrhenius.

Arrhenius Definitions

• Acid: A substance that yields hydrogen ions (H⁺) when dissolved in water.

• Base: A substance that yields hydroxide ions (OH⁻) when dissolved in water.

• The ion produced in aqueous solution by Arrhenius acids is better represented by H₃O⁺ (hydronium ion). H⁺ is used as shorthand but can be misleading in some contexts.

• Limitations of Arrhenius definitions:

  • They are restricted to aqueous solutions.

  • Not all acids contain H, and not all bases contain OH.

Brønsted-Lowry Definitions

• Expanded definitions that do not depend on the solvent:

  • Acid: A proton donor (H⁺).

  • Base: A proton acceptor.

• This definition modified the identity of the species acting as the base. For example, NaOH is called a base as it produces OH⁻ in water. However, OH⁻ is the proton acceptor in reactions.

Conjugate Acid-Base Pairs

• When an acid donates a proton, the species left behind becomes a conjugate base; conversely, when a base accepts a proton, it becomes a conjugate acid.

• A pair of species that differ by one proton is known as a conjugate acid-base pair.

  • Example Reaction: a) HCl(aq) + H₂O(l) → H₃O⁺(aq) + Cl⁻(aq)

    • HCl is the acid and Cl⁻ is the conjugate base.

    • H₂O is the base and H₃O⁺ is the conjugate acid.

  • Example Reaction:
    b) H₂O(l) + SO₄²⁻(aq) ⇌ HSO₄⁻(aq) + OH⁻(aq)

• Autoionization of Water: Even in pure water, molecules can act as acids and bases with the reaction:
  $H_2O(l) + H_2O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)$.

Ion-Product Constant of Water, Kw

• Equilibrium constant expression for water's autoionization:
  $K_w = [H₃O^+][OH^-]$

• At 25°C, $[H₃O^+] = [OH^-] = 1.00 imes 10^{-7} ext{ M}$ leads to
  $K_{w}=1.00\cdot10^{-14}$ .

• Solutions can be neutral ($[H₃O^+] = [OH^-]$), acidic ($[H₃O^+] > [OH^-]$), or basic ($[H₃O^+] < [OH^-]$).

pH Scale

• A logarithmic scale used to express hydrogen ion concentration:
  $pH=-lo{g}[H^{+}]$ .

• Example Calculation: At $[H^+] = 1.5 imes 10^{-4}$ M,
  $pH=-{log}(1.5\cdot10^{-4})=3.82$ .

• The pH is 7 at neutrality, $[H^+] = 1.00 imes 10^{-7}$ M, and decreases with increasing hydrogen ion concentration.

• Significant Figures: The pH reflects significant figures only from the decimal part of the logarithm.

Strong Acids and Bases

• Define strength based on tendency to ionize in solution:

  • Strong acids/bases: Completely ionize (100%).

  • Weak acids/bases: Do not ionize completely.

• Typical strong acids: HCl, HBr, HI, H₂SO₄, HNO₃, HClO₄ (six common strong acids).

• Strong Bases: Hydroxides of Group IA and IIA metals (e.g., NaOH, KOH, Ca(OH)₂).

Acid Strength and Ionization Constants

• Acid-ionization constant (Kₐ) measures the strength of an acid; larger Kₐ indicates stronger acids.

• Weak Acid Example: $HA <br>ightleftharpoons H^+ + A^-$ with
  $K_a = rac{[H^+][A^-]}{[HA]}$.

• For polyprotic acids, each ionization has its own Kₐ (e.g., $K_{a1} > K_{a2} > K_{a3}$).

Relationship Between Kₐ and Kₑ

• For acid-base pairs, you find
  $K_{a}\cdot K_{b}=K_{w}$ .

• At 25 °C,
  $pK_a + pK_b = pK_w = 14$.

Salt Solutions and Their pH

• Salts from strong acid-strong base reactions do not affect pH.

• Salts from weak acid-strong base reactions can yield basic solutions (e.g., sodium acetate).

• Structure of salts can predict acidic or basic character depending on their constituents (conjugate acids of weak bases are weak acids, while conjugate bases of weak acids are weak bases).

Chemical Properties of Acids and Bases

• Acids are electron pair acceptors in Lewis definitions, which extend concepts beyond proton exchange.

• Electronegativity and bond strength are key factors influencing acid strength.

• Comparative acidity of nonmetal hydrides decreases from HF to HI despite increasing polarity.

• For oxoacids, strength is influenced by the number of oxygen atoms bonded to the central atom.

Observations and Summary

• The stronger the acid, the weaker its conjugate base and vice versa, particularly for strong acids and bases.

• Acid-base reactions can often be better understood through the lens of the Bronsted-Lowry and Lewis definitions to encompass more complex interactions.

Additional Examples and Practice

• Example calculations involving pH from H⁺ and OH⁻ concentrations, applications of Kₐ and K_b involving weak acids and bases, and assessments of salts produced in reactions to determine their effect on pH.

• Utilize tables listing common acids and bases along with their ionization constants.