Acids and Bases - In Depth Notes

Learning Outcomes

• Contrast the Arrhenius, Bronsted-Lowry, and Lewis models of acids and bases.
• Identify conjugate acid-base pairs and compare their strengths.
• Compare strengths of acids and bases using ionization constants ($Ka$, $Kb$) and/or $pKa/pKb$ values.
• Relate acid strength to molecular composition.
• Convert between $pH$, $pOH$, $[H_3O^+]$, and $[OH^-]$ for acidic and basic solutions.
• Calculate the $pH$ and/or ion concentrations of solutions with strong acids, weak acids, and bases.
• Calculate percentage ionization of weak acids.
• Determine $pH$ of salt solutions.

Definitions of Acids and Bases

Arrhenius Definition

• Acid: Produces $H^+$ ions in aqueous solution.
  • Example: $HCl(aq)
    ightarrow H^+(aq) + Cl^-(aq)$
• Base: Produces $OH^-$ ions in aqueous solution.
  • Example: $NaOH(aq)
    ightarrow Na^+(aq) + OH^-(aq)$
• Shortcomings: Ignores that $H^+$ exists as $H_3O^+$ and is limited to aqueous solutions.

Bronsted-Lowry Definition

• Acid: Donates a proton ($H^+$).
  • Example: $HCl(aq) + H2O(l) ightarrow H3O^+(aq) + Cl^-(aq)$
• Base: Accepts a proton.
  • Example: $NH3(aq) + H2O(l)
    ightarrow NH_4^+(aq) + OH^-(aq)$
  • Acids and bases work together in pairs.

Lewis Definition

• Lewis Acid: Electron pair acceptor.
• Lewis Base: Electron pair donor.

Conjugate Acid-Base Pairs

• Two substances differing by the presence/absence of a proton.
  • A base accepts a proton to become a conjugate acid.
  • An acid donates a proton to become a conjugate base.

Strength of Acids

• Strong Acids: Completely dissociate in solution.
  • Example: $1.0 ext{ M } HCl
    ightarrow 1.0 ext{ M } [H_3O^+]$ and $1.0 ext{ M } [Cl^-]$
• Weak Acids: Partially dissociate in solution.
  • Example: $1.0 ext{ M } HF
    ightarrow 0.025 ext{ M } [H_3O^+]$ and $0.025 ext{ M } [F^-]$
• Strong acids have high $Ka$ values, while weak acids have low $Ka$ values.

Molecular Structure and Acidity

Binary Acid Strength

• Depends on bond strength and stability of the conjugate base ($X^-$).
  • H-F < H-Cl < H-Br < H-I (increasing strength)

Oxoacid (Oxyacid) Strength

• Structure: Contains $O-H$ bonds.
• Acidity impacted by:
  • Electronegativity of the central atom (Y)
  • Number of $O$ atoms. More $O$ atoms increase electron-withdrawing power, enhancing acidity.

Base Definitions

• Strong Bases: Completely dissociate in solution (e.g., $NaOH$).
• Weak Bases: Partially dissociate (e.g., $NH3$ producing $OH^-$ through reaction with $H2O$).

Ionization Constants

• $Ka$ and $Kb$ used to describe strength of acids and bases, respectively.
• Relationship: $Ka imes Kb = Kw$ (where $Kw$ is the ion product constant of water).

Percent Ionization of Weak Acids

• Percent ionization quantifies how much of a weak acid dissociates:
  ext{Percent Ionization} = rac{[ ext{ionized acid}]}{[ ext{acid}]_{initial}} imes 100 ext{%}

Mixtures of Acids and Bases

Strong Acid and Weak Acid

• The strong acid suppresses the contribution of the weak acid to $[H_3O^+]$.

Weak Acid and Weak Acid

• The strongest weak acid will dominate the $[H_3O^+]$ concentration.

Special Cases: Polyprotic Acids

• Polyprotic acids can donate more than one $H^+$; each step has its own $K_a$ value.
  • Example: $H2SO4$ has a complete first ionization, then a weaker second ionization.

pH of Salt Solutions

Neutral Salts

• E.g., $NaCl$ do not hydrolyze in water.

Acidic Salts

• Cations of weak bases are acidic (e.g., $NH4^+$ produces $H3O^+$).

Basic Salts

• Anions of strong acids do not hydrolyze significantly (e.g., $Cl^-$).

Important Calculations

• Autoionization of water:
  Kw = [H3O^+][OH^-] ext{ at 25°C: } K_w = 1.0 imes 10^{-14}
• Relationship between pH and pOH:
  pH + pOH = 14

Practice Problems

• Calculate the $pH$ for solutions with strong and weak acids/bases using provided ionization constants and concentrations.
• Analyze mixtures of acids for $[H_3O^+]$ contributions, considering both strong and weak acids.
• Determine the ionization constants and derivatives, like $Ka$ and $Kb$ for specific acid-base pairs based on provided data.