Acids and Bases

Arrhenius

• Acid dissociates to make $H^+$
• Base dissociates to make $OH^-$
• Water is not an Arrhenius acid

Brønsted–Lowry

• Acid donates an $H^+$ ion
• Water is an acid here
• Base accepts an $H^+$ ion
• Not limited to aqueous solutions
• Acids and bases always occur in pairs

Lewis

• Lewis acid = e⁻ pair acceptor
• Lewis base = e⁻ pair donor
• One species pushes lone pair to form a bond with another
• Coordinate covalent bond formation
• Most inclusive definition
• BF₃ and AlCl₃ can accept e⁻ pairs but don’t donate $H^+$

Amphoteric species

• Can act as acid or base
• Amphiprotic = Brønsted–Lowry sense
• Acts like acid in basic environment or base in acidic environment
• Can act as reducing or oxidizing agent
• Conjugate base of polyvalent acid is amphoteric
  • Example: HSO₄⁻ can gain or lose proton
• Zwitterions have both characters

Nomenclature

• Anions ending in ide → ic acid
• Anions ending in ite → ous acid
• Anions ending in ate → ic acid

Autoionization of water and H equilibria

• Amphoteric compounds autoionize
• Water forms H₃O⁺ and OH⁻
• $K_w = [H_3O^+][OH^-] = 10^{-14}$
• In neutral solution, each ion = $10^{-7}$
• $K_w$ changes only with temperature (↑T → ↑ $K_w$)
• Changing one concentration shifts equilibrium to compensate

pH and pOH scales

• $pH = -\log[H^+] = \log \frac{1}{[H^+]}$
• $pOH = -\log[OH^-] = \log \frac{1}{[OH^-]}$
• Pure water pH = 7

Estimating scale values

• $-\log(n \times 10^{-m}) = m - \log(n)$
• n between 1 and 10 → log(n) between 0 and 1
• p-value ≈ m − 0.n
• Example: if $K_a = 1.8 \times 10^{-5}$, then $pK_a = 5 - .18 = 4.82$

Strong acids and bases

• Completely dissociate
• Strong acids: HCl, HBr, HI, H₂SO₄, HNO₃, HClO₄, H₃PO₄
• Bases: NaOH, KOH
• pH of 10 M HClO₄: $-\log(10) = -1$
• Diprotic example: H₂SO₄ gives 2 protons → multiply concentration by 2 for $[H^+]$

Weak acids and bases

• Weak monoprotic acid partially dissociates
• HA + H₂O → H₃O⁺ + A⁻
• $K_a = \frac{[H_3O^+][A^-]}{[HA]}$
• Smaller $K_a$ → weaker acid
• Water excluded since it's a pure liquid

Conjugate acid–base pairs

• CA forms when base gains proton
• CB forms when acid loses proton
• HCO₃⁻ + H₂O → CO₃²⁻ + H₃O⁺
• Adding reversible reactions gives net: H₂O → H₃O⁺ + OH⁻
• $K_a$ and $K_b$ inversely related
• Strong acid → weak CB
• Weak acids → weak CBs

Effect of induction

• Electronegative atoms pull e⁻ density → ↑acid strength by facilitating dissociation

Applications of Ka and Kb

• Write $K_a$ expression, substitute concentrations
• Often $[H_3O^+]$ equals conjugate base concentration for simple monoprotic dissociation

Salt formation

• Neutralization: acid + base → salt
• Often condensation-type (e.g., peptide bond)
• Salt may precipitate or remain ionized
• Reverse reaction = hydrolysis

Strong acid + strong base

• Makes salt + water
• Equivalence point = pH 7

Strong acid + weak base

• Forms salt only (weak bases aren't hydroxides)
• Cation of salt may reform weak base by hydrolysis

Weak acid + strong base

• Salt hydrolyzes → basic pH

• Acid equivalent = one mole of $H^+$
• Base equivalent = one mole of $OH^-$
• Polyvalent species liberate more than one proton
• Polyprotic in Brønsted–Lowry sense
• Normality measures acidic/basic capacity
• Gram equivalent weight = mass that donates one equivalent
  • Example: H₂SO₄ has molar mass 98 g/mol and is diprotic → GEW = 49 g

General principles

• Add small volumes of known concentration (titrant) to known volume of unknown (titrand)
• Equivalence point reached when equivalents acid = equivalents base
• $N_a V_a = N_b V_b$
• Found graphically or with indicator

Indicators

• Weak organic acids/bases with different colors when protonated/deprotonated
• Must be weaker than analyte
• Endpoint ≠ equivalence point, but close if indicator chosen well
• Need at least one strong acid/base for distinct curve
• If both weak, curve is shallow

Strong acid + strong base

• Example: HCl and NaOH
• Equivalence point = pH 7
• Endpoint slightly above 7
• Adding NaOH gradually increases pH until sudden jump

Weak acid + strong base

• Initial pH > strong acid case
• More sudden rise at equivalence
• Equivalence > 7

Strong acid + weak base

• Curve is inverse of weak acid + strong base
• Equivalence < 7

Weak acid + weak base

• Initial pH between 3–11
• Shallow changes in pH

Polyvalent acids and bases

• Multiple equivalence points
• Amino acid titrations typically have 3

Buffers

• Weak acid + salt (conjugate base + cation) or weak base + salt
• Examples:
  • CH₃COOH + CH₃COO⁻Na⁺
  • NH₃ + NH₄⁺Cl⁻
• Added base: OH⁻ reacts with H₃O⁺ → acetic acid dissociates → neutralizes base
• Added acid: H⁺ reacts with acetate → forms acetic acid
• Smaller pH changes than without buffer

Bicarbonate buffer system

• CO₂ + H₂O ⇌ H₂CO₃ ⇌ HCO₃⁻ + H⁺
• Adding CO₂ shifts right
• In acidosis: blow off more CO₂ → shift left → ↓[H⁺]
• Optimal activity range: ±1 pH unit
• Acidemia more common than alkalemia
• More severe acidemia → buffer more effective

Henderson–Hasselbalch equation

• $pH = pK_a + \log \frac{[A^-]}{[HA]}$
• Derived from $K_a$ expression
• Changing concentrations but keeping ratio constant maintains pH
• Buffering capacity ↑ with proportionally larger amounts of conjugate pair