Topic 6: Acids, Bases, and Buffers - The pH Scale

pH - Definition

Concentration of H+ ions relative to that in pure water to identify the acidic/basic nature of a system

pOH - Definition

Concentration of OH- ions relative to that in pure water to identify the acidic/basic nature of a system

pH Scale and its Mechanism

• Adding acid to water → [H₃O⁺] ↑ and [OH⁻] ↓ to maintain the Kw constant by reforming products into reactants

• Adding base to water → [OH⁻] ↑ and [H₃O⁺] ↓ to maintain the Kw constant by reforming products into reactants.

• Acid/base addition can shift concentrations over 14 orders of magnitude.

• H₂O + H₂O ⇌ H₃O⁺ + OH⁻.

pH - Formula

pH = –log₁₀[H₃O⁺]

Change of 1 in the pH = change in [H₃O⁺] by a factor of 10

pOH - Formula

pOH = –log₁₀[OH⁻].

Change of 1 in the pH = change in [OH⁻] by a factor of 10

Relationship Between pH and pOH

pH + pOH = 14 (at 25 °C).

Calculating [H₃O⁺] and [OH⁻] from pH and pOH

• [H₃O⁺] = 10⁻ᵖᴴ

• [OH⁻] = 10⁻ᵖᴼᴴ.

pH Scale - Neutral

pH = 7 ([H₃O⁺] = [OH⁻])

pH Scale - Acidic

pH < 7 ([H₃O⁺] > [OH⁻]).

pH Scale - Basic

pH > 7 ([H₃O⁺] < [OH⁻]).

Ionization

• Neutral molecular compounds (usually covalent) react in water to form ions that weren't there before - proton transfer reaction

• E.g: HCl (g) + H₂O (l) → H₃O⁺ (aq) + Cl⁻ (aq).

Dissociation

• Ionic compound already has ions in its lattice. When dissolved, the ions separate into solution.

• E.g: NaCl (s) → Na⁺ (aq) + Cl⁻ (aq).

• Whenever dissociation occurs, the real acid-base reaction referred to for the calculations is the ionization undergone later by the product that will act as an acid/base

  • NH₄Cl (s) → NH₄⁺ (aq) + Cl⁻ (aq)

  • The acid-base chemistry centers around NH₄⁺ as the Cl⁻ is just a spectator ion. NH₄Cl is just a solution of NH₄⁺ 

Strong Acids

• Most are covalent molecules (e.g. HCl, HNO₃, H₂SO₄).

• In water, they ionize completely (not dissociate, because they are not ionic solids to begin with).

  • Have very weak conjugate bases as a result, leaving the conjugate base and H⁺ in the solution

• Reaction: HCl + H₂O → H₃O⁺ + Cl⁻

• Arrow: Single arrow (→), because ionization is essentially 100%.

• It can be assumed that [H₃O⁺] are stoichiometrically equal to the concentration of the acid in question, because it ionizes in one step

Strong Acids to Remember

Weak Acids

• Also covalent molecules (e.g. CH₃COOH, HF).

• In water, they ionize partially (proton transfer to water, equilibrium between ionized and unionized form).

• Reaction: CH₃COOH + H₂O ⇌ H₃O⁺ + CH₃COO⁻

• Arrow: Double equilibrium arrow (⇌), because ionization is incomplete.

• Some weak acids can have multiple conjugate bases from how many H+ ions it loses from each deprotonation step

  • E.g: Citric acid (H₃C₆H₅O₇) → 1st: H₃C₆H₅O₇ ⇌ H⁺ + H₂C₆H₅O₇⁻ → 2nd: H₂C₆H₅O₇⁻ ⇌ H⁺ + HC₆H₅O₇²⁻ → 3rd: HC₆H₅O₇²⁻ ⇌ H⁺ + C₆H₅O₇³⁻

 

Strong Bases

• Many are ionic compounds (e.g. NaOH, KOH, Ca(OH)₂).

• In water, they simply dissociate completely into pre-existing ions.

• Reaction: NaOH (s) → Na⁺ (aq) + OH⁻ (aq)

• Arrow: Single arrow (→), since dissociation is essentially 100%.

• It can be assumed that [OH-] are stoichiometrically equal to the concentration of the base in question, because it dissociates in one step

 

Strong Bases to Remember

Weak Bases

• Typically molecular compounds (e.g. NH₃, amines).

• They ionize in water by proton transfer (accept H⁺ from H₂O to form OH⁻).

• Reaction: NH₃ + H₂O ⇌ NH₄⁺ + OH⁻

• Arrow: Double equilibrium arrow (⇌), because only partial ionization occurs.

Acid Dissociation Constant - K_a

Smaller K_a → weaker acid; larger K_a → stronger acid.

Smaller pK_a → stronger acid; larger pK_a → weaker acid.

Where aA + bB ⇌ dD + eE

K_a = [D]^d[E]^e/[A]^a[B]^b

pK_a = -log₁₀K_a

Units: mol/L

Base Dissociation Constant - K_b

Smaller K_b → weaker base; larger K_b → stronger base.

Smaller pK_b → stronger base; larger pK_b → weaker base.

Where aA + bB ⇌ dD + eE

K_b = [D]^d[E]^e/[A]^a[B]^b

pK_b = -log₁₀K_a

Conjugate Pairs - Strong and Weak Acids and Bases

K_a, K_b, and K_w Relationships

• For a conjugate acid–base pair: K_a × K_b = K_w = 1.0 × 10⁻¹⁴.

• Therefore: pK_a + pK_b = 14 (at 25 °C).

Weak Acid/Base Pairs

pH Calculations

• Goal: Find the [H₃O⁺] or [OH⁻] to be plugged into the pH or pOH formula. Set up an ICE table to find the concentrations of the substances involved, then sub them into the K_a/K_b formula to find the [H₃O⁺] or [OH⁻]. Note that since K_a or K_b is so small, x is negligible.

• Strong acids: [H₃O⁺] ≈ initial acid concentration.

• Strong bases: [OH⁻] ≈ initial base concentration.

• Weak acids/bases: [H₃O⁺] or [OH⁻] must be calculated using K_a or K_b.

• Use K_w to interconvert: [H₃O⁺] × [OH⁻] = 10⁻¹⁴.

• pH + pOH = 14.

Common Polyatomic Ions

Cations

• Ammonium: NH₄⁺

• (Most others are anions)

Anions

• Hydroxide: OH⁻

• Nitrate: NO₃⁻

• Nitrite: NO₂⁻

• Carbonate: CO₃²⁻

• Bicarbonate (hydrogen carbonate): HCO₃⁻

• Sulfate: SO₄²⁻

• Sulfite: SO₃²⁻

• Hydrogen sulfate (bisulfate): HSO₄⁻

• Phosphate: PO₄³⁻

• Hydrogen phosphate: HPO₄²⁻

• Dihydrogen phosphate: H₂PO₄⁻

• Acetate: CH₃COO⁻ (sometimes written C₂H₃O₂⁻)

• Cyanide: CN⁻

• Permanganate: MnO₄⁻

• Chromate: CrO₄²⁻

• Dichromate: Cr₂O₇²⁻

Ionic Compound - Metal + Nonmetal

• Electrons transferred from metal → nonmetal.

• Forms a crystalline lattice of cations + anions.

• Example: NaCl, MgO, CaF₂.

Ionic Compound - Metal + Polyatomic ion

• Still ionic (metal forms cation, polyatomic ion is an anion).

• Example: NaNO₃, CaSO₄.

Ionic Compound - Polyatomic Cation + Polyatomic Anion

• Less common but exists.

• Example: NH₄NO₃ (ammonium nitrate).

Molecular (Covalent) Compound - Nonmetal + Nonmetal

• Electrons shared, molecules formed.

• Example: H₂O, CO₂, CH₄.

Tip on Weak Acids

If a problem provides a pK_a value, it’s a weak acid.

General Acid Dissociation Reaction

HA (aq) + H₂O (l) ⇌ H₃O⁺ (aq) + A⁻ (aq)

K_a = [H₃O⁺][A⁻]/[HA]

Water is the solvent and its concentration is considered constant, so it is omitted from the equilibrium expression.

Weak Acid Dissociation Reaction

HA ⇌ H⁺ + A⁻

At equilibrium, [H⁺] ≈ [A⁻], and the initial acid concentration [HA]₀ is much greater than the amount dissociated

K_a ≈ [H⁺][A^-]/ [HA]

K_a vs. pK_a and K_b vs. pK_b Relationship

Each 10-fold increase in K_a corresponds to a 1-unit decrease in pK_a.

Each 10-fold increase in K_b​ corresponds to a 1-unit decrease in pK_b.

And vice versa

General Base Dissociation Reaction

B (aq) + H₂O (l) ⇌ BH⁺ (aq) + OH⁻ (aq)

[BH⁺][OH⁻]/[B]