Acids and Bases: Brønsted, Lewis, HSAB, pH, Buffers, Hydrolysis and Solubility Product

3.1Brønsted and Lewis theories

Three definitions are in use. Each one widens the one before it.

• Arrhenius: an acid gives H⁺ (as H₃O⁺) in water, a base gives OH⁻. It works only in water and cannot explain the basic nature of NH₃ or Na₂CO₃ without bringing in hydrolysis.
• Brønsted–Lowry: an acid is a proton donor, a base a proton acceptor. Every acid–base reaction is a proton transfer between two conjugate pairs: HA + B ⇌ A⁻ + HB⁺.
• Lewis: an acid is an electron-pair acceptor, a base an electron-pair donor; the product is an adduct with a coordinate bond (BF₃ + NH₃ → F₃B←NH₃).

Conjugate pairs

• Conjugate base = acid minus one H⁺; conjugate acid = base plus one H⁺. H₃PO₄ → H₂PO₄⁻ → HPO₄²⁻ → PO₄³⁻: each species is the conjugate base of the one before it.
• The stronger the acid, the weaker its conjugate base: for any pair, K_a × K_b = K_w.
• Amphiprotic species can both give and take a proton: H₂O, HCO₃⁻, H₂PO₄⁻, HPO₄²⁻, HS⁻.
• Autoprotolysis (self-ionisation): one solvent molecule passes a proton to another. 2H₂O ⇌ H₃O⁺ + OH⁻; 2NH₃ ⇌ NH₄⁺ + NH₂⁻; 2H₂SO₄ ⇌ H₃SO₄⁺ + HSO₄⁻.

The solvent decides how an acid behaves

• In a strongly basic solvent (liquid NH₃) even weak acids give up their protons completely: acetic acid behaves as a strong acid. All acids stronger than NH₄⁺ look equally strong there: the levelling effect.
• In water acetic acid is a weak acid (K_a = 1.8 × 10⁻⁵). HCl, HBr, HI, HNO₃, HClO₄ are all levelled to H₃O⁺ in water.
• In a strongly acidic solvent (pure H₂SO₄, HF) acetic acid accepts a proton and behaves as a base: CH₃COOH + H₂SO₄ → CH₃C(OH)₂⁺ + HSO₄⁻. A less basic solvent such as acetic acid itself differentiates strong acids (HClO₄ > HBr > H₂SO₄ > HCl > HNO₃).

Lewis acids and bases

• Lewis acids: molecules with an incomplete octet (BF₃, AlCl₃, BeCl₂), cations (Ag⁺, Fe³⁺, H⁺ itself), molecules with vacant d orbitals (SiF₄, SnCl₄) and molecules with polar multiple bonds (CO₂, SO₃). BF₃ is a Lewis acid but not a Brønsted acid.
• Lewis bases: anions (F⁻, OH⁻, CN⁻) and molecules with lone pairs (NH₃, H₂O, R₃P, CO). Every Brønsted base is also a Lewis base.
• Proton affinity measures gas-phase basicity (energy released when a species takes up H⁺). For the same row, the less electronegative donor holds its lone pair less tightly: NH₃ (854) > H₂O (691 kJ mol⁻¹); NH₃ also exceeds CH₃COOH and H₂S.
• Steric effects on basicity: in R₃N, bulky R groups open the C–N–C angle and flatten the nitrogen (B-strain). The C–N bonds take more s character, so the lone pair gains more p character; at the same time the crowded nitrogen cannot reach a Lewis acid easily, so donation becomes poorer. With bulky acids such as B(CH₃)₃, Et₃N is a weaker base than Et₂NH.
• Acidity of water and alcohols (in solution): H₂O > RCH₂OH > R₂CHOH > R₃COH. Alkyl groups push electron density onto O⁻ and the bulky alkoxide ions are poorly solvated, so the anion is less stable.

3.2Hard and soft acids and bases (HSAB)

Pearson’s principle: hard acids prefer to combine with hard bases, and soft acids with soft bases. Hard–hard bonding is mainly ionic; soft–soft bonding is mainly covalent.

• So S²⁻ binds best to heavy metal ions of low oxidation state (Cu⁺, Ag⁺, Hg²⁺, Cd²⁺, Pb²⁺): these occur in nature as sulphide ores. Hard ions (Na⁺, Mg²⁺, Ca²⁺, Al³⁺) occur as oxides, carbonates, silicates.
• Predicting reactions: in Nb₂S₅ + 5HgO ⇌ Nb₂O₅ + 5HgS, the products pair hard Nb⁵⁺ with hard O²⁻ and soft Hg²⁺ with soft S²⁻, so the products are favoured.
• The same idea explains why AgI is far less soluble than AgF, and why CO and R₃P bind to metals in low oxidation states.

3.3Chemical and ionic equilibrium

Law of mass action: for aA + bB ⇌ cC + dD at equilibrium and a fixed temperature,

• Δn_g = moles of gaseous products − moles of gaseous reactants. When Δn_g = 0 (H₂ + I₂ ⇌ 2HI; N₂ + O₂ ⇌ 2NO), K_p = K_c.
• K changes only with temperature. Comparing the reaction quotient Q with K tells the direction: Q < K forward, Q > K backward.

Le Chatelier’s principle

If a system at equilibrium is disturbed, it shifts in the direction that partly undoes the disturbance.

• Pressure (or volume): higher pressure favours the side with fewer gas moles. N₂ + 3H₂ ⇌ 2NH₃ shifts right; N₂O₄ ⇌ 2NO₂ shifts left; reactions with Δn_g = 0 do not shift. Heat terms play no part in the pressure effect.
• Temperature: heating favours the endothermic direction, and this is the only factor that changes K. N₂ + O₂ ⇌ 2NO (ΔH = +180 kJ mol⁻¹) gives more NO when hot (lightning, car engines).
• Concentration: adding a reactant or removing a product drives the reaction forward.
• Inert gas: at constant volume no shift; at constant pressure it acts like a lower pressure and favours the side with more gas moles.
• Catalyst: reaches equilibrium faster; no shift.

Ionic equilibrium is the same law applied to the partial ionisation of weak electrolytes in solution: HA ⇌ H⁺ + A⁻, with K_a = [H⁺][A⁻]/[HA]. Strong electrolytes are fully ionised and have no meaningful equilibrium constant.

3.4Strengths of acids and bases

• A larger K_a (smaller pK_a) means a stronger acid. Acetic acid pK_a 4.76; NH₄⁺ 9.25 (so NH₃ pK_b 4.75); HF 3.2; H₂CO₃ 6.4; HCN 9.2; boric acid 9.2.
• Polyprotic acids ionise in steps with K_a1 ≫ K_a2 ≫ K_a3 (H₃PO₄: 7.5 × 10⁻³, 6.2 × 10⁻⁸, 4.8 × 10⁻¹³): removing H⁺ from an already negative ion is harder.
• Hydracids HX: acid strength rises down a group (HF < HCl < HBr < HI) because the H–X bond weakens; across a period it rises with electronegativity (CH₄ < NH₃ < H₂O < HF).
• Oxyacids: strength rises with the number of oxygens not bonded to H (HClO < HClO₂ < HClO₃ < HClO₄) and with the electronegativity of the central atom (HOI < HOBr < HOCl).
• Hydrated metal ions are acidic when small and highly charged: [Al(H₂O)₆]³⁺ and [Fe(H₂O)₆]³⁺ give H⁺.