Part 1: Proton transfer, acid strength and the pH scale

Connect acid–base definitions to particles, then calculate pH for strong acids and bases without confusing strength with concentration.

Acids and bases are roles in proton transfer

A Brønsted–Lowry acid donates a proton, H⁺; a Brønsted–Lowry base accepts a proton. In HCl + H₂O → H₃O⁺ + Cl⁻, HCl is the donor and water is the acceptor. In water, a proton is hydrated: H₃O⁺ is a useful explicit representation, while H⁺(aq) is the conventional abbreviation in calculations.

After HA loses H⁺ it becomes A⁻, its conjugate base. After B gains H⁺ it becomes BH⁺, its conjugate acid. A conjugate pair differs by exactly one proton, not one electron. In NH₃ + H₂O ⇌ NH₄⁺ + OH⁻, the pairs are NH₄⁺/NH₃ and H₂O/OH⁻. NH₃ and H₂O react with each other but are not a conjugate pair.

Water can donate or accept a proton depending on its partner and is amphiprotic. For HSO₄⁻ + H₂O ⇌ SO₄²⁻ + H₃O⁺, HSO₄⁻ acts as an acid; for HSO₄⁻ + H₃O⁺ ⇌ H₂SO₄ + H₂O it acts as a base. Follow the transferred H and the charge rather than classifying every negatively charged ion as only a base.

Strong and concentrated describe different things

A strong acid is essentially completely dissociated in dilute aqueous solution. A weak acid establishes an equilibrium in which only a proportion of its molecules has donated a proton. Concentration instead measures the total amount of solute per volume. A dilute strong acid can have a higher pH than a concentrated weak acid.

For equal analytical concentrations of monobasic acids, a strong acid normally gives a larger [H⁺] than a weak acid. For equal amounts of monobasic acid, however, the same amount of hydroxide is needed for complete neutralisation: removing H⁺ makes more weak acid dissociate. Weak does not mean that some acid can never react.

A strong soluble hydroxide supplies its hydroxide ions essentially completely; a weak base such as ammonia reacts only partly with water. Strong/weak describes extent of reaction with water, whereas soluble/insoluble describes how much material enters solution. Do not use these terms interchangeably.

The pH scale is logarithmic

At this level, pH = −log₁₀[H⁺], using the numerical concentration in mol dm⁻³. The inverse is [H⁺] = 10⁻ᵖᴴ mol dm⁻³. A fall of one pH unit means ten times the hydrogen-ion concentration; pH itself is not a concentration and has no units.

For 0.0300 mol dm⁻³ HNO₃, complete dissociation gives [H⁺] = 0.0300 mol dm⁻³ and pH = −log₁₀(0.0300) = 1.52. Conversely pH 3.40 gives [H⁺] = 10⁻³·⁴⁰ = 3.98 × 10⁻⁴ mol dm⁻³. Use base-ten logarithms here, not the natural logarithm used with Arrhenius or Gibbs energy.

If 20.0 cm³ of 0.150 mol dm⁻³ HCl is diluted to a total volume of 100.0 cm³, n(H⁺) = 0.150 × 0.0200 = 0.00300 mol and [H⁺] = 0.00300/0.1000 = 0.0300 mol dm⁻³, giving pH 1.52. “Add 100 cm³ water” would make a different total volume.

For a strong monoprotic acid, [H⁺] ≈ acid concentration provided its contribution dominates that from water. Do not blindly multiply every diprotic acid concentration by two: sulfuric acid has different successive dissociation behaviour and the assumptions must be stated or supplied. At very high dilution, water prevents an acid solution from becoming alkaline simply because a naive −log c exceeds 7 at 25 °C.

Kw connects hydrogen and hydroxide ions

Water self-ionises according to 2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq). Its ionic product is Kw = [H⁺][OH⁻], with units mol² dm⁻⁶ in the concentration convention. At 25 °C, Kw is approximately 1.00 × 10⁻¹⁴ mol² dm⁻⁶. Kw changes with temperature.

A neutral solution has [H⁺] = [OH⁻], so [H⁺] = √Kw and neutral pH = ½pKw. Define pKw = −log₁₀Kw and pKa = −log₁₀Ka using the quoted numerical constants. Neutral pH is 7.00 only when pKw = 14.00; warm pure water can have pH below 7 while remaining neutral.

For 0.0200 mol dm⁻³ NaOH at 25 °C, [OH⁻] = 0.0200, [H⁺] = 1.00 × 10⁻¹⁴/0.0200 = 5.00 × 10⁻¹³ mol dm⁻³ and pH = 12.30. For a fully dissociated M(OH)₂ solution of stated concentration 0.00500 mol dm⁻³, [OH⁻] = 0.0100 mol dm⁻³ and pH = 12.00. Account for the formula before applying Kw.

Equivalently pH + pOH = pKw, where pOH = −log₁₀[OH⁻]. The frequently used 14 − pOH shortcut assumes 25 °C; use the supplied Kw at other temperatures.

Interpret measured pH, including salts

For equimolar solutions at a fixed temperature, compare the extent of ion formation. HCl gives more H⁺ than ethanoic acid; NaOH gives more OH⁻ than ammonia. A pH measurement alone cannot establish strength unless the analytical concentration and conditions are known.

NaCl is approximately neutral because neither ion reacts appreciably with water. Sodium ethanoate is alkaline: CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻. Ammonium chloride is acidic: NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺. The spectator counter-ion balances charge but need not determine pH.

Calibrate a pH probe using appropriate known buffers, rinse between samples and keep temperature comparable. Universal indicator can show broad differences, but a colour category is too coarse for a reliable Ka calculation. A lower recorded pH might reflect a higher concentration, an acidic impurity or calibration error, as well as greater acid strength.

Quick checks

Original Finesse questions. Reveal the indicative worked solutions after attempting each question; these are not official Edexcel mark allocations.

Sources