Chemistry of Aqueous Solutions

A strong acid is essentially fully ionised in dilute aqueous solution; a weak acid establishes an equilibrium with only a fraction ionised. For a weak monoprotic acid, HA(aq) ⇌ H⁺(aq) + A^-(aq). A strong base such as dissolved NaOH provides hydroxide essentially completely; a weak base such as NH₃ reacts only partly with water: NH₃ + H₂O ⇌ NH₄⁺ + OH^-.

At the same analytical concentration, a weak monoprotic acid usually gives a lower hydrogen-ion concentration than a strong monoprotic acid. Dilution can increase the fraction of weak acid ionised even while the absolute hydrogen-ion concentration decreases. Degree of ionisation and [H⁺] must not be treated as the same quantity.

At 298 K, K_w is approximately 1.00 × 10^-14 mol² dm^-6, so pH + pOH = 14.00 under the usual concentration convention. K_w changes with temperature. A neutral solution always has [H⁺] = [OH^-], but neutral pH is exactly 7.00 only when pK_w = 14.00.

For a conjugate pair HA/A^-, K_a(HA)K_b(A^-) = K_w, hence pK_a + pK_b = pK_w. The species must be a conjugate pair. Multiplying the acid constant of ethanoic acid by the base constant of ammonia does not give K_w.

The weak-acid approximation comes from K_a = x²/(c - x), with x = [H⁺] = [A^-]. If x is small compared with c, replace c - x with c. A small computed ionised fraction supports the approximation. If it is not small, the approximation is not justified; the required syllabus problems will not demand solving a quadratic.

An acid-base indicator is usually a weak acid or base whose two forms have different colours. Its visible colour change occurs over a pH interval, commonly around pK_a ± 1. The endpoint is the observed colour change; the equivalence point is the stoichiometric point. They should be close, but they are not definitions of the same event.

A transition interval does not have to be centred at pH 7. The useful question is how much titrant volume changes during the indicator transition. In a steep region this volume is small, so the endpoint error is small. If given unfamiliar indicators, compare their ranges directly with the curve rather than choosing a familiar name.

An acidic buffer contains appreciable amounts of a weak acid HA and its conjugate base A^-, often made by mixing the acid with a soluble salt or partially neutralising the acid. Added H⁺ is consumed by A^-; added OH^- is consumed by HA. An alkaline buffer similarly contains B and BH⁺, such as NH₃/NH₄⁺.

These reactions prevent the added strong acid or base from remaining freely in solution. The component ratio changes only modestly when the addition is small relative to both reservoirs, so pH changes modestly. A buffer does not keep pH perfectly fixed, and it fails when one component is substantially exhausted.

Buffers are used to maintain suitable pH for enzyme reactions, chemical measurements and calibration. Diluting both components by the same factor leaves their ratio approximately unchanged, so ideal buffer pH changes little, but the smaller amounts per volume give lower buffer capacity. At extreme dilution, the simple approximation also breaks down.

Rearrange K_a = [H⁺][A^-]/[HA]: pH = pK_a + log₁₀([A^-]/[HA]). When both components share a solution volume, their mole ratio gives the same ratio. This buffer approximation uses the analytical component amounts after any strong acid/base reaction, provided equilibrium ionisation changes are small relative to those amounts.

For a weak base B and conjugate acid BH⁺, either use the acid constant of BH⁺ in the same equation or use pOH = pK_b + log₁₀([BH⁺]/[B]), followed by pH = pK_w - pOH. Equal amounts of NH₃ and NH₄⁺ with K_b = 1.80 × 10^-5 give pH about 9.26 at 298 K.

The pair HCO₃^-/CO₃^2- is an acid/conjugate-base buffer: carbonate accepts H⁺, while hydrogencarbonate can consume OH^- to form carbonate and water. Ocean water contains other buffering species too, but this pair links increasing atmospheric CO₂ directly to carbonate availability.

The rapid atmospheric CO₂ increase drives additional uptake by surface waters. Buffering consumes carbonate as it resists the added acidity, so it has finite capacity and the equilibrium pH decreases. Ocean acidification means a fall in pH; it does not require seawater to become acidic below pH 7. Reduced carbonate availability also affects the equilibria involved in forming calcium carbonate shells and skeletons.

For AgCl(s) ⇌ Ag⁺(aq) + Cl^-(aq), K_sp = [Ag⁺][Cl^-]. The pure solid is omitted. For CaF₂(s) ⇌ Ca²⁺(aq) + 2F^-(aq), K_sp = [Ca²⁺][F^-]². The exponent follows the dissolution coefficient.

The ionic product Q has the same form as K_sp but uses the current free-ion concentrations. Q < K_sp means unsaturated; Q = K_sp means equilibrium saturation; Q > K_sp makes precipitation thermodynamically favoured. When mixing solutions, first calculate concentrations in the combined volume.

Adding Cl^- to saturated AgCl solution increases a product concentration and favours precipitation, reducing the salt's solubility. If a 0.0100 mol dm^-3 chloride background dominates the tiny dissolved contribution, [Ag⁺] ≈ K_sp/[Cl^-] = 1.80 × 10^-8 mol dm^-3. The approximation must be checked when the background common-ion amount is not large.

Ammonia binds free silver ions: Ag⁺(aq) + 2NH₃(aq) ⇌ [Ag(NH₃)₂]⁺(aq). Removing free Ag⁺ lowers [Ag⁺][Cl^-] below K_sp, so more AgCl dissolves. The total dissolved silver can increase while the free Ag⁺ concentration remains small. K_sp uses the free ion, not the sum of free and complexed silver.

Nitric acid removes interfering carbonate or hydroxide without introducing a halide. Hydrochloric acid would introduce chloride and give a false positive. The ammonia trend reflects the balance between the very small solubility products and complex formation, rather than a claim that ammonia breaks every silver-halide lattice equally easily.

Buffers resist small changes by consuming the addition; they have finite capacity. Ocean CO₂ uptake consumes carbonate and lowers pH. For solubility, compare the free-ion product with K_sp: a common ion suppresses dissolution, while complexing a dissolved ion can promote it.