3.1 Proton transfer reactions

A Brønsted–Lowry acid donates H+ and a Brønsted–Lowry base accepts H+. An alkali is a base that is soluble in water.

Follow the proton: the species losing it is the acid and the species gaining it is the base.

Pair species that differ by exactly one H⁺ to identify conjugate acid–base pairs. Charge alone does not decide the role: in NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺, NH₄⁺ is the proton donor and water is the acceptor.

A conjugate base is what remains after an acid donates one proton. A conjugate acid is formed when a base accepts one proton; the pair differs by exactly one H+.

Remove H+ to find the conjugate base or add H+ to find the conjugate acid, then check the charge changes by one unit.

NH₄⁺/NH₃ and H₂CO₃/HCO₃⁻ are conjugate pairs because each pair differs by one H⁺. Removing H⁺ lowers charge by one; adding H⁺ raises it by one. Do not pair species merely because they occur on opposite sides of an equation—trace the specific proton transfer.

An amphiprotic species can donate H+ in one reaction and accept H+ in another.

Write one equation in which the species becomes its conjugate base and another in which it becomes its conjugate acid.

For HCO₃⁻, donation gives CO₃²⁻ whereas acceptance gives H₂CO₃. Showing both reactions is the evidence for amphiprotic behaviour; one acid–base equation alone is insufficient.

pH is logarithmic: a one-unit change represents a tenfold concentration change. Universal indicator gives a colour range; a pH probe gives an instrumental pH measurement.

For [H⁺] = 2.0 × 10⁻³ mol dm⁻³, pH = 2.70; the leading 2 makes the answer non-integer. A colour indicator estimates a range, whereas a calibrated probe supports a numerical measurement.

At 25 °C, Kw = 1.0 × 10⁻¹⁴, so a neutral solution has [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³. Neutrality always means equal ion concentrations; neutral pH is not necessarily 7 when temperature changes.

At a fixed temperature, Kw is constant, so [OH-] = Kw/[H+]: a higher [H+] means a lower [OH-]. For example, at pH 9.3 and 25 C, [OH-] = 2.0 x 10^-5 mol dm^-3. Classify a solution from the ion comparison; do not assume neutral pH is 7 at every temperature.

A strong acid or base ionizes completely in aqueous solution; a weak acid or base ionizes only partially. The equilibrium favours the weaker conjugate species.

Strength is the extent of ionization, whereas concentration is the amount of solute per volume. A concentrated weak acid can be more acidic than a dilute strong acid.

Represent a strong acid with essentially complete ionization and a weak acid with an equilibrium containing substantial undissociated acid. Strength is an equilibrium property, while concentration is an initial amount per volume; pH depends on both, so strength alone cannot rank arbitrary solutions.

Acids neutralize metal oxides and hydroxides to form salt and water. Carbonates and hydrogencarbonates also produce carbon dioxide when the reaction requires it; balance all formulae and coefficients.

Identify the parent acid and parent base of a salt by tracing its anion and cation back to the neutralization reactants.

Balance proton capacity as well as atoms: H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O, while an acid–carbonate reaction also releases CO₂. To identify parents of Na₂SO₄, trace SO₄²⁻ to the acid and Na⁺ to the base rather than treating the salt name as a reaction equation.

The equivalence point is where stoichiometric amounts of analyte and titrant have reacted. A monoprotic strong-acid–strong-base curve has a steep neutral region centred at the equivalence point.

Read the initial pH, steep intercept region and final plateau; curve direction depends on whether acid or base is added.

For a strong acid titrated with strong base at 25 °C, calculate the initial pH from excess acid, locate equivalence from stoichiometric moles, and place the steep section around pH 7. Equivalence is a mole condition; it is not the same as equal solution volumes unless concentrations and stoichiometry make it so.

Move between pH and pOH, then between the logarithm and concentration. Keep the 25 °C condition attached to pH+pOH=14.

A reliable route is [OH⁻] → pOH → pH → [H⁺], or the reverse, with each logarithm shown. Use pH + pOH = pKw; replacing pKw by 14 is valid only at 25 °C.

Worked pOH example: for $0.025\,\mathrm{mol\,dm^{-3}}$ $\ce{KOH(aq)}$, complete dissociation gives $[\ce{OH^-}]=0.025\,\mathrm{mol\,dm^{-3}}$. Therefore $\mathrm{pOH}=-\log_{10}(0.025)=1.60$. The low pOH is consistent with a basic solution; at 298 K, $\mathrm{pH}=14.00-1.60=12.40$.

Ka and Kb measure dissociation extent. pKa = −log Ka, so a lower pKa indicates a stronger acid; use the corresponding comparison for bases and pKb.

Large Ka and small pKa both indicate the stronger acid; large Kb and small pKb indicate the stronger base. Strength describes extent of ionization, whereas concentration describes amount per volume—dilute and weak are not synonyms.

For a conjugate pair, calculate the missing constant by dividing Kw by the known Ka or Kb, keeping the pair direction consistent.

Match the constants to one conjugate pair: Ka(HA) × Kb(A⁻) = Kw. A stronger acid therefore has a weaker conjugate base at the same temperature; do not multiply constants belonging to unrelated species.

Worked conjugate-constant example at 298 K: methylamine has $\mathrm{p}K_b=3.34$, so for its conjugate acid $\ce{CH3NH3+}$, $\mathrm{p}K_a=\mathrm{p}K_w-\mathrm{p}K_b=14.00-3.34=10.66$. Equivalently, $K_aK_b=K_w$. This relationship applies only to a conjugate acid–base pair at the same temperature.

Trace each salt ion to its parent acid or base. A conjugate base from a weak acid can hydrolyse water to produce OH− and an alkaline solution; a conjugate acid from a weak base can produce H3O+.

Spectator ions from strong parents do not control pH. NH₄Cl is acidic because NH₄⁺ donates a proton to water, while a carbonate salt is basic because CO₃²⁻ accepts one; write the hydrolysing ion, not the intact salt, in the equilibrium.

Compare all four strong/weak combinations by starting pH, buffer region, equivalence-point pH and steep-section position. For a weak acid titrated with strong base, half-equivalence gives pH = pKa and the equivalence solution is basic. For a weak base titrated with strong acid, half-equivalence gives pOH = pKb (then pH = pKw − pOH) and the equivalence solution is acidic. Weak–weak curves often lack a sufficiently steep indicator region.

A buffer region contains appreciable weak acid and conjugate base, so the pH changes relatively slowly as titrant is added.

A weak acid–strong base curve starts at a higher pH than an equally concentrated strong acid, contains a buffer region, has pH = pKa at half-equivalence, and has an alkaline equivalence point from conjugate-base hydrolysis. Weak–weak titrations often lack a sufficiently steep jump for a simple indicator endpoint.

HInd and Ind− have different colours. Changing pH shifts their ratio; the visible transition occurs around pH ≈ pKa. Universal indicator is a mixture of indicators with different transition ranges.

Added acid shifts HInd ⇌ H⁺ + Ind⁻ toward the HInd colour; added base favours Ind⁻. The visible transition spans a range around pKa because both colours must change in relative abundance. Universal indicator combines several such equilibria and is not one substance with every colour.

Choose an indicator whose endpoint transition range lies within the steep pH change around the equivalence point. Use salt identity to predict whether that equivalence pH is acidic, neutral or alkaline.

The equivalence point is the stoichiometric condition; the endpoint is the observed indicator colour change. A good indicator makes them coincide closely.

Overlay the indicator transition range on the titration curve and require the whole visible change to fall inside the steep region. A weak acid–strong base equivalence is alkaline and favours an alkaline-range indicator; a strong acid–weak base equivalence is acidic. Endpoint proximity, not a memorized indicator name alone, is the criterion.

An acidic buffer contains a weak acid and its conjugate base; a basic buffer contains a weak base and its conjugate acid. The pair resists pH change when small amounts of strong acid or base are added.

The conjugate base consumes added H+; the weak acid equilibrium supplies H+ when added OH− removes it. In both cases the conjugate equilibrium shifts to oppose the change.

In an ethanoic acid/ethanoate buffer, CH₃COO⁻ consumes added H⁺ and CH₃COOH consumes added OH⁻, so the conjugate ratio changes only slightly. A buffer resists small additions but has finite capacity; once one component is nearly exhausted, the pH can change sharply.

Buffer pH depends on pKa and the conjugate-to-parent ratio. Dilution changes both concentrations by the same factor, so the ratio and pH remain approximately constant.

When a small amount of acid is added, A⁻ removes it to form HA; added base is removed by HA to form A⁻. Dilution leaves their ratio nearly unchanged but reduces buffer capacity, so resistance to a large addition is not unchanged.

Worked buffer example: an ethanoate buffer contains $0.100\,\mathrm{mol\,dm^{-3}}$ $\ce{CH3COOH}$ and $0.200\,\mathrm{mol\,dm^{-3}}$ $\ce{CH3COO^-}$, with $\mathrm{p}K_a=4.76$. Substitution gives $\mathrm{pH}=\mathrm{p}K_a+\log_{10}([\ce{A^-}]/[\ce{HA}])=4.76+\log_{10}(0.200/0.100)=5.06$. The pH is above $\mathrm{p}K_a$ because the conjugate base is more concentrated than the acid.