Required Practical 9: Titration and pH Curves

Required Practical 9 is the AQA A-Level capstone titration. Unlike the volumetric titration of Required Practical 1 (atomic-structure lesson 8), where the goal is simply to find an unknown concentration using an indicator end-point, RP9 demands a full pH-versus-volume curve traced point-by-point with a calibrated pH meter. The shape of that curve is the experimental signature of acid-base strength: a sharp vertical jump for strong-strong combinations; a buffered shoulder followed by a smaller jump for weak-strong; an asymmetric jump landing on an acidic equivalence pH for strong-weak. This lesson sets out the apparatus, the general protocol, the three specific protocols required by AQA, and the data-analysis manoeuvre that lifts RP9 above the mark-recipe titration of RP1 — reading the pKa of a weak acid directly off the curve at the half-equivalence point. Indicator selection, the CPAC1-5 evidence map, and a fully resolved uncertainty budget all follow. Closing material includes a full specimen exam question across five parts, AO-tagged mark scheme, and grade-band model answers for C, B, and A*.

Spec mapping (AQA 7405): This lesson is the anchor for Required Practical 9 (§3.1.12 — investigation of pH curves and titration of weak acids and weak bases). It draws directly on lessons 1-5 of this acids-and-buffers course (Brønsted-Lowry theory, pH and Kw, Ka and pKa, buffer action, and the equivalence/half-equivalence concept) and cross-references atomic-structure lesson 8 (titration calculations and Required Practical 1). The RP9 specification expects students to (i) use a pH meter or appropriate indicator, (ii) plot pH against volume of titrant, (iii) identify the equivalence point from the curve, (iv) determine Ka from half-equivalence pH, and (v) evaluate sources of error. Refer to the official AQA specification document for the exact wording of §3.1.12.

Assessment objectives: AO1 covers recall of apparatus, calibration steps, and the standard procedure (pipette analyte, add titrant in known increments, record pH). AO2 covers the analytical operations — reading equivalence volume from the curve, computing analyte concentration via stoichiometry, locating the half-equivalence point and reading pKa. AO3 — the genuinely A-Level-discriminating tier — covers evaluation: assessing whether a given indicator is fit-for-purpose by overlaying its pH range on the curve, reasoning about the dominant error sources, and propagating quantitative uncertainties through the final Ka or concentration value.

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Apparatus

The RP9 kit list is more elaborate than the simple burette-and-flask of RP1, reflecting the move from end-point detection to full curve tracing:

• pH meter with combination glass electrode, calibrated immediately before use against two or three standard buffer solutions that bracket the pH range to be measured. For a strong-strong titration, pH 4.00 and pH 10.00 buffers are conventional; for weak-acid work where the half-equivalence pH may sit between 4 and 5, a pH 4.00, pH 7.00, and pH 10.00 three-point calibration is preferred. Modern pH meters report calibration slope (mV/pH) — accept readings only if slope is within 95-102% of theoretical Nernstian (59.16 mV/pH at 298 K).
• Magnetic stirrer with stirrer bar — continuous gentle stirring is essential. The pH probe responds to the local proton activity at its membrane; without stirring, the bulk solution near the burette tip becomes locally acidic or basic, the probe lags the true bulk pH by tens of seconds, and the curve develops false plateaus.
• Burette, 50 cm³, class B, with ±0.05 cm³ resolution per reading (so ±0.10 cm³ on a typical titre, since two readings are subtracted). A class A burette tightens this to ±0.05 cm³ per titre but is rarely available in school labs.
• Pipette, 25.0 cm³, class B, ±0.06 cm³, with pipette filler. Used to deliver the analyte aliquot.
• Beaker, 250 cm³ tall-form — preferred over a conical flask because the pH probe must be fully immersed without the stirrer bar fouling it. A conical flask works only if the probe is short.
• Retort stand, boss, and clamp to hold the pH probe vertically with the membrane submerged but not in contact with the stirrer bar.
• Balance, 2-d.p. (±0.005 g) for routine work, 4-d.p. (±0.00005 g) for preparing the primary standard if one is required.
• Volumetric flasks (250 cm³ ±0.15 cm³ or 100 cm³ ±0.08 cm³) for preparing standard solutions of the titrant or analyte.
• Wash bottle of deionised water, plastic dropping pipette for the drop-by-drop endgame near equivalence, and lint-free tissue for drying the pH probe between rinses.

The pH meter and burette are the dominant instruments. Everything else is support.

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General Method

The procedure is the same across all three protocols; only the identity of the analyte and titrant changes:

1. Calibrate the pH meter against two (or three) standard buffer solutions. Rinse the probe with deionised water between buffers and dab dry with tissue — do not wipe, which can strip the hydrated gel layer from the glass membrane.
2. Pipette 25.0 cm³ of the analyte solution (the acid or base whose pH curve is to be mapped) into the tall-form beaker. Add ~25 cm³ of deionised water if necessary to ensure the probe membrane is fully submerged with the stirrer bar still clear.
3. Place the beaker on the magnetic stirrer, drop in the stirrer bar, and start gentle stirring (fast enough for good mixing, slow enough to avoid a vortex that traps air around the probe).
4. Clamp the pH probe vertically with the membrane fully submerged and well clear of the stirrer bar.
5. Fill the burette with the titrant, record the initial reading to two decimal places, and position the tip just above the beaker.
6. Record the initial pH (zero added volume).
7. Add titrant in 5.0 cm³ increments, recording the volume from the burette and the steady pH after each addition. "Steady" means the displayed pH has not drifted by more than 0.01 unit in 10-15 seconds.
8. As the equivalence point approaches (signalled by the pH change per 5 cm³ aliquot growing rapidly — for a strong-strong titration, when ΔpH per 5 cm³ exceeds 0.5 units), reduce the increment to 1.0 cm³, then to 0.1 cm³ in the steep region.
9. Continue past equivalence for at least another 10-15 cm³ to capture the post-equivalence plateau (which determines the final pH and feeds into the indicator-selection analysis).
10. Repeat the titration in full — a single RP9 curve is descriptive; concordant repeats are required to claim a quantitative equivalence volume. Two curves agreeing on V_eq to within 0.20 cm³ count as concordant.
11. Plot pH (y-axis) against V_titrant (x-axis) on graph paper or in a spreadsheet, joining points with a smooth curve (not straight-line segments).

The drop-by-drop endgame near equivalence is what separates RP9 from RP1. In RP1 the end-point colour change happens in a single drop; in RP9 the pH is changing by several units per cm³ across the steep region, and the curve cannot be located unless that region is sampled finely.

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Three Protocols

AQA expects familiarity with three combinations: strong-strong, weak-strong, and strong-weak. (Weak-weak is not required at A-Level — its equivalence point is too poorly defined for an undergraduate titration; see Going Further.)

Protocol A: Strong acid + strong base (HCl + NaOH)

Analyte: 25.0 cm³ of 0.100 mol dm⁻³ HCl in the beaker. Titrant: 0.100 mol dm⁻³ NaOH in the burette.

Curve features:

• Initial pH ≈ 1.0 (negligible volume of strong acid, [H⁺] = 0.100, pH = 1.00).
• Gentle rise from pH 1 to pH 3 over the first 24 cm³ (acid being progressively neutralised; pH governed by [H⁺] = c_acid(1 − V/V_eq)).
• Sharp vertical jump from pH ~3 to pH ~11 over a volume change of only ~0.2 cm³ centred on V_eq = 25.0 cm³.
• Equivalence pH = 7.00 (salt NaCl is neutral; only water self-ionisation determines pH).
• Post-equivalence pH rises to ~12.5 as excess NaOH dominates.

The strong-strong jump is the sharpest of the three and accommodates virtually any indicator whose range lies between pH 3 and 11 — methyl orange (3.1-4.4), bromothymol blue (6.0-7.6), and phenolphthalein (8.3-10.0) all work.

Protocol B: Weak acid + strong base (CH₃COOH + NaOH)

Analyte: 25.0 cm³ of 0.100 mol dm⁻³ ethanoic acid (CH₃COOH; pKa = 4.76). Titrant: 0.100 mol dm⁻³ NaOH.

Curve features:

• Initial pH ≈ 2.87 (weak acid; pH = ½(pKa − log c) = ½(4.76 + 1.00) = 2.88).
• Buffer plateau between V = 5 and V = 20 cm³, where pH rises slowly from ~4.1 to ~5.4. This plateau is the diagnostic signature of a weak-acid titration. Within it, the Henderson-Hasselbalch equation applies: pH = pKa + log([A⁻]/[HA]), with [A⁻]/[HA] running from ~0.2 (V = 5 cm³) to ~4.0 (V = 20 cm³).
• Half-equivalence point at V = 12.5 cm³, where exactly half the CH₃COOH has been neutralised: [CH₃COOH] = [CH₃COO⁻], and pH = pKa = 4.76. This is the experimental hook for determining Ka.
• Steep jump from pH ~6 to pH ~10.5 centred on V_eq = 25.0 cm³.
• Equivalence pH ≈ 8.7 — basic because the salt (sodium ethanoate) hydrolyses: CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻.
• Post-equivalence pH rises to ~12.5.

The vertical rise is smaller than in Protocol A (~4 pH units rather than ~8), and indicator selection is now critical: methyl orange (3.1-4.4) changes colour during the buffer plateau and is useless; phenolphthalein (8.3-10.0) sits squarely within the steep region and is the correct choice.

Protocol C: Strong acid + weak base (HCl + NH₃)

Analyte: 25.0 cm³ of 0.100 mol dm⁻³ NH₃ (aq) (pKb = 4.75; pKa of NH₄⁺ = 9.25). Titrant: 0.100 mol dm⁻³ HCl.

Note the inversion: here the analyte in the beaker is the weak base and the strong acid is the titrant. The pH starts high and falls.

Curve features:

• Initial pH ≈ 11.13 (weak base; pOH = ½(pKb − log c) = ½(4.75 + 1.00) = 2.87; pH = 14.00 − 2.87 = 11.13).
• Buffer plateau between V = 5 and V = 20 cm³, pH falling slowly from ~10.0 to ~8.6.
• Half-equivalence point at V = 12.5 cm³, where [NH₃] = [NH₄⁺] and pH = pKa(NH₄⁺) = 9.25, equivalently 14 − pKb(NH₃) = 14 − 4.75 = 9.25.
• Steep drop from pH ~8 to pH ~3.5 centred on V_eq = 25.0 cm³.
• Equivalence pH ≈ 5.3 — acidic because the salt (NH₄Cl) hydrolyses: NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺.
• Post-equivalence pH falls to ~1.5.

The steep region sits in acidic territory: methyl orange (3.1-4.4) or methyl red (4.4-6.2) is the correct indicator; phenolphthalein, which changes between 8.3 and 10.0, would flag a false end-point during the buffer plateau.

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Data Analysis

Three operations turn the raw pH/V table into A-Level marks:

Equivalence volume. The equivalence point is mathematically the inflection of the curve — the steepest point of the vertical rise. Practically, it is read as the midpoint of the vertical segment, i.e. the volume halfway between the last pre-jump point and the first post-jump point. For a curve where points have been taken every 0.1 cm³ in the steep region, V_eq is read to ±0.05 cm³. A first-derivative plot (ΔpH/ΔV vs V) makes the peak more obvious and is the standard treatment in undergraduate work.

Analyte concentration. Once V_eq is known, stoichiometry gives the analyte concentration. For a 1:1 acid-base reaction (HCl + NaOH, CH₃COOH + NaOH, HCl + NH₃):

c_analyte × V_analyte = c_titrant × V_eq

For 25.0 cm³ of analyte titrated by 25.0 cm³ of 0.100 mol dm⁻³ titrant: c_analyte = 0.100 × 25.0 / 25.0 = 0.100 mol dm⁻³. (This is the trivial case; in a real RP9 the analyte concentration is unknown and the titrant is the standard.)

pKa from half-equivalence pH. This is the genuinely RP9-flavoured manoeuvre. At V = ½V_eq, exactly half of the weak acid has been converted to its conjugate base. The Henderson-Hasselbalch equation reduces to pH = pKa + log(1) = pKa. Read pH directly off the curve at V = ½V_eq and you have read pKa.

Worked Example: Determining Ka of CH₃COOH from the curve

A student titrates 25.0 cm³ of CH₃COOH(aq) of unknown concentration against 0.100 mol dm⁻³ NaOH. The curve shows a sharp jump at V_eq = 24.80 cm³ and a half-equivalence pH of 4.78 at V = 12.40 cm³.

1. Concentration of CH₃COOH: c = (0.100 × 24.80) / 25.0 = 0.0992 mol dm⁻³ (3 s.f.).
2. Half-equivalence volume: V_½ = 24.80 / 2 = 12.40 cm³. ✓ (matches observation).
3. At V_½, pH = pKa, so pKa = 4.78, hence Ka = 10⁻⁴·⁷⁸ = 1.66 × 10⁻⁵ mol dm⁻³.

The literature value of Ka for ethanoic acid at 298 K is 1.74 × 10⁻⁵ mol dm⁻³ (pKa = 4.76). Agreement to within 5% is excellent for a school-laboratory measurement and validates the method.

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Indicator Selection from the Curve

An indicator is fit for purpose if its colour-change pH range sits entirely within the vertical (steep) region of the curve. If the range straddles the start or end of the jump, the colour change spans a measurable volume of titrant and the end-point becomes a smear rather than a sharp signal.

Indicator	pH range (low → high colour)	Strong-strong	Weak-strong	Strong-weak
Methyl orange	3.1-4.4 (red → yellow)	✓ usable	✗ inside buffer plateau	✓ ideal
Methyl red	4.4-6.2 (red → yellow)	✓ usable	✗ partially buffered	✓ usable
Bromothymol blue	6.0-7.6 (yellow → blue)	✓ ideal (centred on pH 7)	✗ on low edge of jump	✗ on high edge of jump
Phenolphthalein	8.3-10.0 (colourless → pink)	✓ usable	✓ ideal	✗ inside buffer plateau

The verification recipe in an exam question: read the pH at the start and end of the steep region from the supplied curve; an indicator works if both ends of its pH range fall between those two values.

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Determining Ka from Half-Equivalence — derivation

For completeness, the algebra behind the half-equivalence trick. Consider the dissociation of weak acid HA:

HA(aq) ⇌ H⁺(aq) + A⁻(aq); Ka = [H⁺][A⁻] / [HA]

Taking logs and rearranging:

pH = pKa + log([A⁻]/[HA]) (Henderson-Hasselbalch)

Now consider the titration with NaOH. After V cm³ of titrant of concentration c have been added to V₀ cm³ of HA at initial concentration c₀:

• Moles of A⁻ formed = c × V/1000.
• Moles of HA remaining = c₀V₀/1000 − cV/1000.

At V = ½V_eq, by definition of equivalence (cV_eq = c₀V₀), we have cV = ½c₀V₀, so:

• Moles A⁻ = ½c₀V₀/1000.
• Moles HA = c₀V₀/1000 − ½c₀V₀/1000 = ½c₀V₀/1000.

Therefore [A⁻] = [HA] (the volume is the same for both — they share the solution), log([A⁻]/[HA]) = log(1) = 0, and pH = pKa exactly. No approximation, no neglect of water self-ionisation (provided the buffer is concentrated enough that c_buffer ≫ Kw/[H⁺]) — the result is essentially exact for any A-Level concentration regime.

This is why half-equivalence is preferred over initial pH for determining Ka: initial pH requires the approximation [H⁺] ≈ √(Kac₀), valid only when α ≪ 1; the half-equivalence reading depends only on equimolarity, which holds for any concentration.

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Uncertainty Budget

A genuine A-Level RP9 write-up tabulates the dominant uncertainties and propagates them to the final Ka:

Source	Magnitude	Relative uncertainty
pH meter resolution (0.01 pH unit at pH 4.78)	±0.01 pH	~0.2% on pH, but ~2.3% on [H⁺] (since [H⁺] = 10⁻ᵖᴴ; Δ[H⁺]/[H⁺] = ln(10)·ΔpH ≈ 2.3% per 0.01 pH unit)
pH meter calibration drift between buffers	±0.02 pH	~4.6% on Ka
Burette reading (±0.05 cm³ × 2 readings) on 25 cm³ titre	±0.10 cm³	0.4% on V_eq
Pipette tolerance (±0.06 cm³ on 25.0 cm³)	±0.06 cm³	0.24% on analyte volume
Temperature variation around 298 K (±0.5 K)	±0.5 K	Affects Kw (~2%) and Ka (~1-2%); enough to shift pH at equivalence by ~0.02 pH units
Stirrer-induced air entrainment	< 0.01 pH if stirring is gentle	usually negligible

Propagation to Ka. Ka is calculated as Ka = 10⁻ᵖᴴ at half-equivalence. The dominant uncertainty is the pH reading itself; calibration drift adds a systematic ~5% on top. Total uncertainty on Ka is typically ±5-7% for a careful school determination — well within the ±10% tolerance that puts a student's number alongside the literature value.

Propagation to analyte concentration. c_analyte = c_titrant × V_eq / V_analyte. Relative uncertainty = √[(Δc_titrant/c_titrant)² + (ΔV_eq/V_eq)² + (ΔV_analyte/V_analyte)²]. With burette ±0.4% and pipette ±0.24%, and a standardised titrant of ±0.5%, total relative uncertainty ≈ √(0.25 + 0.16 + 0.06) ≈ ±0.7%. Concentration is the easy number in RP9 — Ka is the hard one.

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CPAC Mapping for RP9

CPAC (Common Practical Assessment Criteria) 1-5 are each independently evidenced by RP9 work:

• CPAC 1 (Follow procedures). Student executes the calibration protocol, pipettes 25.0 cm³ of analyte without overdraw, fills the burette to the meniscus without trapped air bubbles, and adds titrant in the increments specified by the method.
• CPAC 2 (Apply investigative approaches). Student decides when to switch from 5 cm³ to 1 cm³ to 0.1 cm³ increments based on the rate of pH change, demonstrating responsive control of the procedure.
• CPAC 3 (Safely use a range of practical equipment). pH probe handled without striking the glass membrane against beaker walls; burette filled below shoulder height with funnel; pipette filler used (mouth pipetting banned).
• CPAC 4 (Use appropriate software / instruments). pH meter calibrated against two or three buffers, slope checked, calibration date recorded. Spreadsheet or graph paper used to plot pH/V.
• CPAC 5 (Use written sources of information). Student references the AQA practical brief, the manufacturer's pH-probe care manual, and the COSHH risk assessment for the acids and bases used.

A teacher signing off RP9 records a tick or a written comment against each CPAC criterion. The CPAC record is what determines the practical-endorsement pass on the certificate.

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Sources of Error and Improvements