Required Practicals: Rates and Equilibria

The AQA A-Level Chemistry specification anchors three Required Practicals to the kinetics and equilibria sections of the syllabus, and this lesson treats all three as a coordinated deep dive: RP3 (effect of temperature on rate, via the thiosulfate–acid "disappearing cross"), RP6 (measuring rate by gas-volume or colour change), and RP7 (measuring Kc for esterification by titration). Each is unpacked end-to-end: apparatus with uncertainties, the underlying rationale, sample data with worked analysis, Arrhenius plotting for RP3, rate-from-gradient analysis for RP6, ICE-table Kc for RP7, uncertainty budgets, mapping to CPAC1–CPAC5, and error-mitigation tables. The lesson closes with a synoptic specimen question covering all three RPs and AO-tagged grade-band model answers at C, B, and A*.

Spec mapping (AQA 7405): RP3 sits under §3.1.5 (kinetics) — "the effect of temperature on the rate of a reaction"; RP6 sits under §3.1.9 (rate equations) — "measuring the rate of a reaction by an initial-rate method or by a continuous method (e.g. gas collection or colour change)"; RP7 sits under §3.1.6 (chemical equilibria) — "determination of an equilibrium constant Kc for a homogeneous system, including an esterification reaction". Cross-reference lesson 0 (collision theory and the Maxwell–Boltzmann distribution), lesson 1 (rate equations, orders, and the integrated half-life expression), lesson 2 (the Arrhenius equation and the ln k vs 1/T graphical method), and lesson 5 (Kc theory and the ICE-table technique). Refer to the official AQA specification document and the AQA Required Practical handbook for the exact wording of each section and for the current CPAC criteria.

Assessment objectives: AO1 — recall of apparatus, reagents, safety controls, and the standard procedure for each RP; recall of the rate ∝ 1/t relationship, of the Arrhenius equation in linear form, and of the Kc expression with units. AO2 — analysis of raw data: deriving rate from a tangent gradient on a V–t plot, computing ln(rate) and 1/T for an Arrhenius plot, extracting Ea from the gradient −Ea/R, and computing Kc from titration-derived equilibrium moles using an ICE table. AO3 — evaluation: identification and quantification of the dominant error in each protocol, proposal of improvements with quantitative justification, and commentary on whether the dataset supports the conclusion (e.g. whether the activation energy obtained falls in the literature range for the chosen reaction).

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RP3: The Effect of Temperature on the Rate of a Reaction

Reaction and Principle

The standard AQA-recommended protocol for RP3 uses the sodium thiosulfate–hydrochloric acid reaction:

Na₂S₂O₃(aq) + 2HCl(aq) → 2NaCl(aq) + SO₂(aq) + S(s) + H₂O(l)

Colloidal sulfur is produced as the reaction proceeds, progressively obscuring a black cross drawn on a piece of paper placed beneath the conical flask. The time t taken for the cross to become invisible is recorded; because the same critical concentration of sulfur is required to obscure the cross each time, the rate of reaction is inversely proportional to t:

rate ∝ 1/t

This is a single-point comparator: it does not give an absolute rate, but allows relative rates to be compared as temperature is varied at fixed concentrations.

Apparatus

Item	Specification	Typical uncertainty
100 cm³ conical flask	Borosilicate, marked	±2 cm³ (irrelevant — used only as a vessel)
25 cm³ measuring cylinder	Class B, for thiosulfate	±0.5 cm³
10 cm³ measuring cylinder	Class B, for HCl	±0.2 cm³
Stopclock	Digital, 0.01 s resolution	±0.5 s (reaction-time scale)
Thermometer	−10 to +110 °C, glass	±0.5 K
Water bath	Adjustable, 20–60 °C	±1 K (temperature stability)
Cross template	Black ink, 5 mm thickness, on white card	—

Reagent concentrations (recommended for clear results at 20–60 °C): 25.0 cm³ of 0.0500 mol dm⁻³ Na₂S₂O₃ mixed with 5.0 cm³ of 1.0 mol dm⁻³ HCl. Total volume 30 cm³; thiosulfate is the limiting reagent.

Procedure

1. Set the water bath to 20 °C. Equilibrate 25.0 cm³ of Na₂S₂O₃ and 5.0 cm³ of HCl in the bath for 5 minutes; record T.
2. Pour the thiosulfate into the conical flask over the cross template. Add the HCl swiftly and start the stopclock. Swirl once.
3. Looking down through the mouth, stop the clock when the cross disappears. Record t.
4. Discard to sulfur-waste; rinse the flask.
5. Repeat at 30, 40, 50, 60 °C, with three repeats per temperature for a mean t.
6. Compute rate = 1/t, ln(rate), and 1/T. Plot ln(rate) vs 1/T; gradient = −Ea/R.

Sample data and analysis

T / °C	T / K	mean t / s	rate = 1/t / s⁻¹	ln(rate)	1/T / 10⁻³ K⁻¹
20	293	145	0.00690	−4.977	3.413
30	303	78	0.01282	−4.358	3.300
40	313	42	0.02381	−3.737	3.195
50	323	23	0.04348	−3.135	3.096
60	333	13	0.07692	−2.565	3.003

Linear regression on ln(rate) vs 1/T yields a gradient of approximately −5870 K. Since the gradient equals −Ea/R:

Ea = −(−5870) × 8.314 = 48 800 J mol⁻¹ ≈ 49 kJ mol⁻¹

The accepted literature value for the activation energy of the thiosulfate–acid reaction lies in the range 47–60 kJ mol⁻¹ depending on conditions and the exact concentration regime; the experimental value of 49 kJ mol⁻¹ falls comfortably inside this band, confirming the validity of the dataset.

Uncertainty budget (RP3)

Percentage uncertainties on the dominant variables:

• Temperature (±0.5 K at 293 K): 0.17%; at 333 K: 0.15%.
• Reaction time (±0.5 s on a 13 s reading): 3.8%; on 145 s: 0.34%.
• Volume of thiosulfate (±0.5 cm³ on 25.0 cm³): 2.0%.
• Volume of acid (±0.2 cm³ on 5.0 cm³): 4.0%.

The dominant single-point uncertainty is the stopclock at the highest temperatures (3.8%), arising because the reaction is so fast at 60 °C that human reaction time becomes a significant fraction of t. The combined uncertainty in rate (added in quadrature with the volume uncertainties, which propagate through concentration) is approximately 6% at 60 °C and 4% at 20 °C. Propagated through the Arrhenius plot, this gives Ea = 49 ± 4 kJ mol⁻¹.

CPAC mapping (RP3)

• CPAC1 (follow procedures): equilibration of reagents in the water bath before mixing; swift, reproducible addition of acid; consistent viewing angle.
• CPAC2 (apparatus and techniques): correct use of the water bath, measuring cylinders, and thermometer; reading the meniscus at eye level.
• CPAC3 (safe and ethical): working at temperatures up to 60 °C (low-burn hazard); SO₂ is produced (work in a well-ventilated lab; avoid asthmatic students inhaling fumes); thiosulfate–acid waste collected and neutralised.
• CPAC4 (research and refer): comparing the experimental Ea to literature ranges; recognising the validity of the rate ∝ 1/t simplification.
• CPAC5 (record and report): raw t values for each repeat, mean and range, calculated rate, ln(rate), 1/T, and the Arrhenius plot with gradient and Ea calculation, all in SI units to appropriate significant figures.

Sources of error and improvements (RP3)

Error source	Effect	Improvement
Subjective judgement of "cross obscured"	Random scatter on t, especially between observers	Use a light sensor and datalogger to trigger automatically at a fixed transmittance threshold
Temperature drift during reaction	Systematic error — actual reaction T differs from bath T	Use a thermostatic water bath (±0.1 K stability); record T immediately before mixing and again at end-point
Variable cross thickness or paper translucency	Different obscuration thresholds between experiments	Standardise cross template (laser-printed on identical paper)
Human reaction time at high T	Random — fractional error grows as t falls	Use light-gate stopping at fixed transmittance; or use lower concentrations at high T to slow the reaction
Volatility of HCl at high T	Loss of acid; lower effective [HCl]	Use a stoppered flask, or pre-equilibrate with stopper on, removing only to add reagent

Practical-skills box (RP3)

Three errors recur in student write-ups: (i) failing to equilibrate the reagents in the bath separately (mixing cold thiosulfate with bath-warm acid gives an undefined initial T); (ii) plotting rate vs T as a straight line — the relationship is exponential, and only the ln(rate) vs 1/T form is linear; (iii) reporting Ea in J mol⁻¹ when the question asks for kJ mol⁻¹ (a 1000-fold error). Always check the units expected and convert.

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RP6: Measuring a Rate by Gas Volume or Colour Change

RP6 requires students to follow a reaction continuously (as opposed to the single-point rate ∝ 1/t method of RP3). Three standard protocols are recommended by AQA, and an A-Level write-up should be familiar with all three.

Protocol A: Magnesium with hydrochloric acid (gas collection)

Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)

Method: 0.060 g of magnesium ribbon (cleaned with emery paper to remove MgO) is dropped into 50.0 cm³ of 1.0 mol dm⁻³ HCl in a conical flask fitted with a delivery tube to a 100 cm³ gas syringe. V(H₂) is recorded every 10 s for 2 minutes.

Apparatus and uncertainties:

Item	Uncertainty
100 cm³ gas syringe	±1 cm³
50 cm³ measuring cylinder for HCl	±0.5 cm³
4-figure balance for Mg	±0.0005 g
Stopclock	±0.5 s
Thermometer	±0.5 K (for V correction)

Sample data and analysis:

t / s	V(H₂) / cm³
0	0
10	18
20	33
30	45
40	54
50	60
60	63
90	65
120	65

The initial rate is the gradient of the tangent at t = 0: approximately 2.0 cm³ s⁻¹. Convert to a rate of reaction in mol dm⁻³ s⁻¹ by dividing by molar volume (24 000 cm³ mol⁻¹ at RTP) and the solution volume (50.0 cm³ = 0.050 dm³):

rate = (2.0 / 24 000) / 0.050 = 1.67 × 10⁻³ mol dm⁻³ s⁻¹

The theoretical maximum volume from 0.060 g Mg (M = 24.3): n(Mg) = 2.47 × 10⁻³ mol; n(H₂) = 2.47 × 10⁻³ mol; V(H₂) = 2.47 × 10⁻³ × 24 000 = 59 cm³. The observed plateau of 65 cm³ exceeds this by ~10%, indicating the gas was collected at a temperature above 25 °C, or some MgO impurity displaced acid without producing H₂ — students should comment on this discrepancy.

Protocol B: Hydrogen peroxide decomposition (catalysed)

2H₂O₂(aq) → 2H₂O(l) + O₂(g), catalysed by MnO₂(s).

Method: 20.0 cm³ of 1.0 mol dm⁻³ H₂O₂(aq) is placed in a flask; 0.10 g of MnO₂ is added; the flask is immediately stoppered with a delivery tube to a gas syringe. Record V(O₂) every 10 s. Because MnO₂ is a heterogeneous catalyst, surface area matters — use a fixed-mass, fixed-mesh sample each time. By varying [H₂O₂] at fixed catalyst mass and analysing initial rates, the order in [H₂O₂] is determined (= 1).

Protocol C: Iodine-clock and colorimetric monitoring

CH₃COCH₃ + I₂ → CH₃COCH₂I + HI (acid-catalysed iodination of propanone)

I₂ is brown in solution; the absorbance at 525 nm (a peak in the I₂ spectrum) is proportional to [I₂] via the Beer–Lambert law (A = εcl). A colorimeter calibrated with standard I₂ solutions converts absorbance to concentration; the rate is then the gradient of the [I₂] vs t plot.

A colorimeter is preferred to visual estimation because absorbance at fixed wavelength is linear in concentration, while visual judgement is subjective. With a datalogger, [I₂] is sampled every second, giving a smooth curve and the gradient at any chosen [I₂].

The rate law is famous in physical chemistry: rate = k[CH₃COCH₃][H⁺], with order zero in [I₂]. The zero-order dependence is revealed by the linear [I₂] vs t plot — rate is constant as iodine is consumed.

Uncertainty budget (RP6)

• Gas-syringe reading (±1 cm³ on 50 cm³): 2.0%.
• Time (±0.5 s on 30 s): 1.7%.
• Mass of Mg (±0.0005 g on 0.060 g): 0.83%.
• Volume of acid (±0.5 cm³ on 50.0 cm³): 1.0%.

The combined uncertainty on a typical initial-rate determination is approximately 3%. For protocol C, the colorimeter contributes ±0.5% in absorbance and the Beer–Lambert calibration adds ~1%, giving an overall ~2% uncertainty.

CPAC mapping (RP6)

• CPAC1: consistent gas-collection technique; tight stoppering; sampling at regular intervals.
• CPAC2: use of gas syringe (held horizontally, lubricated, leak-tested); use of colorimeter (zeroed against water, calibrated with I₂ standards).
• CPAC3: H₂ ignition risk (no naked flames); H₂O₂ irritant (eye protection); I₂ vapour (work in fume hood for protocol C).
• CPAC4: comparing observed gradient to theoretical from stoichiometry; recognising the catalyst's role.
• CPAC5: continuous time–volume (or time–absorbance) table; gradient calculated explicitly with units; comparison to predicted final volume from stoichiometry.

Sources of error and improvements (RP6)

Error source	Effect	Improvement
Gas escape from delivery tube	Volume reading systematically low	Pressure-test the assembly with a closed-bulb syringe before each run; use Vaseline on joints
Gas dissolution in solution (H₂ slightly, O₂ more)	Volume low at early time	Use a saturated salt solution gas-collection trough instead (for gases insoluble in NaCl(aq))
Reaction initiated before stoppering	First few seconds unreliable	Pre-mix solution and catalyst quickly; record first reading at t = 5 s, not t = 0
Temperature variation between runs	Comparing rates at different T	Use a water bath at fixed T (e.g. 25.0 °C)
Colorimeter drift (protocol C)	Absorbance baseline shifts	Re-zero between every reading; use a sealed reference cell

Practical-skills box (RP6)

Common errors: (i) failing to clean the magnesium ribbon — the oxide layer slows initial reaction, giving an artificially low rate at t = 0; (ii) confusing "rate" (cm³ s⁻¹) with "rate of reaction" (mol dm⁻³ s⁻¹) — the conversion through molar volume and solution volume is the AO2 marking point; (iii) drawing the tangent at the wrong place — the initial rate is the gradient at t = 0, not at t = 30 s.

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RP7: Determination of Kc for an Esterification Equilibrium

Reaction and Principle

The esterification equilibrium between ethanoic acid and ethanol, catalysed by a strong mineral acid (typically HCl):

CH₃COOH(l) + C₂H₅OH(l) ⇌ CH₃COOC₂H₅(l) + H₂O(l)

This is a homogeneous-liquid equilibrium for which Kc is dimensionless because moles of products equal moles of reactants on each side, and the volumes of liquid components cancel in the expression. Equilibrium is established slowly at room temperature; the protocol requires the mixture to be sealed for approximately one week before titration.

Apparatus

Item	Specification	Uncertainty
25 cm³ pipette, class B	Bulb pipette	±0.06 cm³
25 cm³ burette, class B	Graduations 0.10 cm³	±0.05 cm³ per reading; ±0.10 cm³ per titre
100 cm³ conical flask	For titration	—
Sample bottles, sealed	30 cm³, screw-cap	—
Phenolphthalein indicator	1% in ethanol	—

Procedure

1. Prepare five mixtures by weighing (±0.01 g) varying mole ratios of CH₃COOH and C₂H₅OH into sealed bottles, with 5.0 cm³ of 1.0 mol dm⁻³ HCl as catalyst. Record masses.
2. Prepare a blank containing only the HCl catalyst, to titrate separately for moles of HCl.
3. Seal all bottles; leave 7 days at ~20 °C to reach equilibrium.
4. Quantitatively transfer each bottle's contents to a flask (rinse with deionised water) and titrate against 1.0 mol dm⁻³ NaOH using phenolphthalein.
5. Total acid titrated = moles of CH₃COOH at equilibrium + moles of HCl. Subtract the blank to find equilibrium moles of CH₃COOH.
6. Use an ICE table to compute Kc.

Sample data and analysis

For one mixture:

• Initial: 0.100 mol CH₃COOH (6.01 g), 0.100 mol C₂H₅OH (4.61 g), 0.005 mol HCl catalyst.
• After 7 days, full-bottle titre against 1.0 mol dm⁻³ NaOH: 38.2 cm³ → total acid 0.0382 mol.
• Blank titre: 5.0 cm³ → 0.005 mol HCl.
• Equilibrium CH₃COOH = 0.0382 − 0.005 = 0.0332 mol.

ICE table (in mol; volume cancels for this Kc because Δn = 0):

Species	Initial / mol	Change / mol	Equilibrium / mol
CH₃COOH	0.100	−0.0668	0.0332
C₂H₅OH	0.100	−0.0668	0.0332
CH₃COOC₂H₅	0	+0.0668	0.0668
H₂O	0	+0.0668	0.0668

Kc = [ester][water] / [acid][alcohol] = (0.0668 × 0.0668) / (0.0332 × 0.0332) = 4.05

(Concentrations cancel because Δn = 0; mole quantities can be used directly in the ratio.)

The accepted literature value for the ethanoic-acid/ethanol esterification Kc at 20 °C lies in the range 3.5–4.5, so this dataset is consistent with the expected value.

Why the catalyst correction matters

A frequent student error is to quote all titrated acid as remaining CH₃COOH. This double-counts the HCl catalyst (a strong acid, titrated alongside ethanoic acid by phenolphthalein). Failing to subtract the blank gives a smaller apparent "change" and a Kc systematically too low.

Uncertainty budget (RP7)

• Pipette / burette (volumes): ±0.5% each.
• Mass of acid (±0.01 g on 6.01 g): 0.17%.
• Mass of alcohol (±0.01 g on 4.61 g): 0.22%.
• Titre (±0.10 cm³ on 38.2 cm³): 0.26%.
• Blank titre (±0.10 cm³ on 5.0 cm³): 2.0%.

The dominant uncertainty is the blank titration (2%), which propagates directly into the equilibrium moles of ethanoic acid. The combined uncertainty in Kc (with errors propagated through ratios of small differences) is approximately ±0.3 absolute, or about 7% relative.

CPAC mapping (RP7)

• CPAC1: weigh-by-difference for liquids; sealed-bottle preservation of equilibrium; full quantitative transfer for titration.
• CPAC2: correct pipette technique (rinsing with reagent, draining for 5 s, last drop touch-off); burette reading from below the meniscus; consistent end-point colour (faintest persistent pink).
• CPAC3: ethanoic acid corrosive; concentrated HCl corrosive; ethyl ethanoate flammable — no naked flames; sealed bottles to avoid solvent evaporation and inhalation.
• CPAC4: comparison of Kc to literature; awareness that Kc depends only on T (not on concentrations or volume); recognition that the protocol is "static" — the equilibrium has had time to fully establish.
• CPAC5: raw masses, raw titres for each mixture, blank titre, full ICE table with units, Kc calculation with units (dimensionless here), and quantitative uncertainty propagation.

Sources of error and improvements (RP7)