Required Practical 2: Enthalpy Determination

This lesson is the deep-dive anchor for AQA Required Practical 2 (RP2): the determination of enthalpy changes by calorimetry. RP2 is the assessed practical strand of the energetics topic and the evidence base for the CPAC (Common Practical Assessment Criteria) report that contributes to the practical endorsement on your A-Level certificate. You will meet RP2 in three standard protocols: (a) enthalpy of combustion using a spirit-burner; (b) enthalpy of neutralisation using a polystyrene-cup calorimeter; and (c) enthalpy of reaction for a displacement or dissolution reaction in the same cup. For each, the lesson covers the apparatus (with precision tolerances), the method, the cooling-curve extrapolation technique used to recover the true peak temperature, the q = mcΔT and ΔH = −q/n calculations, the uncertainty budget assembled from each instrument, and a comprehensive sources-of-error/improvements analysis. The CPAC criteria are mapped to RP2 evidence so that you know exactly what your lab book must demonstrate.

Spec mapping (AQA 7405): This lesson anchors Required Practical 2 in the AQA practical strand of §3.1.4 (Energetics). It builds directly on lesson 0 of this course (the q = mcΔT calorimetry framework), depends on §3.1.2.5 stoichiometry for the per-mole conversion ΔH = −q/n, sits alongside lesson 1 (bond-enthalpy estimates as a theoretical comparator), and connects to lesson 2 (Hess's law as the alternative indirect-route method). Refer to the official AQA specification document and the AQA Practical Handbook for A-Level Chemistry for the exact wording of the RP2 brief and the CPAC criteria.

Assessment objectives: AO1 marks reward recall of the apparatus list with correct precision tolerances, the standard method steps for each RP2 protocol, and the CPAC criteria. AO2 marks reward q = mcΔT calculations applied to calorimetry data, the cooling-curve extrapolation procedure to recover the true ΔT, and the conversion to ΔH per mole in kJ mol⁻¹. AO3 marks reward critical evaluation of sources of error, proposal of improvements with justification, and quantitative assessment of the overall percentage uncertainty budget. Practical-skills questions appear on every Paper 1 and Paper 2, typically worth 8–15 marks across two parts of a long-response question.

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Why a Required Practical?

The Required Practicals are a fixed list of twelve experiments specified by AQA. Each is the basis for CPAC assessment of the five practical-skill competencies (planning, implementation, research, analysis, evaluation), and each can be examined in the written papers under "practical skills" questions. You will not be assessed on RP2 in a lab exam — the assessment is of your written work about the practical. Your lab book or practical portfolio must therefore record:

• the method you followed (with any modifications and a justification);
• the raw data you collected (with units and precision matched to your instruments);
• the processed results (with worked calculations and uncertainty estimates);
• an evaluation that identifies the main sources of error and proposes specific, justified improvements.

The same skill set is then tested in written-paper questions that may ask you to interpret a cooling-curve graph, calculate ΔH from supplied calorimetry data, identify the limiting error, or suggest an improvement to a stated method.

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The Three Standard RP2 Protocols

AQA does not prescribe a single procedure for RP2; centres choose from a set of standard calorimetry experiments. The three most common are described below. The underlying physics — q = mcΔT for the energy transferred to the water/solution, then ΔH = −q/n for the molar enthalpy — is the same across all three.

Protocol A — Enthalpy of Combustion (Spirit-Burner Method)

Reaction studied. The complete combustion of a liquid fuel, typically a small alcohol (methanol, ethanol, propan-1-ol, butan-1-ol):

C₂H₅OH(l) + 3 O₂(g) → 2 CO₂(g) + 3 H₂O(l) ΔᶜH°(ethanol) = −1367 kJ mol⁻¹ (literature)

Apparatus.

Item	Purpose	Precision
Spirit burner (with wick), filled with the fuel	Combustion source; weighed before and after	—
2-decimal-place balance	Weighing the spirit burner	±0.005 g
Copper calorimeter (can)	Holds the water; high thermal conductivity, low heat capacity	—
Measuring cylinder (100 cm³) or volumetric flask	Measuring the water volume	±0.5 cm³ on 100 cm³
Thermometer (−10 to 110 °C, 0.1 K resolution) or digital probe	Reads water temperature	±0.1 K
Draught shield (three sides of card/foil)	Reduces heat loss to surroundings	—
Clamp stand, ring, gauze	Holds calorimeter above flame	—

Method (outline).

1. Weigh the filled spirit burner (with lid) to ±0.005 g. Record m₁.
2. Measure 100 cm³ of cold tap water into the copper can. Record the initial water temperature T₁ after 2–3 minutes of equilibration with stirring.
3. Light the burner and place under the can immediately. Stir the water gently and continuously with the thermometer.
4. Allow the temperature to rise by a fixed amount (typically ΔT = 20 K) — or burn for a fixed time, whichever the procedure specifies. Extinguish the flame using the lid (snuffing it out).
5. Continue stirring; record the highest temperature T₂ reached after extinction (the water continues to heat for a few seconds after the flame goes out).
6. Re-weigh the burner with lid to ±0.005 g. Record m₂.
7. Compute the mass of fuel burnt: Δm = m₁ − m₂.

Calculation. Energy transferred to the water:

q = m_water × c_water × ΔT

with m_water in g (100 cm³ water ≈ 100 g), c_water = 4.18 J g⁻¹ K⁻¹, and ΔT in K.

Moles of fuel burnt: n_fuel = Δm / M (where M is the molar mass of the fuel).

Enthalpy of combustion (per mole, in kJ mol⁻¹):

ΔᶜH = −q / (1000 × n_fuel)

The negative sign reflects that combustion is exothermic — the system (the fuel) loses the energy that the water gains.

Typical experimental result for ethanol. Students typically obtain ΔᶜH ≈ −800 to −900 kJ mol⁻¹, compared with the literature standard enthalpy of combustion of −1367 kJ mol⁻¹. The discrepancy is large — roughly 35–40% — and is dominated by:

• Incomplete combustion of the fuel — the yellow part of the flame and any soot deposited on the can are evidence that some fuel oxidises only as far as carbon or CO rather than CO₂; the partial-oxidation products carry away unrecovered energy.
• Heat loss to the surroundings — to the air above the flame, to the air around the can, by convection currents, by radiation from the hot can surface, and through the gauze.
• Evaporation of water — water vapour escapes from the open top of the can carrying away latent heat of vaporisation.
• Heat absorbed by the calorimeter itself — the copper can warms up and is not counted in the q = mcΔT calculation as written (this can be corrected by adding a calorimeter heat-capacity term C_cal × ΔT, but is usually ignored at A-Level).
• Mass of fuel that evaporates rather than burns — uncontrolled if the burner is open during the experiment.

Protocol A has poor accuracy but is pedagogically valuable: it makes the heat-loss problem visible. The bond-enthalpy estimate (from lesson 1) gives ΔᶜH ≈ −1280 kJ mol⁻¹ for ethanol, and the Hess-cycle calculation using ΔfH° values gives the exact −1367 kJ mol⁻¹ — so students see all three approaches side by side and rank their reliability.

Protocol B — Enthalpy of Neutralisation (Polystyrene-Cup Calorimeter)

Reaction studied. A strong acid and a strong alkali, in equimolar amounts:

HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l) ΔneutH° = −57.6 kJ mol⁻¹ (literature)

The reaction is effectively H⁺(aq) + OH⁻(aq) → H₂O(l) — the same per-mole-of-water enthalpy for any pairing of fully-dissociated strong acid with fully-dissociated strong alkali.

Apparatus.

Item	Purpose	Precision
Polystyrene cup (~100 cm³), with a fitting cardboard or polystyrene lid	Adiabatic-approximation calorimeter	—
250 cm³ glass beaker	Sleeve to hold the cup upright	—
25.00 cm³ volumetric pipette (×2) — or two measuring cylinders	Measuring acid and alkali volumes	±0.06 cm³ on 25.00 cm³ (pipette)
Thermometer (0.1 K resolution) or digital probe	Reads solution temperature	±0.1 K
Stopwatch	Times the temperature readings for the cooling-curve plot	±0.5 s
Stirring rod or magnetic stirrer	Mixes the contents thoroughly	—

Method (outline).

1. Pipette 25.0 cm³ of 1.00 mol dm⁻³ HCl(aq) into the polystyrene cup. Replace the lid (with the thermometer through the hole).
2. Record the temperature every 30 s for 2–3 minutes to establish a stable baseline.
3. At a recorded time (call it t = mixing), quickly add 25.0 cm³ of 1.00 mol dm⁻³ NaOH(aq) (which has been allowed to equilibrate to the same room temperature). Replace the lid; stir thoroughly.
4. Continue to record the temperature every 30 s for a further 5–10 minutes — long enough to see the rise to the maximum and the subsequent linear cooling decay.
5. Plot temperature vs time. Apply the cooling-curve extrapolation procedure (described below) to recover the corrected ΔT at the moment of mixing.

Calculation. Energy released, transferred to the combined solution:

q = (m_HCl + m_NaOH) × c × ΔT_corrected

with m_HCl + m_NaOH = 50.0 g (assuming density of dilute aqueous solution = 1.00 g cm⁻³), c = 4.18 J g⁻¹ K⁻¹.

Moles of water formed = moles of limiting reagent = 0.0250 × 1.00 = 0.0250 mol.

ΔneutH = −q / (1000 × 0.0250) kJ mol⁻¹

Typical experimental result. Students typically obtain ΔneutH ≈ −55 to −58 kJ mol⁻¹, in good agreement with the literature −57.6 kJ mol⁻¹. Protocol B is the gold-standard RP2 experiment because the polystyrene cup is a very good adiabatic approximation (low thermal conductivity, low heat capacity), the solutions are aqueous and well-stirred, and the reaction is fast (instantaneous on the timescale of mixing).

Protocol C — Enthalpy of Reaction (Displacement or Dissolution)

Example reaction. Magnesium displacing hydrogen from hydrochloric acid:

Mg(s) + 2 HCl(aq) → MgCl₂(aq) + H₂(g) ΔᵣH° ≈ −467 kJ mol⁻¹ (literature, per mole Mg)

Apparatus. As Protocol B (polystyrene cup, lid, thermometer, stopwatch). Additionally: 2-decimal-place balance for the solid, weighing boat.

Method (outline).

1. Pipette 50.0 cm³ of excess HCl(aq) (e.g. 1.00 mol dm⁻³) into the polystyrene cup. Record temperature every 30 s for 2–3 min to set the baseline.
2. Weigh 0.24 g (≈0.010 mol) of magnesium ribbon — slightly less than half the moles of acid, so Mg is the limiting reagent and the reaction goes to completion.
3. At a recorded mixing time, tip the magnesium into the cup. Replace the lid; stir until all the magnesium has reacted (typically 1–2 minutes — judged by the disappearance of solid and the cessation of bubbling).
4. Continue recording temperature every 30 s for 5–10 min for the cooling-curve plot.
5. Extrapolate back to the moment of mixing to recover ΔT_corrected.

Calculation.

q = m_acid × c × ΔT_corrected (the magnesium mass is negligible)

n_Mg = m_Mg / M(Mg) = 0.24 / 24.3 = 0.00988 mol (the limiting reagent)

ΔᵣH = −q / (1000 × n_Mg) kJ mol⁻¹

Typical experimental result. ΔᵣH ≈ −430 to −460 kJ mol⁻¹, somewhat less exothermic than the literature value because the reaction is slow on the cooling-curve timescale — even with extrapolation, some heat is lost during the slow dissolution. Magnetic stirring and powdered (rather than ribbon) magnesium reduce the time-lag.

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The Cooling-Curve Extrapolation Technique

Without correction, the experimental ΔT is systematically underestimated: while the reaction is still proceeding and the solution is still warming, it is simultaneously losing heat to the surroundings. By the time the maximum temperature is recorded, several percent of the heat has already escaped. The correction recovers the temperature the solution would have reached at the moment of mixing if the heat had been deposited instantaneously and adiabatically.

Procedure.

1. Plot temperature (y-axis, K) against time (x-axis, seconds or minutes). Use the full A4 sheet of graph paper or a software equivalent (Logger Pro, Excel, Python).
2. Mark the time of mixing on the x-axis as t = 0 (or whatever the reference is in your data).
3. Pre-mixing baseline. Draw the best-fit horizontal line through the points recorded before mixing. This is your reference T₁.
4. Post-mixing cooling line. After the temperature has peaked and begun to decay, the curve becomes approximately linear (Newton's law of cooling: rate of heat loss is proportional to temperature difference from surroundings; for small ΔT this is approximately linear in time). Draw a best-fit straight line through the post-peak linear region.
5. Back-extrapolate this cooling line back to t = mixing. The intercept on the y-axis at t = mixing gives the corrected T_max, the temperature the solution would have reached if no heat had been lost during the warming phase.
6. ΔT_corrected = T_max,corrected − T₁. Use this value in q = mcΔT.

Schematic of the cooling-curve plot:

T (K)
 │
 │              ┌──╲
 │             /    ╲
 │            /      ╲╲                  back-extrapolated
 │           /         ╲╲                line (dashed)
 │          /            ╲ ╲
 │         /               ╲ ╲
 │        /                  ╲ ╲
 │       /                     ╲ ╲ ← cooling line (linear)
 │      /
 │─────/───────────── pre-mixing baseline (T₁)
 │
 └────────────────── t (s)
       ↑
   mixing time

The dashed extrapolated line cuts the y-axis (at the mixing time) above the raw peak temperature; the corrected T_max is therefore larger than the raw maximum, and ΔT_corrected is larger than the raw ΔT.

Worked Cooling-Curve Example

A student does Protocol B (HCl + NaOH neutralisation). The raw temperature-time data:

Time / s	T / K
−180	294.1
−150	294.1
−120	294.2
−90	294.1
−60	294.2
−30	294.1
0 (mix)	—
30	299.5
60	300.3
90	300.6
120	300.5
150	300.3
180	300.1
210	299.9
240	299.7
300	299.4
360	299.0

Step 1. Pre-mixing baseline: average of the points at t = −180 to −30 s = (294.1 + 294.1 + 294.2 + 294.1 + 294.2 + 294.1) / 6 = 294.13 K.

Step 2. Post-mixing cooling line: fit the points from t = 120 s onwards (where the temperature is decaying approximately linearly). A simple two-point estimate using (120, 300.5) and (360, 299.0) gives a gradient of (299.0 − 300.5) / (360 − 120) = −1.5/240 = −0.00625 K s⁻¹.

Step 3. Back-extrapolate to t = 0: T_max,corrected = 300.5 − (−0.00625)(120 − 0) = 300.5 + 0.75 = 301.25 K.

(Equivalently, extending the line y = 300.5 − 0.00625 × (t − 120) back to t = 0 gives y = 300.5 + 0.75 = 301.25 K.)

Step 4. ΔT_corrected = 301.25 − 294.13 = 7.12 K.

Note that the raw peak (300.6 K at t = 90 s) gives ΔT_raw = 300.6 − 294.13 = 6.47 K — a 10% underestimate. The cooling-curve correction is essential for A-Level accuracy.

Step 5. Plug into q = mcΔT: q = 50.0 × 4.18 × 7.12 = 1488 J.

Step 6. ΔneutH = −q / (1000 × n) = −1488 / (1000 × 0.0250) = −59.5 kJ mol⁻¹.

Compare with the literature value of −57.6 kJ mol⁻¹: the experimental result is within 3.3% — well inside the combined experimental uncertainty (see below).

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Apparatus Precision and Percentage Uncertainties

A formal RP2 evaluation should report a combined percentage uncertainty in the final ΔH value. The procedure is:

1. List each instrument and its absolute precision.
2. Convert each absolute precision to a percentage of the measured value.
3. Sum the percentage uncertainties for measurements that appear in the final calculation (this is the worst-case combined uncertainty; for independent random errors, the combination in quadrature gives a smaller figure, but at A-Level the linear sum is conventional).

For Protocol B with the data above:

Measurement	Instrument	Absolute precision	Measured value	% uncertainty
Volume of HCl	25.00 cm³ pipette	±0.06 cm³	25.00 cm³	0.24%
Volume of NaOH	25.00 cm³ pipette	±0.06 cm³	25.00 cm³	0.24%
Mass of solution	(from volume × density 1.00)	—	50.0 g	(carried from volumes) ~0.48%
ΔT_corrected	Thermometer 0.1 K	±0.2 K (read twice, T_max and T_initial)	7.12 K	2.81%
Sum of % uncertainties				~3.3%

The thermometer reading dominates. Replacing the analogue 0.1 K thermometer with a digital probe of ±0.01 K would drop the temperature uncertainty to ~0.3% and the total below 1%.

In addition, the polystyrene-cup adiabatic approximation carries an unquoted systematic uncertainty estimated at 3–5% (residual heat loss not eliminated by the cooling-curve extrapolation, plus the heat absorbed by the polystyrene itself). For the spirit-burner method (Protocol A), the heat-loss systematic uncertainty is far larger — typically 30–40%, dominating any random-error sum.

For Protocol A (combustion):

Measurement	Instrument	Absolute precision	Measured value	% uncertainty
Mass of fuel	2-d.p. balance	±0.005 g (×2 weighings) = ±0.01 g	~0.5 g	2.0%
Volume of water	measuring cylinder	±0.5 cm³	100 cm³	0.5%
ΔT	0.1 K thermometer	±0.2 K	20 K	1.0%
Sum of random % uncertainties				~3.5%
Heat-loss systematic	—	—	—	~30–40%

The random uncertainty is small; the systematic heat loss is large. Protocol A is therefore a good vehicle for teaching uncertainty analysis (and the limits of polystyrene-vs-copper-can calorimetry), even though the answer is poor.

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CPAC Criteria — How RP2 Evidence Maps

The five Common Practical Assessment Criteria apply across all twelve required practicals. For RP2, the evidence your lab book should record is:

CPAC 1 — Following written procedures. Your method section transcribes the procedure (with any modifications and justifications); you record exactly what you did, including any deviations and why.

CPAC 2 — Applying investigative approaches and methods when using instruments and equipment. You record the apparatus used (with precision tolerances), your stirring/mixing procedure, the calibration check on the thermometer, the equilibration of the alkali to room temperature before mixing, and any safety adjustments (e.g. wearing eye protection, using a clamp to hold the burner stable).

CPAC 3 — Safely using a range of practical equipment and materials. You include a risk assessment: corrosive HCl and NaOH (1 mol dm⁻³ — irritant; eye protection mandatory); flammable fuel (Protocol A — keep the spirit burner away from other open flames; have a damp cloth at hand); hot copper can (Protocol A — handle with tongs after the experiment).

CPAC 4 — Making and recording observations. You record raw temperature-time data in a table with column headings, units (K, s), and precision (e.g. "T / K to nearest 0.1"), and you tabulate or graph the data immediately rather than copying it later.

CPAC 5 — Researching, referencing and reporting. You compare your experimental ΔH against a cited literature value (with source — e.g. the AQA datasheet or CRC Handbook), discuss the magnitude and direction of the discrepancy, and propose specific, justified improvements (not generic "use better apparatus" but e.g. "replace the analogue thermometer with a digital probe of ±0.01 K to reduce the temperature uncertainty from 2.8% to 0.3%").

Your CPAC report does not need to be long — typically 1–2 sides of A4 plus the data tables and the graph. But it must address each of the five criteria explicitly. Centres are inspected on CPAC documentation; missing criteria reduce the practical-endorsement pass rate.

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Sources of Error and Improvements

The following table is the kind of analysis that earns AO3 marks in a written-paper evaluation question. Each source of error is paired with a specific improvement, not a vague one.