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Calorimetry: measuring reaction enthalpies

With two polystyrene cups, a temperature probe and a stirrer, calibrate the calorimeter, then measure the heat of neutralisation and the enthalpies of solution inside cold and hot packs.

Difficulty ●●○ ≈ 25 min

Aim Determine the calorimeter constant CcalC_\text{cal} of an unknown calorimeter, then use it to measure the enthalpy of neutralisation of HX++OHX−→HX2O\ce{H+} + \ce{OH-} \mathrel{\ce{->}} \ce{H2O} and the enthalpies of solution of NHX4NOX3\ce{NH4NO3} and CaClX2\ce{CaCl2}.
Virtual experiment · heat-balance model + data logger

Coffee-cup calorimeter

qhot=(mcoldc+Ccal) ΔTcoldq_{\text{hot}} = (m_{\text{cold}}c + C_{\text{cal}})\,\Delta T_{\text{cold}}

21.20°C00:00LOGroom 22.0 °C
Time 00:00
Probe 21.20°C
Heat leak +0.10 W Total heat capacity 233 J/K
0246810Time t / min2020.52121.522Temperature / °C
  • Logger readings (every 5 s)
Log a 1–2 minute baseline first, then mix.

Lab notebook

Nothing recorded yet.

Computed: one well-stirred heat capacity C = C_cal + m·c exchanges heat with the room (C·dT/dt = P − h(T − T_room)); the heat of reaction or solution is released exponentially after mixing. The probe lags by about 4 s; readings are logged every 5 s to 0.01 °C with a small seeded jitter. Reaction enthalpies are infinite-dilution values computed from the formation table (neutralisation −55.8, NH₄NO₃ +25.7, CaCl₂ −81.3 kJ/mol); solutions are taken to have c = 4.184 J/(g·K) and density 1.00 g/mL, with heats of dilution and the solid’s own heat capacity neglected. Illustrative: the look of the cups, stirrer and heat-flow arrow.

Procedure

  1. Choose a calorimeter number. Experiment “Calibration”: the cup holds 50 g of cold water, with 50 g of hot water beside it. Press “Start logging”, record about 2 minutes of baseline, pour in the hot water, and keep logging for at least 4 more minutes.
  2. Tick “Extrapolate to the mixing time”, read off the calorimeter constant and press “Record the result” — later runs use this CcalC_\text{cal} automatically.
  3. Switch to “Neutralisation”: 50.0 mL of 1.00 M HCl in the cup, 50.0 mL of 1.00 M NaOH in the cylinder. Again log a baseline, pour, keep logging, and extrapolate to get ΔH.
  4. Measure “Dissolving ammonium nitrate” and “Dissolving calcium chloride” in turn (5.00 g of solid in 100 g of water each).
  5. Untick “Lid and double cup” and measure calcium chloride again, comparing ΔH with and without extrapolation. Finally reveal the true CcalC_\text{cal} and estimate how much error it caused.

What to notice

  • In the calibration the mixed temperature is always below the average of the two portions — the “missing” heat went into the cup, which is exactly what the calorimeter constant measures.
  • The heat of neutralisation comes out near −56 kJ/mol whichever strong acid and base you use: the only reaction really happening is H⁺ + OH⁻ → H₂O.
  • Dissolving a solid takes tens of seconds, so the extreme of the curve comes late; meanwhile heat has leaked, and the extrapolation recovers it.
  • Without a lid the leak is much faster: ΔH from the extreme reading can be 5–10 % off, while the extrapolated value stays within about 1 %.

In a real lab

  • Wear eye protection; 1 M NaOH is corrosive. Anhydrous calcium chloride dissolves with vigorous heating — add it while stirring.
  • Measure both solutions’ temperatures before mixing, and let them stand in the same room until they are close.
  • Real solutions differ slightly from water in specific heat and density, and heats of dilution are not zero; these cause systematic errors of 1–3 %, which this simulation treats as water.
  • Ammonium nitrate is a strong oxidiser — keep it away from combustibles; dispose of the solutions as your school requires.

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