Lab, Coffee-Cup Calorimetry & Hess's Law · AP Chemistry

A pair of nested Styrofoam coffee cups makes a surprisingly good constant-pressure calorimeter. In this lab you run three related reactions involving sodium hydroxide and hydrochloric acid, measure the temperature change of the solution each time, and use q = mcΔT to find the enthalpy of reaction ΔH for each. You then test Hess's Law by checking whether ΔH for the direct reaction equals the sum of the two stepwise reactions.

CED 6.4–6.6 (Calorimetry, Energy of Phase/Reaction, Enthalpy of Reaction & Hess's Law) · Unit 6. ~1 block · FORMATIVE-category: short worked write-up, not a formal report. Hand in the data tables + analysis answers.

Background CED 6.4–6.6

Calorimetry measures heat by watching a known mass of water change temperature. If a reaction releases heat, that heat warms the surrounding solution; we read the warming and work backward to the energy released.

The core equation: q = mcΔTheat absorbed by the solution equals its mass (m, in grams) × specific heat (c) × temperature change (ΔT = T_final − T_initial). For dilute aqueous solutions we assume c = 4.18 J/g°C (same as water) and density ≈ 1.00 g/mL, so the mass of solution in grams equals its volume in mL.

Sign convention. The heat the solution gains, q_solution, is the heat the reaction lost: q_rxn = −q_solution. These reactions are exothermic: the solution gets warmer, ΔT is positive, so q_rxn is negative and ΔH is negative. To put ΔH on a per-mole footing: ΔH = −q_solution / n(limiting reactant), in J/mol, then divide by 1000 for kJ/mol.

Why a coffee cup ≈ constant-pressure calorimeter. The cup is open to the room, so the reaction happens at constant atmospheric pressure, and at constant pressure the heat released is the enthalpy change, q_p = ΔH. Styrofoam is a poor conductor, so very little heat leaks to the room during the short measurement. We assume no heat is lost to the surroundings or absorbed by the cup itself (the cup's heat capacity is treated as negligible). That assumption is the main source of error you will reason about later.

The three reactions.

(1) NaOH(s) → Na⁺(aq) + OH⁻(aq) heat of solution of solid NaOH

(2) NaOH(aq) + HCl(aq) → NaCl(aq) + H₂O(l) heat of neutralization

(3) NaOH(s) + HCl(aq) → NaCl(aq) + H₂O(l) solid NaOH straight into acid

Add reaction (1) to reaction (2): the Na⁺(aq) and OH⁻(aq) produced in (1) are exactly the species consumed in (2), so they cancel and the sum is reaction (3).

Hess's Law. Because enthalpy is a state function, the energy change depends only on the start and end states, not the path. So whether you dissolve the NaOH first and then neutralize it (steps 1 + 2), or drop the solid straight into acid (step 3), the total enthalpy change must be the same: ΔH₃ = ΔH₁ + ΔH₂. This lab measures all three independently and tests that equality.

Reality check. Your measured ΔH₃ will not match ΔH₁ + ΔH₂ to the last decimal. The hotter, longer-running reaction (3) loses the most heat to the room and the cup, so its |ΔH| usually reads a little low. Agreement within a few percent confirms Hess's Law for our purposes.

Safety read before you start

Solid NaOH, corrosive. Sodium hydroxide pellets cause severe skin and eye burns and are hygroscopic (they pull water from the air and your skin). Handle the pellets quickly with the weighing boat and spatula (never with bare fingers) and keep the stock bottle capped.

1.0 M HCl and 1.0 M NaOH, corrosive. Both the acid and the base burn skin and eyes. Wipe spills immediately and rinse the area with plenty of water.

The reactions are exothermic, the solution gets hot. Reaction (3) in particular can climb 12 °C or more. Hold the cup by the rim, do not lean over it, and let it cool before disposal.

PPE, every student, the whole period: splash goggles and nitrile gloves whenever NaOH or HCl is out. Tie back hair. No food or drink.

Disposal: the three reactions are acid–base; the final mixtures are near-neutral salt water but may not be exactly pH 7. Pour all used solutions into the labelled NaOH/HCl waste container as directed, do not pour down the sink unless Dr. Mulinta confirms it has been neutralized. Spills: alert Dr. Mulinta and use the bench neutralizing kit.

Materials & Equipment low-gear setup

Everything here is standard school chem stock. There is no specialized instrument, the "calorimeter" is two stacked Styrofoam cups.

Per group: 2 nested Styrofoam coffee cups + a lid with a hole · thermometer or temperature probe (± 0.1 °C) · 100 mL graduated cylinder · weighing boats + spatula · glass stirring rod · paper towel.

Shared at stations: balance (± 0.01 g) · solid NaOH pellets (capped) · 1.0 M NaOH · 1.0 M HCl · distilled water · NaOH/HCl waste container · neutralizing spill kit.

Mrs. Kathy (lab tech) will pre-set: the 1.0 M NaOH and 1.0 M HCl bottles and a fresh, capped bottle of NaOH pellets at each station; the balances zeroed; the distilled-water wash bottles; the labelled NaOH/HCl waste container and the neutralizing spill kit. Solutions are made up ahead of time so class time goes to measuring, not mixing.

Procedure rinse & dry the cup between reactions

For every reaction: assemble the calorimeter (one cup inside the other), record the initial temperature of the liquid, add the second reactant, stir gently, and watch the thermometer until it peaks: record that peak as T_final. Rinse and dry the cups before the next reaction.

Reaction 1: Heat of solution: NaOH(s) → Na⁺(aq) + OH⁻(aq)

Measure 100.0 mL of distilled water in the graduated cylinder and pour it into the nested cups. Put on the lid and probe; let it settle, then record the water temperature as T_initial.
On a weighing boat, mass out about 2.0 g of NaOH pellets to ± 0.01 g, work quickly, the pellets absorb moisture. Record the exact mass.
Lift the lid, add all the NaOH at once, replace the lid, and stir gently and continuously with the probe/rod until the pellets fully dissolve.
Watch the temperature climb. Record the highest steady reading as T_final.
Pour into the waste container. Rinse and dry both cups.

Reaction 2: Heat of neutralization: NaOH(aq) + HCl(aq) → NaCl(aq) + H₂O(l)

Measure 50.0 mL of 1.0 M HCl into the cups. Lid + probe; record T_initial. (If the acid and base were stored together they should already be at the same room temperature, if not, average the two starting temperatures.)
Measure 50.0 mL of 1.0 M NaOH in the rinsed graduated cylinder.
Add the NaOH to the acid all at once, replace the lid, and stir gently.
Record the peak temperature as T_final.
Pour into the waste container. Rinse and dry both cups.

Reaction 3: Direct: NaOH(s) + HCl(aq) → NaCl(aq) + H₂O(l)

Measure 100.0 mL of 1.0 M HCl into the cups. Lid + probe; record T_initial. (The HCl is in excess so all the NaOH reacts; NaOH is the limiting reactant.)
Mass out about 2.0 g of NaOH pellets to ± 0.01 g, quickly. Record the exact mass.
Add all the NaOH at once, replace the lid, and stir until fully dissolved and reacted.
Record the peak temperature as T_final. This run gets the hottest, hold the cup by the rim.
Pour into the waste container. Rinse the cups.

Reaction	NaOH	HCl / water	T_initial (°C)	T_final (°C)	ΔT (°C)
1 · NaOH(s) in water	______ g	100.0 mL H₂O	________	________	________
2 · NaOH(aq) + HCl(aq)	50.0 mL 1.0 M	50.0 mL 1.0 M	________	________	________
3 · NaOH(s) + HCl(aq)	______ g	100.0 mL 1.0 M	________	________	________

Analysis Questions show all work · units · sig figs

Answer on your own paper. Show every formula and substitution, full credit needs the math, not just the answer. Treat each solution's mass as its volume in mL × 1.00 g/mL, and c = 4.18 J/g°C throughout.

Moles of limiting reactant. For each reaction, find the moles of the limiting reactant. Reactions 1 and 3: mol NaOH = mass ÷ 40.00 g/mol. Reaction 2: mol = M × V for whichever of NaOH/HCl is limiting (here they are equal, 1.0 M × 0.0500 L).
Heat absorbed by the solution. For each reaction, use q = mcΔT to find q_solution in joules. Use the total solution mass (Reaction 1: 100.0 g; Reaction 2: 100.0 g; Reaction 3: 100.0 g).
Enthalpy per mole. For each reaction, find ΔH = −q_solution / n(limiting), then convert to kJ/mol. State the sign and explain what it tells you about the reaction (endo- or exothermic).
Reaction 1, ΔH₁. Report your heat of solution of solid NaOH, in kJ/mol. (Literature ≈ −44 kJ/mol.)
Reaction 2, ΔH₂. Report your heat of neutralization, in kJ/mol. (Literature for a strong acid + strong base ≈ −57 kJ/mol.)
Reaction 3, ΔH₃. Report your enthalpy for solid NaOH reacting directly with HCl, in kJ/mol.
Show the Hess's Law sum on the equations. Write reactions (1) and (2) one above the other, cancel the species that appear on both sides, and show that they add to reaction (3). Name the property of enthalpy that makes this valid.
Hess's Law check. Compute ΔH₁ + ΔH₂ and compare it to your measured ΔH₃. Find the percent difference: |（ΔH₁+ΔH₂) − ΔH₃| ÷ |ΔH₁+ΔH₂| × 100%. Does your data support Hess's Law?
Error analysis (this is the graded reasoning). Using q = mcΔT and the "no heat lost to the surroundings or the cup" assumption, answer all three:
1. Give one source of error that would make your measured |ΔH| read too LOW. Explain the direction through q = mcΔT.
2. Give one source of error that would make your measured |ΔH| read too HIGH. Explain the direction through q = mcΔT.
3. Explain why your measured ΔH₃ might not exactly equal ΔH₁ + ΔH₂, referring to the heat-loss-to-calorimeter assumption and which reaction is most affected.

Lab · Coffee-Cup Calorimetry & Hess's Law