The Exothermic Reaction in a Water Bath
A student mixes 50 cm3 of 1.0 mol/dm3 hydrochloric acid with 50 cm3 of 1.0 mol/dm3 sodium hydroxide in a polystyrene cup, recording the temperature every 30 s. The temperature rises from 21.0 °C to 27.8 °C. A second trial, using 50 cm3 of 2.0 mol/dm3 acid and 50 cm3 of 2.0 mol/dm3 alkali, gives a rise from 21.0 °C to 34.5 °C. A third trial uses 100 cm3 of 1.0 mol/dm3 acid and 100 cm3 of 1.0 mol/dm3 alkali and gives a rise from 21.0 °C to 27.6 °C. The student is asked to explain the pattern and to judge whether the reaction is a good choice for a hand-warmer.
1. Explain the temperature rises in the three trials using ideas about moles reacting and energy released.
Read the worked answer
The reaction is H+ + OH- → H2O, and the energy released is proportional to the number of moles of water formed. In trial 1, 0.050 dm3 × 1.0 mol/dm3 = 0.050 mol of each ion reacts, giving 0.050 mol water. In trial 2, 0.050 dm3 × 2.0 mol/dm3 = 0.100 mol of each ion reacts, doubling the energy released. The total volume is the same (100 cm3), so the same mass of solution absorbs twice the energy, giving roughly twice the temperature rise: 6.8 °C versus 13.5 °C, close to the expected doubling. In trial 3, 0.100 mol of each ion reacts, doubling the moles compared with trial 1, but the volume is also doubled to 200 cm3. The energy per unit mass is therefore unchanged, so the rise (6.6 °C) is almost the same as trial 1.
2. Calculate the enthalpy change of neutralisation from trial 1, assuming the solution has density 1.0 g/cm3 and specific heat capacity 4.2 J/(g °C).
Read the worked answer
Mass of solution = 100 g. Energy released = m × c × ΔT = 100 × 4.2 × 6.8 = 2856 J ≈ 2.86 kJ. Moles of water formed = 0.050 mol. Enthalpy change = -2.86/0.050 = -57 kJ/mol (negative because heat is released). This is close to the accepted value of about -57 kJ/mol, which supports the method. The polystyrene cup reduces heat loss, but some heat is still lost to the surroundings, so the true value would be slightly more exothermic than calculated.
3. Judge whether this reaction is suitable for a hand-warmer, giving two reasons.
Read the worked answer
It is unsuitable. First, the reactants are corrosive solutions of acid and alkali; a leak would burn the skin, and the product is a salt solution that must be contained safely. Second, the reaction is not easily reversible once the acid and alkali are mixed, so the warmer could not be recharged by heating as a crystallisation-type warmer can. A safer design uses a reversible physical change, such as crystallisation of sodium ethanoate, which releases heat on demand and can be reset in hot water.