The Warm Flask That Would Not Cool
A student dissolves 8.00 g of ammonium nitrate (molar mass 80.0 g/mol) in 100.0 g of water in a polystyrene cup calorimeter. The temperature falls from 22.4 °C to 16.9 °C. The student calculates ΔH_solution and reports it as the enthalpy of solution. The specific heat capacity of the solution is taken as 4.18 J g⁻¹ K⁻¹ and the calorimeter heat capacity is neglected. A second student repeats the experiment but adds the salt slowly over 3 minutes while stirring, and obtains a smaller temperature drop. The accepted value for ΔH_solution of NH4NO3 is about +25.7 kJ/mol.
1. Calculate the enthalpy of solution from the first student's data and compare with the accepted value.
Read the worked answer
Heat absorbed by solution: q = mcΔT = 100.0 g × 4.18 J g⁻¹ K⁻¹ × (22.4 − 16.9) K = 100.0 × 4.18 × 5.5 = 2299 J ≈ 2.30 kJ.
Moles NH4NO3 = 8.00/80.0 = 0.100 mol.
ΔH_solution = +q/n = +2.30/0.100 = +23.0 kJ/mol (endothermic, sign positive because temperature fell).
This is lower in magnitude than the accepted +25.7 kJ/mol (about 10% low). The main neglected term is the heat capacity of the calorimeter itself and heat gained from the surroundings during the slow dissolution, both of which reduce the observed ΔT and hence underestimate |ΔH|. Including the calorimeter heat capacity would raise the value toward the accepted figure.
2. Explain why the second student's slower addition gives a smaller temperature drop, and state whether that makes the result more or less accurate.
Read the worked answer
Adding the salt slowly over 3 minutes allows heat to leak in from the warmer surroundings throughout the process, so the minimum temperature reached is higher (smaller ΔT). The measured temperature change therefore underestimates the true endothermic effect, giving a smaller |ΔH|.
This makes the result less accurate for determining ΔH, not more. Fast addition minimises heat exchange with the surroundings and is the correct procedure. The second student's method introduces a systematic error in the same direction as the neglected calorimeter heat capacity, compounding the underestimate. A correction would require a cooling-curve extrapolation to the moment of mixing, or a properly insulated calorimeter with a known heat capacity.