Final answer:
To calculate ΔH for the dissolution of ammonium nitrate in water, the heat absorbed by the solution is found using q = m · c · ΔT. This value was then divided by the number of moles of ammonium nitrate, resulting in a ΔH value of -24.05 kJ/mol, which indicates an endothermic process.
Step-by-step explanation:
When a 4.25 g sample of solid ammonium nitrate dissolves in 60.0 g of water in a coffee-cup calorimeter, the temperature of the system drops, indicating the dissolution process is endothermic. To calculate the ΔH (enthalpy change) for the solution process NH4NO3(s) → NH4+(aq) + NO3−(aq), we use the formula q = m · c · ΔT. Given that the specific heat (c) is 4.184 J/g°C (same as water), the mass of the water (m) is 60.0 g, and the temperature change (ΔT) is (16.9°C - 22.0°C) = -5.1°C, we find q, the heat absorbed or released by the solution.
q = (60.0 g) · (4.184 J/g°C) · (-5.1°C) = -1277.784 J. To convert this to kJ, we divide by 1000, resulting in -1.277784 kJ. Next, we convert the mass of NH4NO3 to moles, using its molar mass (80.04 g/mol): (4.25 g)/(80.04 g/mol) = 0.0531 mol. Finally, ΔH per mole of NH4NO3 is calculated by dividing the energy (in kJ) over the number of moles: ΔH = -1.277784 kJ / 0.0531 mol = -24.05 kJ/mol.