A student plans to determine the enthalpy change of hydration of magnesium ions, ΔhydH(Mg2+)\Delta_{\text{hyd}}H(\text{Mg}^{2+})ΔhydH(Mg2+). The student finds the following information from data tables: Lattice enthalpy of magnesium chloride, ΔLEH(MgCl2)=−2526 kJ mol−1\Delta_{\text{LE}}H(\text{MgCl}_2) = -2526\text{ kJ mol}^{-1}ΔLEH(MgCl2)=−2526 kJ mol−1; Enthalpy change of hydration of chloride ions, ΔhydH(Cl−)=−378 kJ mol−1\Delta_{\text{hyd}}H(\text{Cl}^-) = -378\text{ kJ mol}^{-1}ΔhydH(Cl−)=−378 kJ mol−1. The student carries out an experiment to find the enthalpy change of solution of magnesium chloride. Student's method: 1. Weigh a bottle containing anhydrous magnesium chloride. 2. Weigh a polystyrene cup. 3. Add water to the polystyrene cup and measure its temperature. 4. Add the magnesium chloride, stir the mixture, and measure the maximum temperature of the final solution. 5. Weigh the empty bottle and weigh the polystyrene cup with the final solution. Mass readings: Mass of bottle + magnesium chloride = 26.15 g26.15\text{ g}26.15 g; Mass of empty bottle = 18.53 g18.53\text{ g}18.53 g; Mass of polystyrene cup = 23.45 g23.45\text{ g}23.45 g; Mass of polystyrene cup + final solution = 128.45 g128.45\text{ g}128.45 g. Temperature readings: Initial temperature of water = 20.5∘C20.5^{\circ}\text{C}20.5∘C; Maximum temperature of final solution = 47.5∘C47.5^{\circ}\text{C}47.5∘C. Calculate the enthalpy change of solution of magnesium chloride and determine the enthalpy change of hydration of magnesium ions. Show your working, including an energy cycle linking the energy changes. Assume that the specific heat capacity, ccc, of the solution is 4.18 J g−1 K−14.18\text{ J g}^{-1}\text{ K}^{-1}4.18 J g−1 K−1 and the molar mass of MgCl2\text{MgCl}_2MgCl2 is 95.3 g mol−195.3\text{ g mol}^{-1}95.3 g mol−1.
