Calculate the heat of the reaction (qrxn) and calculate the enthalpy. Mass of empty calorimeter: 18.600 g. Mass of magnesium reacted: 0.150 g. Initial temperature in the calorimeter: 21.5°C. Final temperature in the calorimeter: 35.6°C. Mass of the calorimeter and its contents after the reaction: 64.620 g.
The Correct Answer and Explanation is:
Correct Answer:
- Mass of solution (water):
64.620 g−18.600 g=46.020 g64.620 \, \text{g} – 18.600 \, \text{g} = 46.020 \, \text{g}64.620g−18.600g=46.020g - Temperature change (ΔT):
35.6∘C−21.5∘C=14.1∘C35.6^\circ C – 21.5^\circ C = 14.1^\circ C35.6∘C−21.5∘C=14.1∘C - Assuming the specific heat capacity of water = 4.18 J/g°C:
qsolution=mcΔT=46.020×4.18×14.1=2711.3 Jq_{\text{solution}} = mc\Delta T = 46.020 \times 4.18 \times 14.1 = 2711.3 \, \text{J}qsolution=mcΔT=46.020×4.18×14.1=2711.3J - Heat of the reaction (qₙ):
The heat released by the reaction is absorbed by the solution:
qrxn=−2711.3 Jq_{\text{rxn}} = -2711.3 \, \text{J}qrxn=−2711.3J - Moles of Mg reacted:
Molar mass of Mg = 24.305 g/mol
0.150 g24.305 g/mol=0.00617 mol\frac{0.150 \, \text{g}}{24.305 \, \text{g/mol}} = 0.00617 \, \text{mol}24.305g/mol0.150g=0.00617mol - Enthalpy change (ΔH):
ΔH=qrxnmol Mg=−2711.30.00617=−439430 J/mol=−439.4 kJ/mol\Delta H = \frac{q_{\text{rxn}}}{\text{mol Mg}} = \frac{-2711.3}{0.00617} = -439430 \, \text{J/mol} = -439.4 \, \text{kJ/mol}ΔH=mol Mgqrxn=0.00617−2711.3=−439430J/mol=−439.4kJ/mol
Explanation (300 words):
To determine the heat of reaction and enthalpy change, it is important to identify the energy exchange during the chemical process. The magnesium undergoes a reaction in a calorimeter, releasing heat that is absorbed by the surrounding water. Measuring the initial and final temperatures allows for calculating the temperature change, which is a crucial factor in determining heat gained by the water.
The difference between the mass of the full calorimeter (with contents) and the empty calorimeter provides the mass of the solution. Assuming the solution behaves like water, the specific heat capacity of 4.18 J/g°C is used. Multiplying mass, specific heat capacity, and the temperature change gives the heat absorbed by the solution. Since this heat originates from the reaction, the system releases an equal amount of energy, but with a negative sign indicating an exothermic process.
After that, determining the number of moles of magnesium allows for expressing the energy change per mole, which represents the enthalpy of the reaction. Dividing the total heat released by the number of moles of magnesium involved gives the enthalpy change in joules per mole. Converting this to kilojoules per mole provides a standard expression for enthalpy.
This negative enthalpy value reflects the exothermic nature of the reaction, confirming that the reaction between magnesium and the aqueous medium releases significant heat. Such values are crucial in thermochemical analysis, helping in the understanding of energy transformations in chemical systems.
