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:
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Correct Answer
Given data:
- Mass of Mg = 0.150 g
- Initial temperature = 21.5 °C
- Final temperature = 35.6 °C
- Mass of calorimeter (empty) = 18.600 g
- Mass of calorimeter and contents after reaction = 64.620 g
Step 1: Calculate mass of solution (contents)Mass of solution=64.620 g−18.600 g=46.020 g\text{Mass of solution} = 64.620\,g – 18.600\,g = 46.020\,gMass of solution=64.620g−18.600g=46.020g
Step 2: Use specific heat of water (assumed solution)
- c=4.18 J/g∘Cc = 4.18\, \text{J/g}^\circ\text{C}c=4.18J/g∘C
- ΔT=35.6∘C−21.5∘C=14.1∘C\Delta T = 35.6^\circ\text{C} – 21.5^\circ\text{C} = 14.1^\circ\text{C}ΔT=35.6∘C−21.5∘C=14.1∘C
Step 3: Calculate heat absorbed by the solutionqcal=m⋅c⋅ΔT=46.020⋅4.18⋅14.1=2711.5 Jq_{cal} = m \cdot c \cdot \Delta T = 46.020 \cdot 4.18 \cdot 14.1 = 2711.5\, \text{J}qcal=m⋅c⋅ΔT=46.020⋅4.18⋅14.1=2711.5J
Step 4: Heat of reaction (qrxn)
Heat released by the reaction is absorbed by the solution, so:qrxn=−qcal=−2711.5 Jq_{rxn} = -q_{cal} = -2711.5\, \text{J}qrxn=−qcal=−2711.5J
Step 5: Convert mass of Mg to moles
Molar mass of Mg = 24.305 g/molMoles of Mg=0.15024.305=0.00617 mol\text{Moles of Mg} = \frac{0.150}{24.305} = 0.00617\, \text{mol}Moles of Mg=24.3050.150=0.00617mol
Step 6: Calculate ΔH (enthalpy change per mole)ΔH=qrxnmol=−2711.50.00617=−439300 J/mol=−439.3 kJ/mol\Delta H = \frac{q_{rxn}}{\text{mol}} = \frac{-2711.5}{0.00617} = -439300\, \text{J/mol} = -439.3\, \text{kJ/mol}ΔH=molqrxn=0.00617−2711.5=−439300J/mol=−439.3kJ/mol
Final Answers
- qrxn=−2711.5 Jq_{rxn} = -2711.5\, \text{J}qrxn=−2711.5J
- ΔH=−439.3 kJ/mol\Delta H = -439.3\, \text{kJ/mol}ΔH=−439.3kJ/mol
Explanation (300 words)
The calorimetric method estimates the heat released or absorbed in a chemical reaction by tracking temperature changes. When magnesium reacts in an aqueous acidic solution, it releases heat. This heat is absorbed by the surrounding solution in the calorimeter, raising its temperature. The amount of heat gained by the solution equals the amount of heat released by the reaction but with opposite sign.
The mass of the solution is found by subtracting the mass of the empty calorimeter from the combined mass after the reaction. With the known specific heat capacity of water (4.18 J/g°C), the energy absorbed is computed using the formula q=mcΔTq = mc\Delta Tq=mcΔT, where mmm is the mass of the solution, ccc is the specific heat, and ΔT\Delta TΔT is the temperature change.
This calculated energy is the heat absorbed by the solution, not the reaction itself. The actual heat of the reaction is equal in magnitude but opposite in sign, because the reaction releases the energy.
To find the enthalpy change per mole of magnesium, the number of moles is calculated from the known mass and molar mass. Dividing the total heat of reaction by the number of moles gives the molar enthalpy change, which represents the heat released when one mole of magnesium reacts under these conditions.
The negative sign in the final enthalpy value indicates that the process is exothermic, releasing heat to the surroundings. This approach highlights the importance of energy conservation in thermodynamic measurements.
