Final answer:
To find the heat of formation of Fe₃O₄(s), calculate the energy transferred to the water, then divide by the moles of Fe₃O₄ formed. The answer is 1166.46 kJ/mol of Fe₃O₄.
Step-by-step explanation:
To calculate the heat of formation of Fe₃O₄(s) under these conditions, we can use the provided data regarding the effect on water temperature to first find out how much energy was released during the reaction. The formula for calculating heat (q) is q = mcΔT, where 'm' is the mass of water, 'c' is the specific heat capacity of water (4.184 J/g°C), and 'ΔT' is the change in temperature.
For the given data, m = 831 g, c = 4.184 J/g°C, and ΔT = 38.0°C - 18.0°C = 20.0°C. Plugging these values into the formula, we get: q = (831 g) × (4.184 J/g°C) × (20.0°C) = 69607.2 J.
Now, to find the enthalpy change for the formation of Fe₃O₄, we divide the heat released by the moles of Fe₃O₄ formed during the burning of 10.00 g of iron. Assuming that the reaction goes to completion and that all the iron is converted to Fe₃O₄, the molar mass of Fe is 55.85 g/mol, so the number of moles of Fe in 10.00 g is 10.00 g / 55.85 g/mol = 0.179 moles. Since it takes 3 moles of Fe to form one mole of Fe₃O₄, we have 0.179 moles / 3 = 0.0597 moles of Fe₃O₄. Finally, we calculate the enthalpy change per mole as ΔH = 69607.2 J / 0.0597 moles = 1166458.30 J/mol of Fe₃O₄, or 1166.46 kJ/mol of Fe₃O₄ when converted to kilojoules.